surface response below API stiffness values, indicating that gapping is an ...... In a series of reports to Shell Development Company, Matlock and his co-workers.
Shaking Table Scale Model Tests of Nonlinear Soil-Pile-Superstructure Interaction In Soft Clay by Philip James Meymand
B.A. (Georgetown University) 1984 B.S. (University of Massachusetts, Lowell) 1993 M.S. (University of California, Berkeley) 1994
A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering-Civil Engineering in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge: Professor Michael F. Riemer, Chair Professor Raymond B. Seed Professor Lane R. Johnson
Fall 1998
The dissertation of Philip James Meymand is approved:
________________________________________________ Chair Date
________________________________________________ Date
________________________________________________ Date
University of California, Berkeley Fall 1998
Abstract SHAKING TABLE SCALE MODEL TESTS OF NONLINEAR SOIL-PILE-SUPERSTRUCTURE INTERACTION IN SOFT CLAY by Philip James Meymand Doctor of Philosophy in Engineering-Civil Engineering University of California, Berkeley Professor Michael F. Riemer, Chair
A significant number of cases of damage to piles and pile-supported structures during earthquakes have been observed, but few instrumented records of the response and performance of such structures during earthquakes have been obtained. To expand the database of pile performance during strong shaking, a series of scale model shaking table tests of model piles in soft clay was performed. This research effort had the goals of providing insight into a variety of seismic soil-pile-supestructure interaction (SSPSI) topics, and generating a data set with which to calibrate advanced SSPSI analysis tools being developed at U.C. Berkeley in a parallel effort. Principles of scale model similitude were used to derive a set of model scaling relationships that recognized the dynamic and nonlinear nature of SSPSI. A specialized flexible wall test container was designed to allow the soil to respond in the same fashion as the free-field, unencumbered by boundary effects.
The shaking table reasonably
reproduced both one-directional and two-directional input motions, and trends of model site response were consistent with free-field behavior; the motions amplified from base to surface and were coherent across the site. Site characterization included laboratory and 1
in-situ testing to establish the undrained shear strength and shear wave velocity profiles. One-dimensional equivalent linear dynamic response analyses were successfully used to simulate the model free-field response, indicating that the model soil-container system adequately reproduced free-field site conditions. The single piles were seen to respond with components of inertial and kinematic interaction, with the inertial components producing upper bound bending moments. The response of pile groups was highly frequency dependent, which calls into question the applicability of applying pseudo-static analyses to such problems. Pile cap and free field motion variations illustrated wave scattering effects and the necessity of developing modified foundation input motions for substructuring analyses. Moderate effects of pile cap embedment were observed, particularly in contributing to pile group rocking stiffness. The influences of two-directional shaking were seen to be minimal, as structural inertial forces tended to resolve the motion to a strong axis for the simple single degree of freedom models tested. For single piles, full perimeter soil resistance was not engaged, as the piles preferentially followed gaps developed in previous cycles. P-y curves derived from the static and seismic test data compared very well to those recommended by API. Degrading behavior due to hysteresis and gapping was observed, softening the nearsurface response below API stiffness values, indicating that gapping is an important feature to model. The application of system identification techniques yielded estimates of single pile and pile group flexible base frequencies and damping factors, which differed significantly from the fixed base assumption. Damping for the single piles and groups was computed to be a function of load level.
2
Estimates of pile head lateral stiffness derived from a suite of pile head loading tests differed over a wide range, and were a function of loading level and consequent soil-pile nonlinearity. The methods examined for computing dynamic stiffness from elastic theory provided unrealistically high estimates of stiffness for the model tests. Appropriately selected secant stiffness values from the static lateral load tests provided more realistic descriptions of the observed soil-pile dynamic response for moderate levels of shaking. ATC-32 chart solutions provided marginally acceptable lower bound pile head stiffness estimates for very strong shaking events.
____________________________ Michael F. Riemer, Thesis Advisor
____________________________ Date
3
For Alice
iii
TABLE OF CONTENTS Abstract........................................................................................................................... 1 List of Figures ............................................................................................................... xii List of Tables.............................................................................................................. xxix Acknowledgments ...................................................................................................... xxxi CHAPTER 1 STATEMENT OF RESEARCH............................................................... 1 1.1
Introduction................................................................................................ 1
1.2
Overview of Observed Pile Response During Earthquakes .......................... 6
1.3
Research Needs and Research Objectives .................................................... 8
1.4
Organization of the Thesis........................................................................... 9
CHAPTER 2 OBSERVED PILE SEISMIC PERFORMANCE.................................... 12 2.1
Observed Pile Damage in Earthquakes ...................................................... 12 2.1.1
San Francisco 1906 ..................................................................... 12
2.1.2
Alaska 1964 ................................................................................ 16
2.1.3
Niigata 1964 ............................................................................... 25
2.1.4
Off-Tokachi 1968........................................................................ 31
2.1.5
San Fernando 1971 ..................................................................... 31
2.1.6
Off-Miyagi Prefecture 1978......................................................... 32
2.1.7
Mexico City 1985 ....................................................................... 33
2.1.8
Loma Prieta 1989........................................................................ 36
2.1.9
Costa Rica 1991.......................................................................... 40
2.1.10
Hyogoken-Nanbu (Kobe) 1995 ................................................... 44 iv
2.2
2.3
Measured Pile Response In Earthquakes ................................................... 52 2.2.1
Building and Industrial Structures in Japan .................................. 53
2.2.2
Building Structures in California.................................................. 60
2.2.3
Bridge Structures ........................................................................ 64
Summary of Observed Pile Performance and Potential Failure Modes........ 72
CHAPTER 3 SSPSI ANALYTICAL METHODS........................................................ 75 3.1
3.2
Analytical Methods ................................................................................... 75 3.1.1
Beam-on-Elastic Foundation ....................................................... 82
3.1.2
Beam-on-Winkler Foundation ..................................................... 84
3.1.3
Elastic Continuum....................................................................... 97
3.1.4
Finite Element Methods ............................................................ 101
3.1.5
Pile Group Effects..................................................................... 104 (a)
Pile Group Interaction Methods..................................... 107
(b)
Pile Group Complete Dynamic Analyses ........................ 116
Building Code Provisions........................................................................ 125 3.2.1
Uniform Building Code/SEAOC Recommendations .................. 125
3.2.2
National Earthquake Hazards Reduction Program ..................... 126
3.2.3
Mexico City Building Code ....................................................... 128
3.2.4
People’s Republic of China Aseismic Building Design Code ...... 128
3.2.5
American Petroleum Institute Recommended Practice ............... 129
3.2.6
Improved Seismic Design Criteria for California Bridges ........... 130
3.2.7
FHWA Seismic Design of Highway Bridge Foundations............ 133
v
3.3
3.4
3.2.8
Japanese Design Specifications of Highway Bridges .................. 134
3.2.9
New Zealand Bridge Design Specifications................................ 135
Current State-of-the-Practice SSPSI Design and Analysis Applications ... 136 3.3.1
National Survey ........................................................................ 137
3.3.2
ASCE Workshop ...................................................................... 138
3.3.3
San Francisco-Oakland Bay Bridge ........................................... 139
3.3.4
San Diego-Coronado Bay Bridge .............................................. 140
3.3.5
Continuous Column-Shafts........................................................ 141
3.3.6
Caltrans Simplified Method ....................................................... 142
3.3.7
Alemany Interchange Retrofit.................................................... 142
3.3.8
Mercer Slough .......................................................................... 143
3.3.9
WSDOT Study.......................................................................... 145
3.3.10
Alaskan Way Viaduct................................................................ 147
3.3.11
Caltrans Liquefaction Mitigation ............................................... 148
3.3.12
Port Mann Bridge ..................................................................... 149
Summary of SSPSI Analytical Methods................................................... 150
CHAPTER 4 PREVIOUS EXPERIMENTAL WORK............................................... 151 4.1
Introduction............................................................................................ 151
4.2
Full Scale Pile Test Programs.................................................................. 151 4.2.1
Field Single Pile Lateral Load Tests........................................... 152
4.2.2
Field Pile Group Lateral Load Tests .......................................... 157
4.2.3
Field Pile Dynamic Tests ........................................................... 163
vi
4.3
4.4
Model Scale Pile Test Programs.............................................................. 171 4.3.1
Model Pile Head Loading Tests................................................. 172
4.3.2
Model Pile Dynamic Tests......................................................... 182
4.3.3
Model Pile Centrifuge Tests ...................................................... 186
4.3.4
Model Pile Shaking Table Tests ................................................ 200
Summary of Experimental Findings ......................................................... 210
CHAPTER 5 ONE-G SCALE MODELING .............................................................. 212 5.1
5.2
5.3
Introduction............................................................................................ 212 5.1.1
Theories of Scale Model Similitude ........................................... 213
5.1.2
Scale Model Similitude As Applied to Soil Mechanics ............... 217
5.1.3
Scale Modeling Methodology and Implied Prototypes .............. 223
5.1.4
Scale Modeling Factors for Shaking Table Testing .................... 225
Model Soil Design .................................................................................. 227 5.2.1
Identification of Soil Modeling Criteria...................................... 228
5.2.2
Definition of Prototype Soil Parameters..................................... 229
5.2.3
Model Soil History.................................................................... 230
5.2.4
Development of Model Soil....................................................... 233
Model Pile Design................................................................................... 242 5.3.1
Identification of Pile Modeling Criteria...................................... 242
5.3.2
Definition of Prototype Pile Parameters..................................... 244
5.3.3
Development of Model Pile....................................................... 245
5.3.4
Four Point Loading Test ........................................................... 249
vii
CHAPTER 6 SHAKING TABLE TEST PROGRAM ................................................ 250 6.1
Introduction – Test Objectives ................................................................ 250
6.2
Earthquake Simulator Facility ................................................................. 251
6.3
Model Testing Container......................................................................... 254
6.4
6.5
6.6
6.3.1
Numerical Modeling of Container Effects.................................. 255
6.3.2
Small Scale Container Shaking Table Tests ............................... 257
6.3.3
Full Scale Container Design and Construction ........................... 259
Test Instrumentation ............................................................................... 262 6.4.1
Accelerometers ......................................................................... 262
6.4.2
Strain Gages ............................................................................. 264
6.4.3
Wire Potentiometers.................................................................. 266
6.4.4
Signal Conditioning and Data Acquisition System ..................... 267
6.4.5
Data Precision and Accuracy..................................................... 269
Model Construction ................................................................................ 270 6.5.1
Model Soil Mixing and Placement ............................................. 271
6.5.2
Installation of Single Piles and Pile Groups................................ 273
6.5.3
Instrumentation......................................................................... 277
Test Parameters ...................................................................................... 282 6.6.1
Selection of Input Motions........................................................ 282
6.6.2
Pile Head Loading Tests............................................................ 285
6.6.3
T-Bar Tests............................................................................... 287
6.6.4
Shear Wave Velocity Tests........................................................ 289
viii
6.6.5
Schedule of Test Conditions...................................................... 290
CHAPTER 7 SHAKING TABLE TEST RESULTS .................................................. 300 7.1
Introduction…… .................................................................................... 300
7.2
Shaking Table Performance..................................................................... 301
7.3
7.2.1
Replication of Command Signals ............................................... 301
7.2.2
Acceleration Response of Table Degrees of Freedom ............... 304
Soil Column Response ............................................................................ 307 7.3.1
Site Amplification ..................................................................... 308
7.3.2
Coherence of Motions............................................................... 308
7.3.3
Vertical Accelerations ............................................................... 311
7.4
Sine Sweep Tests.................................................................................... 314
7.5
Kinematic vs. Inertial Pile Response ........................................................ 316
7.6
7.7
7.8
7.5.1
Test 1.15................................................................................... 316
7.5.2
Test 2.24................................................................................... 320
Pile Group Frequency Response.............................................................. 323 7.6.1
Test 1.26................................................................................... 323
7.6.2
Test 2.37................................................................................... 327
Pile Cap Embedment Effects ................................................................... 330 7.7.1
Test 1.37................................................................................... 330
7.7.2
Test 2.55................................................................................... 333
Pile Group and Single Pile Subjected to 2-D Shaking .............................. 336 7.8.1
Test 2.46................................................................................... 336
ix
7.9
Pile Raft Foundation Performance........................................................... 340 7.9.1
Test 1.37................................................................................... 340
7.10 Effects of Water/Scour on Pile Group Response ..................................... 341 7.10.1
Test 1.46................................................................................... 343
7.11 Summary of Experimental Findings ......................................................... 345 CHAPTER 8 ANALYSIS AND DISCUSSION OF EXPERIMENTAL RESULTS... 348 8.1
Introduction…….. .................................................................................. 348
8.2
Soil Shear Strength Profile ...................................................................... 348
8.3
8.2.1
T-Bar Tests............................................................................... 348
8.2.2
UUTX Tests ............................................................................. 350
8.2.3
Vane Shear Tests ...................................................................... 352
8.2.4
Best Estimate Strength Profiles ................................................. 353
Shear Wave Velocity Profile ................................................................... 354 8.3.1
Phase I Hammer Blow Tests ..................................................... 354
8.3.2
Phase II Hammer Blow Tests .................................................... 355
8.3.3
Baseline Shear Wave Velocity Profiles ...................................... 357
8.4
Model Soil Modulus Degradation and Damping Curves .......................... 360
8.5
Container Performance and Observed Free Field Response...................... 362
8.6
Pile Head Loading Tests ......................................................................... 372 8.6.1
Static Lateral Load Tests .......................................................... 372
8.6.2
Pile Head Impact Test ............................................................... 374
8.6.3
Pile Head Forced Vibration Tests .............................................. 378
x
8.6.4
Pile Head Static Axial Loading Test .......................................... 378
8.6.5
Pile Head Cyclic Axial Loading Test ......................................... 379
8.7
Pile Group Effects................................................................................... 382
8.8
2-D Shaking Effects................................................................................ 385
8.9
Experimental P-Y Curves........................................................................ 389 8.9.1
Static P-Y Curves ..................................................................... 394
8.9.2
Dynamic P-Y Curves................................................................. 394
8.10 System Identification............................................................................... 397 8.11 Pile Head Stiffness .................................................................................. 403 8.12 Conclusions……..................................................................................... 408 CHAPTER 9 SUMMARY AND CONCLUSIONS.................................................... 411 9.1
Scope of Research .................................................................................. 411
9.2
Research Findings and Recommendations ............................................... 412
9.3
Recommendations for Future Research ................................................... 416 9.3.1
Data Mining.............................................................................. 416
9.3.2
Improved Test Procedures ........................................................ 417
9.3.3
Future Shaking Table Research Topics...................................... 418
REFERENCES............................................................................................................ 420 APPENDIX A
Similitude For Model Tests in a 1-g Gravitational Field.................... 458
APPENDIX B
Model Pile Design Spreadsheet ........................................................ 459
APPENDIX C
Analysis of Seismic Response of Cylindrical Tank ............................ 460
xi
LIST OF FIGURES Figure 1.1 - Effect of Soil-Structure Interaction on Seismic Base Shear Coefficient......... 2 Figure 1.2 - Comparison of 1985 Mexico City Earthquake SCT Response Spectra with 1997 NEHRP Code Recommendations........................................................ 2 Figure 1.3 - Schematic of Modes of Single Pile Seismic Response................................... 5 Figure 1.4 - Potential Failure Modes for Pile Group Foundations Subjected To Seismic Shaking ......................................................................................................... 7 Figure 2.1 - Regions Most Intensively Damaged During the 1906 San Francisco Earthquake, and the Historic Shoreline (after Seed et al., 1990) ..................... 13 Figure 2.2 - Ground Failure during the 1906 San Francisco Earthquake in the Vicinity of the U.S. Post Office at Mission and Seventh Streets (after Wood, 1908)....... 14 Figure 2.3 - Failure of Pile Supported Pier of the Salinas Bridge during the 1906 San Francisco Earthquake (after Wood, 1908) ............................................................... 15 Figure 2.4 - Collapse of Timber Pile Supported Railroad Bridge at Moss Landing due to Lateral Spreading during the 1906 San Francisco Earthquake (after Wood, 1908) ........................................................................................................ 15 Figure 2.5 - Deformation of Pile Supported Inverness Piers due to Lateral Spreading during the 1906 San Francisco Earthquake (after Wood, 1908) ..................... 15 Figure 2.6 - Collapse of Snow River Bridge 605 due to Liquefaction during the 1964 Alaskan Earthquake (after Ross et al., 1969) ................................................... 17 Figure 2.7 - Liquefaction Induced 15 degree Tilt of Snow River Bridge 605A Foundations during the 1964 Alaskan Earthquake (after Ross et al., 1969)..................... 17 Figure 2.8 - Collapsed Concrete Deck of Bridge 629 over the Placer River Penetrated by Timber Piles during the 1964 Alaskan Earthquake (after Ross, et al., 1969) ................................................................................................ 18 Figure 2.9 - Wreckage of Portage Creek Bridges, adjacent to Alaskan Railroad Grade and Bridges, during the 1964 Alaskan Earthquake (after Kachadoorian, 1968) ............................................................................................ 18 Figure 2.10 - Collapsed Bridges over the Twentyninemile River during the Alaskan Earthquake of 1964 (after Ross et al., 1969)..................................................... 19
xii
Figure 2.11 - Collapsed Twentyninemile River Bridge with Timber Piles Punched through Deck during the Alaskan Earthquake of 1964 (after Ross et al., 1969) .............. 19 Figure 2.12 - Collapsed Kenai River Bridge with Piles Punched through Concrete Deck during the Alaskan Earthquake of 1964 (after Ross et al., 1969) ............ 20 Figure 2.13 - Sheared Rail Piles on Scott Glacier Bridge 6 during the Alaskan Earthquake of 1964 (after Kachadoorian, 1968)............................................................. 20 Figure 2.14 - Million Dollar Bridge Collapse during the Alaskan Earthquake of 1964 (after Kachadoorian, 1968) ............................................................................... 21 Figure 2.15 - Collapsed Deck of Flagg Point Bridge 331 due to LiquefactionInduced Settlements during the Alaskan Earthquake of 1964 (after Ross et al., 1969) ................................................................................................. 22 Figure 2.16 - Damage Intensity during the 1964 Niigata Earthquake Related to SPT Blowcount and Foundation Embedment Depth (after Seed and Idriss, 1966) .......................................................................................... 25 Figure 2.17 - Liquefaction Induced Collapse of Showa Bridge during the 1964 Niigata Earthquake (after Iwasaki, 1972) ....................................................................... 27 Figure 2.18 - Permanent Deformation of Pile Extracted from Showa Bridge Foundation during the 1964 Niigata Earthquake (after Iwasaki, 1972) ........................... 27 Figure 2.19 - Cracked Precast Reinforced Concrete Piles from Yachiyo Bridge during the 1964 Niigata Earthquake (after Fukuoka, 1966) ............................................ 28 Figure 2.20 - Liquefaction Related Settlement of Pile Supported Sakae Bridge during the 1964 Niigata Earthquake (after Kawakami and Asada, 1966) ........................ 28 Figure 2.21 - Piles Supporting the NHK Building Sheared by Lateral Spreading during the 1964 Niigata Earthquake (after Hamada, 1991)............................................. 29 Figure 2.22 - Damage Pattern to Foundation Piles Supporting the Niigata Family Courthouse during the 1964 Niigata Earthquake (after Hamada, 1991) .......................... 30 Figure 2.23 - Correlation of Pile Damage to Site Conditions at a) Niigata Family Courthouse and b) NHK Building during the Niigata Earthquake (after Doi and Hamada, 1992)........................................................................................ 30 Figure 2.24 - Failure at Connection Detail Between Drilled Shaft and Bridge Column at the Golden State Freeway/ Foothill Freeway Interchange during the 1971 San Fernando Earthquake (after Penzien, 1971).................................... 32 xiii
Figure 2.25 - Types of Foundations Used in the Soft Soil Deposits of Mexico City (after Mendoza and Auvinet, 1988) ........................................................................ 34 Figure 2.26 - Ten Story Pile Supported Building founded on Soft Soils during the 1985 Mexico City Earthquake: a) Elevation including Geotechnical Conditions; b) Overturned Structure (after Mendoza and Auvinet, 1988).......................................... 35 Figure 2.27 - Highway 1 Crossing Struve Slough near Watsonville Collapsed during the 1989 Loma Prieta Earthquake, with Pile Punching through Deck (after Seed et al., 1990) ................................................................................................. 37 Figure 2.28 - Formation of Gap Adjacent to One of the Piles Supporting the Collapsed Struve Slough Crossing during the 1989 Loma Prieta Earthquake (after Seed et al., 1990) ................................................................................................. 37 Figure 2.29 - Flexural Shear Failure of Pile to Bent Connection of the Struve Slough Crossing during the 1989 Loma Prieta Earthquake (after Seed et al., 1990)........ 37 Figure 2.30 - Damaged Batter Piles at Port of Oakland 7th Street Terminal during the 1989 Loma Prieta Earthquake (after SEAOC, 1991) ..................................... 39 Figure 2.31 - Damaged Batter Piles at Port of San Francisco Piers 27 & 29 during the 1989 Loma Prieta Earthquake (after SEAOC, 1991) ..................................... 39 Figure 2.32 - Liquefaction Induced Rotation of Rio Banano Bridge Pile Cap during the 1991 Costa Rican Earthquake (after Priestly et al., 1991) .............................. 41 Figure 2.33 - Preferential Damage to Front Batter Piles of Rio Banano Bridge during the 1991 Costa Rican Earthquake (after Priestly et al., 1991) .............................. 41 Figure 2.34 - a) Failure of Rio Viscaya Bridge Piles during the Costa Rican Earthquake; b) Liquefaction Failure of Rio Viscaya Bridge (after Priestly et al., 1991).............................................................................................. 42 Figure 2.35 - Rio Bananito Bridge Liquefaction Failure during the 1991 Costa Rican Earthquake (after Priestly et al., 1991) ................................................................. 42 Figure 2.36 - Rotation of Caissons Supporting Rio Bananito Rail Bridge during the 1991 Costa Rican Earthquake (after Priestly et al., 1991) ......................................... 43 Figure 2.37 - Tilting of Rio Bananito Rail Bridge due to Foundation Failure during the 1991 Costa Rican Earthquake (after Priestly et al., 1991) .............................. 43 Figure 2.38 - Sheared Concrete Piles Supporting a Railroad Trestle at the Almirante Port during the 1991 Costa Rican Earthquake (after Priestly et al., 1991)....... 43 xiv
Figure 2.39 - Collapsed Section of Hanshin Expressway ............................................... 44 Figure 2.40 - Response Spectra Recorded in Vicinity of Collapsed Hanshin Expressway Illustrating Effects of Period Lengthening due to Foundation Flexibility on Increased Structural Forces (after Gazetas and Mylonakis, 1998).............. 45 Figure 2.41 - Collapsed Pile Supported Ramp Structure at the Higashi-Kobe Ferry Pier during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995) ...................... 45 Figure 2.42 - Nonexistent Connection Details Between Failed Piles and Pile Cap Supporting the Higashi-Kobe Ferry Pier (after U.C. Berkeley, 1995) ...................... 46 Figure 2.43 - Inadequate Connection Details Between Failed Piles and Pile Cap Supporting the Higashi-Kobe Ferry Pier (after U.C. Berkeley, 1995) ...................... 46 Figure 2.44 - Differential Settlement Between Pile Supported Roadway on Port Island and Surrounding Ground during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995)............................................................................................ 46 Figure 2.45 - Concrete Pile Sheared at Head on Port Island during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995)................................................................ 48 Figure 2.46 - Relative Soil-Pile Movement Leaving Gap Around Pile on Rokko Island during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995) ................. 48 Figure 2.47 - Collapsed Span of Nishinomiya Bridge during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995) ......................................................................... 48 Figure 2.48 - Lateral Spreading Damage to Pile during the 1995 Kobe Earthquake (after Tokimatsu et al., 1996) ...................................................................... 51 Figure 2.49 - Pile Damaged by Superstructure Inertial Forces during the 1995 Kobe Earthquake (after Tokimatsu et al., 1996) .................................................... 51 Figure 2.50 - Progression of Soil-Pile-Structure Interaction and Pile Bending Moments During Liquefaction (after Tokimatsu et al., 1998) ......................................... 51 Figure 2.51 - a) Apartment House Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Kawamura and Ikeda, 1981) .............. 54 Figure 2.52 - a) Petrochemical Plant Towers Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Hagio et al., 1980) .......... 55 Figure 2.53 - a) Spherical Tank Structure Instrumentation Plan; b) Pile Cap to Free Field Transfer Function (after Hamada and Ishida, 1980)........................................ 56 xv
Figure 2.54 - a) Eleven Story Apartment House Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Ohta et al., 1980) ............ 57 Figure 2.55 - a) Two Story Reinforced Concrete Building Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Abe et al., 1984) ...... 58 Figure 2.56 - LNG Storage Tank Pile Bending Stain and Ground Surface Velocity Spectra at Two Tank Liquid Heights (after Tsujino et al., 1987) .................................... 59 Figure 2.57 - LNG Storage Tank Pile Bending and Axial Stain Spectra at Two Tank Liquid Heights (after Tsujino et al., 1987)............................................................. 59 Figure 2.58 - Hollywood Storage Building Parking Lot/Basement Transfer Function during the 1987 Whittier Narrows Earthquake (after Fenves and Serino, 1992).............. 61 Figure 2.59 - Imperial County Services Building Ground Level to Free Field Transfer Function during the 1979 Imperial Valley Earthquake (after Hadjian et al., 1990)........... 62 Figure 2.60 - Meloland Road Overpass Free Field and Base of Pier Fourier Amplitude Spectra during the 1979 Imperial Valley Earthquake (after Werner et al., 1987)............. 65 Figure 2.61 - Ohba Ohashi Bridge: a) Bridge Elevation and Soil Conditions; b) Instrumentation Plan (after Ohira et al., 1984); c) Pile Cap to Free Field Transfer Function (after Gazetas et al., 1993) .............................................................................. 67 Figure 2.62 - a) Hayward BART Section Pier Base to Free Field Longitudinal Transfer Function; b) Transverse Transfer Function (after Tseng et al., 1992) ................ 70 Figure 3.1 - Pile Curvature Profile Derived from Site Response Analysis (after Margasson and Holloway, 1977) .......................................................................... 76 Figure 3.2 - Flexible Pile Stiffness Matrix (after Kriger and Wright, 1980) .................... 77 Figure 3.3 - Selection of Secant Stiffness Value at Design Level Displacement from Nonlinear Soil-Pile Force-Displacement Curve (after Kriger and Wright, 1980) ..... 77 Figure 3.4 - Substructuring Concept: a) Definition of Problem; b) Decomposition into Inertial and Kinematic Interaction Problems; c) Two-step Analysis of Inertial Interaction (after Gazetas, 1984).................................................................................... 78 Figure 3.5 - Soil-Pile Load Displacement Diagrams for Various Modes of Loading (after Mosikeeran, 1990).................................................................................. 80 Figure 3.6 - Rigid Versus Flexible Pile Behavior (after Kulhawy and Chen, 1995) ......... 81
xvi
Figure 3.7 - Rigid Pile Lateral Loading Resistance Components (after Kulhawy and Chen, 1995) ............................................................................................................ 81 Figure 3.8 - Lateral Loading Near Surface Passive Wedge Geometry and Soil-Pile Forces (after Reese, 1958) ............................................................................... 86 Figure 3.9 - Definition of P-Y Concept with a) Pile at Rest; b) Laterally Loaded Pile Mobilizing Soil Resistance (after Thompson, 1977) .................................... 86 Figure 3.10 - Typical Family of P-Y Curves, Progressively Stiffer with Depth (after Meyer and Reese, 1979)............................................................................. 86 Figure 3.11 - Characteristic Shape of P-Y Curve in Soft Clay for a) Static Loading; b) Cyclic Loading (after Matlock, 1970).......................................................... 87 Figure 3.12 - SPASM 8 a) Soil-Pile-Superstructure Model; b) Variation in Load-Deflection Behavior versus Depth (after Matlock and Foo, 1978) ..................... 89 Figure 3.13 - SPASM 8 Sub-element Nonlinear Spring Model (after Matlock and Foo, 1978) ................................................................................................ 89 Figure 3.14 - SPASM 8 a) Soil-Pile Gapping Model; b) Force-Displacement Behavior (after Matlock and Foo, 1978) ........................................................................ 89 Figure 3.15 - Characteristic Shape of P-Y Curve in Sand (after Reese et al., 1974) ....... 90 Figure 3.16 - Characteristic Shape of P-Y Curve in Stiff Clay for a) Static Loading; b) Cyclic Loading (after Reese et al., 1975)..................................................... 90 Figure 3.17 - Lateral Bearing Capacity Factor Np with Respect to Normalized Depth (after Stevens and Audibert, 1979) ...................................................................... 93 Figure 3.18 - Hysteretic Backbone Curve (after Kagawa and Kraft, 1981) .................... 93 Figure 3.19 - PAR Analytical Model (after Bea et al., 1984) ......................................... 94 Figure 3.20 - Nogami’s Beam-on-Winkler Foundation Soil-Pile Interaction Model (after Nogami et al., 1988).................................................................................. 95 Figure 3.21 - Nogami’s Inner Field and Near Field Soil-Pile Models for: a) Vertical Excitation; b) Horizontal Excitation (after Otani et al., 1991)........................ 95 Figure 3.22 - Nogami’s Far Field Soil-Pile Models for: a) Vertical Excitation; b) Horizontal Excitation (after Nogami et al., 1988)....................................................... 95
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Figure 3.23 - One- and Two-Dimensional Radiation Damping Models (after Gazetas and Dobry, 1984) .................................................................................. 100 Figure 3.24 - Pile Group Interaction as Function of Pile Spacing (after Bogard and Matlock, 1983)................................................................................ 104 Figure 3.25 - Components of Pile Group Response Under Lateral Loading (after O’Neill and Dunnavant, 1985) ............................................................................ 106 Figure 3.26 - Pile Group Unit Load Transfer Method (after Bogard and Matlock, 1983)................................................................................ 109 Figure 3.27 - Vertical and Horizontal Dynamic Pile Interaction Factors (after Kaynia and Kausel, 1982).................................................................................. 111 Figure 3.28 - Normalized Horizontal and Vertical Dynamic Stiffness and Damping of 4x4 Pile Group in Soft Soil (after Kaynia and Kausel, 1982) ..................... 112 Figure 3.29 - Distribution of Horizontal and Vertical Forces in 4x4 Pile Group in Soft Soil Medium (after Kaynia and Kausel, 1982) ........................................ 112 Figure 3.30 - Generalized Pile Head/Free Field Transfer Function for Kinematic Interaction (after Fan and Gazetas, 1991) .................................................... 114 Figure 3.31 - Schematic of Three-Step Procedure for Computing Pile-Soil-Pile Interaction (after Makris and Gazetas, 1992) ............................................................... 114 Figure 3.32 - Substructuring Method for Seismic Soil Pile Superstructure Interaction Analysis (after Gazetas et al., 1993) ........................................................... 115 Figure 3.33 - Separation of SSPSI Analysis into Kinematic and Inertial Interaction Components (after Waas and Hartmann, 1981) .......................................... 117 Figure 3.34 - a) Definition of Transfer Function; b) Transfer Function without Building Mass for Soft Soil; c) Transfer Function without Building Mass for Stiff Soil; d) Transfer Function for Different Building Masses in Stiff Soil (after Waas and Hartmann, 1981) ................................................................................ 117 Figure 3.35 - Example of Substructuring Approach (after Kagawa, 1991)................... 119 Figure 3.36 - Soil Displacements due to Ring Loading (after Kagawa, 1991) .............. 119 Figure 3.37 - Dynamic Response of Pile Supported Foundation Indicating Influence of Group Effects and Weak Zone (after Sheta and Novak, 1982) .................. 120
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Figure 3.38 - Platform Response to Wave Loading with Pile Group Interaction both Considered and Neglected (after Mitwally and Novak, 1987) ............................... 121 Figure 3.39 - Nonlinear Model for Dynamic Axial Response of Single Pile (after El Naggar and Novak, 1994b) ............................................................................ 122 Figure 3.40 - Nonlinear Model For Dynamic Lateral Response of Pile Groups (after El Naggar and Novak, 1995) .............................................................................. 122 Figure 4.1 - Example of Pile Load Test Set Up for Combined Lateral and Axial Load (after ASTM, 1996)................................................................................... 152 Figure 4.2 - Characteristic Fixed Head Laterally Loaded Pile Bending Moment Pattern (after Matlock, 1962)....................................................................................... 154 Figure 4.3 - P-Y Curves Developed from Static and Cyclic Lateral Load Tests on 24-in Diameter Pile in Stiff Clay (after Reese et al., 1975).............................. 155 Figure 4.4 - Static Lateral Load Test Results for Piles at Dry and Flooded Bay Mud Sites, Superimposed with COM624P Predicted Response (after Gill, 1968).......................................................................................................... 156 Figure 4.5 - Field Pile Group Load Test Results Indicating Preferential Load Distribution to Leading Piles (after Holloway et al., 1982) ........................................... 160 Figure 4.6 - Field Pile Group Load Test Results Depicting; a) Cyclic Degradation of Resistance; b) Distribution of Load by Row (after Brown et al., 1987) ............................................................................................ 161 Figure 4.7 - Dynamic Pile Response from Forced Vibration Tests: a) Linear Response; b) Nonlinear Response due to Removal of Supporting Soil Near Pile Head (after Petrovski and Jurokovski, 1973)......................................................... 165 Figure 4.8 - Field Pile Forced Vibration Test Set Up (after Scott et al., 1982) ............. 168 Figure 4.9 - Field Pile Forced Vibration Test and Earthquake Observation: a) Test Set Up and Seismometer Arrangement; b) Forced Vibration Test Results Illustrating Influence of Lateral Support Condition; c) Structure to Free Field Transfer Function for Three Backfill Cases; d) Observed and Computed Response Spectra for Seismic Event (after Kobori et al., 1991) ............ 170 Figure 4.10 - Stress Fringe Patterns of Rigid Cylinder Laterally Translating in Elastic Medium (after Matlock and Ripperger, 1957) ............................................... 174
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Figure 4.11 - a) Schematic of Pot Test; b) Typical Loading Cycle with Slack Zone while Traversing Gap (after Matlock, 1962)........................................................ 175 Figure 4.12 - Model Pile Head Loading Test Bending Moment Diagram: a) Variation with Overburden Pressure; b) Dynamic and Static Loading (after Gaul, 1958) ........................................................................................................ 176 Figure 4.13 - Comparison of Experimental and Analytical Model Pile p-y Curves (after Allen and Reese, 1980) ........................................................................... 177 Figure 4.14 - Shear Zone Behavior in Axially Loaded Model Pile in Remolded Clay (after Matlock et al., 1982) .................................................................................. 178 Figure 4.15 - Shear Transfer Behavior During Cyclic Axial Loading of Model Pile in Remolded Clay (after Matlock et al., 1982) ....................................................... 179 Figure 4.16 - Shear Transfer Under Progressively Increasing Displacements During Cyclic Axial Loading of Model Pile in Remolded Clay (after Matlock et al., 1982) .......................................................................................... 179 Figure 4.17 - Group Efficiency As a Function of Pile Spacing As Determined by Model Pile Tests (after Cox et al., 1983) ................................................................. 179 Figure 4.18 - Diagram of Laterally Loaded Model Soil-Pile Displacement Vectors Obtained by X-Ray Technique Illustrating Gap Infill in Sand and Open Gap in Clay (after Kishida et al., 1985) ........................................................................ 180 Figure 4.19 - Layout of 102 Model Pile Group Subjected To Dynamic Testing (after Novak and El Sharnouby, 1992) ......................................................................... 184 Figure 4.20 - Experimental Model Pile Group Horizontal Response Curve Compared With Theoretical Models: P, Equivalent Pier; K, Kaynia and Kausel Interaction Factors; and W, Waas and Hartmann Direct Analysis (after Novak and El Sharnouby, 1992).............................................................................................. 185 Figure 4.21 - Representation of Centrifuge Testing Scheme (after Scott, 1994)........... 187 Figure 4.22 - Laterally Loaded Model Pile Centrifuge Test Data Compared with Prototype Results of Mustang Island (MI) Test (after Scott, 1981) .............................. 191 Figure 4.23 - Centrifuge Test Model Pile Forced Vibration Displacement and Bending Moment Response Compared with Prototype (P9) Test Results (after Scott et al., 1982)............................................................................................... 191
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Figure 4.24 - Influence of In-Flight Pile Installation on Subsequent Load Deformation Response of Model Pile in Centrifuge Test (after Craig, 1985)................. 193 Figure 4.25 - Laminar Box for Centrifuge Testing (after Hushamand et al., 1988) ....... 195 Figure 4.26 - Centrifuge Modeling of Laterally Loaded Pile Groups in Sand: a) Effect of Relative Density on Group Capacity; b) Load Distribution By Rows; b) Effect of Pile Spacing on Total Lateral Resistance; d) Influence of Acceleration Level During Driving on Total Lateral Resistance (after McVay et al., 1994) ............... 197 Figure 4.27 - Comparison of Centrifuge Test Experimental and DRAIN-2D Computed Acceleration Response Spectra at Pile Head and Superstructure (after Wang et al., 1998).............................................................................................. 199 Figure 4.28 - SSPSI Shaking Table Model: a) Influence of Three Foundation Conditions on Superstructure Response; b) Comparison of Experimental and Recorded Seismic Response (after Mizuno and Iiba, 1982) .......................................... 204 Figure 4.29 - Comparison of Shaking Table Model Pile Liquefaction Response to Analytically Computed Fourier Amplitude Spectra (after Nomura et al., 1991) ........ 206 Figure 4.30 - Fourier Spectra Illustrating Effect of Viscous Damping Device in Shaking Table Model Test of Pile Foundation (after Yamamoto et al., 1992) ............... 207 Figure 4.31 - Shaking Table Model Pile Group Interaction Factor Versus Pile Spacing, Experimental Data, and as Computed by a Variety of Methods (after Sreerama, 1993) ................................................................................................. 209 Figure 5.1 - Scale Model Constitutive Behavior Described by Stress and Strain Scaling Factors (after Rocha, 1957) ............................................................................. 218 Figure 5.2 - Critical State Soil Mechanics Concept of Geometrically Similar Stress Paths for Prototype A1Z1 and Model A2Z2 (after Roscoe, 1968)......................... 218 Figure 5.3 - Tangent Modulus Formulation for Scale Modeling of Soil Constitutive Behavior (after Iai, 1989) ......................................................................... 219 Figure 5.4 - Definition of Model Soil Properties Based on Steady-State Line (after Gibson, 1996)..................................................................................................... 222 Figure 5.5 - Scale Modeling Methodology of Implied Prototypes ................................ 224 Figure 5.6 - Variation of Shear Wave Velocity with the Undrained Shear Strength (Static) of Shallower Cohesive Soils (after Dickenson, 1994)......................... 230
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Figure 5.7 - Model Soil Undrained Shear Strength Versus Water Content As Determined by Various Researchers (after Lazarte, 1996)....................................... 233 Figure 5.8 - Unconsolidated-Undrained Triaxial Compression Test Results For Model Soil Mixture with 20% Fly Ash at Four Water Contents ............................. 235 Figure 5.9 - Model Soil Undrained Shear Strength Versus Water Content of Clay Fraction........................................................................................................... 235 Figure 5.10 - Model Soil Unconsolidated-Undrained Triaxial Compression Test Results Showing Effects of Strain Rate and Confining Pressure (after Gruber, 1996) ... 237 Figure 5.11 - Bay Mud Unconsolidated-Undrained Triaxial Compression Test Results Showing Effects of Strain Rate and Confining Pressure (after Gruber, 1996) ... 237 Figure 5.12 - Ratio of Undrained Shear Strength at Dynamic (4.5 in./min.) and Static (0.045 in./min.) Strain Rates for Model Soil in Unconsolidated-Undrained Triaxial Compression Tests (after Gruber, 1996).......................................................... 237 Figure 5.13 - Shear Wave Velocity Versus Cure Age for Model Soil Specimens with Varying Fly Ash Contents (after Wartman, 1996)................................................. 240 Figure 5.14 - Void Ratio Versus log Pressure for Constant Rate of Strain Consolidation Test of Model Soil Specimen................................................................. 240 Figure 5.15 - Theoretical Lower and Upper Bound Moment-Curvature Relations for Prototype Pile as Determined by COM624P ........................................................... 248 Figure 5.16 - Diagram of Four-Point Loading Test of Model Pile................................ 248 Figure 5.17 - Theoretical and Experimental Moment-Curvature Relations for 2” Diameter x 0.028” Wall Aluminum Tube Model Pile ............................................... 248 Figure 6.1 - Shaking Table Layout .............................................................................. 252 Figure 6.2 - Comparison of Free-Field Soil Response in Four Model Containers (after Fiegel, 1995) ...................................................................................................... 255 Figure 6.3 - Evolution of Model Container Design for this Research Project ............... 256 Figure 6.4 - Comparison of Free-Field Soil Response of Rigid and Flexible Wall Model Containers with Prototype Condition ........................................................ 256 Figure 6.5 - Small Scale Model Container Testing on Davis Hall Shaking Table .......... 257
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Figure 6.6 - Site Response in Small Scale Model Container Illustrating Correlation Between Observed and Computed Response ............................................. 258 Figure 6.7 - Pressure Test of Rubber Cylinder for Design of Band Spacing ................. 260 Figure 6.8 - Full Scale Container Mounted on Shaking Table, with Support Struts, and Soil Mixer/Pump in Background ................................................................ 261 Figure 6.9 - Calibration Record of Typical IC Sensors 3022-005g Accelerometer ....... 263 Figure 6.10 - IC Sensors Accelerometer Mounted in Protective Case and 3-D Array... 264 Figure 6.11 - Section Showing Model Pile Strain Gage Locations Relative to Ground Surface and Position of Supestructure Accelerometers .................................... 265 Figure 6.12 - Diagram of Wheatstone Bridge for Detecting: a) Pile Bending Strains; b) Pile Axial Strains (after Gohl, 1991)............................................................ 266 Figure 6.13 - Shaking Table Control Console.............................................................. 268 Figure 6.14 - As-Placed Model Soil Water Content During a) Phase I; b) Phase II ..... 271 Figure 6.15 - Sand Gradation Curve for Bearing Stratum in Phase II........................... 272 Figure 6.16 - Schematic of Chemgrout Mixer/Pump.................................................... 273 Figure 6.17 - Model Pile Installation Through Template.............................................. 274 Figure 6.18 - Design Detail of 3x3 Pile Group............................................................. 275 Figure 6.19 - Installation of 3x3 Pile Group ................................................................ 276 Figure 6.20 - Phase I Accelerometer Array ................................................................. 278 Figure 6.21 - Phase II Accelerometer Array ................................................................ 278 Figure 6.22 - Acceleration, Velocity, and Displacement Time Histories, and Acceleration Response Spectra for the Yerba Buena Island Record 90 Degree Component from the Loma Prieta Earthquake (YBI90) ............................................... 284 Figure 6.23 - Acceleration, Velocity, and Displacement Time Histories,and Acceleration Response Spectra for the Port Island Downhole Array -79 meter Record North 00 East Component from the Kobe Earthquake (KPI79N00). ................ 285
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Figure 6.24 - Sinsweep Consisting of 65 Second Duration Record Sweeping at 4 Octaves Per Minute from 0 to 20 Hz with Ramped Transitions at the Beginning and End of Signal ........................................................................................................ 285 Figure 6.25 - Single Pile Lateral Load Test 2.20g at Maximum Deflection .................. 286 Figure 6.26 - Pile Group Lateral Load Test 2.31 at Maximum Deflection.................... 287 Figure 6.27 - Cyclic Axial Load Test 2.20b Setup ....................................................... 287 Figure 6.28 - Surface Hammer Test to Determine Shear Wave Velocity Profile........... 290 Figure 6.29 - Model 1.1 Layout with Four Single Piles................................................ 293 Figure 6.30 - Model 1.2 Layout with Two 3x3 Pile Groups......................................... 293 Figure 6.31 - Model 1.3 Layout with Two 3x3 Pile Groups and One Pile Raft Foundation........................................................................................................... 294 Figure 6.32 - Model 1.4 Layout with Two 2x2 Pile Groups......................................... 294 Figure 6.33 - Model 1.5 Layout with No Piles............................................................. 295 Figure 6.34 - Model 2.1 Layout with No Piles............................................................. 297 Figure 6.35 - Model 2.2 Layout with Nine Single Piles................................................ 298 Figure 6.36 - Model 2.3 Layout with Two 3x3 Pile Groups......................................... 298 Figure 6.37 - Model 2.4 Layout with One 5x3 Pile Group and Single Pile ................... 299 Figure 6.38 - Model 2.5 Layout with Two 2x2 Pile Groups......................................... 299 Figure 7.1 - Shaking Table Response Spectra for YBI90 Input Motions...................... 302 Figure 7.2 - Shaking Table Accelerometer Layout....................................................... 302 Figure 7.3 - Shaking Table Response Spectra for KPI79N00 Motions......................... 303 Figure 7.4 - Test 2.37 Shaking Table Accelerometer Time Histories ........................... 305 Figure 7.5 - Test 2.37 Shaking Table Accelerometer FFTs .......................................... 306 Figure 7.6 - Test 2.24 Soil Accelerometer Array #1 Time Histories and FFTs ............. 309
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Figure 7.7 - Test 1.18 Soil Accelerometer 5%Damped Response Spectra.................... 310 Figure 7.8 - Comparison of Vertical Accelerations for Soil Deformation Modes.......... 312 Figure 7.9 - Test 2.46 Accelerometer 5% Damped Response Spectra and Transfer Function ...................................................................................................................... 313 Figure 7.10 - Test Series 2.2 Sine Sweeps, Pile Resonant Frequency Response ........... 315 Figure 7.11 - Test 2.26 Gap Formed Around Pile S2................................................... 315 Figure 7.12 - Test Series 1.1 Setup ............................................................................. 316 Figure 7.13 - Test 1.15 Pile Head Accelerometer Time Histories and FFTs ................. 318 Figure 7.14 - Test 1.15 Pile Bending Moment Envelopes ............................................ 319 Figure 7.15 - Test 1.15 Pile Head:Free-field Transfer Functions .................................. 319 Figure 7.16 - Test Series 2.2 Setup ............................................................................. 320 Figure 7.17 - Test 2.24 Pile Head Accelerometer Time Histories and FFTs ................. 321 Figure 7.18 - Test 2.24 Pile Bending Moment Envelopes ............................................ 322 Figure 7.19 - Test 2.24 Pile Head:Free-field Transfer Functions .................................. 323 Figure 7.20 - Test Series 1.2 Setup ............................................................................. 324 Figure 7.21 - Test 1.26 Accelerometer/Strain Gage 5% Damped Response Spectra .... 325 Figure 7.22 - Test 1.26 Pile Bending Moment Envelopes ............................................ 326 Figure 7.23 - Test Series 2.3 Setup ............................................................................. 327 Figure 7.24 - Test 2.37 Accelerometer/Strain Gage 5% Damped Response Spectra .... 328 Figure 7.25 - Test 2.37 Pile Bending Moment Envelopes ............................................ 329 Figure 7.26 - Test Series 1.3 Setup ............................................................................. 331 Figure 7.27 - Test 1.37 Accelerometer/Strain Gage 5% Damped Response Spectra .... 332 Figure 7.28 - Test 1.37 Pile Bending Moment Envelopes ............................................ 333
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Figure 7.29 - Test Series 2.5 Setup ............................................................................. 334 Figure 7.30 - Test 2.55 Accelerometer/Strain Gage 5% Damped Response Spectra .... 335 Figure 7.31 - Test 2.55 Pile Bending Moment Envelopes ............................................ 336 Figure 7.32 - Test Series 1.4 Setup ............................................................................. 337 Figure 7.33 - Test 2.46 Accelerometer/Strain Gage 5% Damped Response Spectra .... 338 Figure 7.34 - Test 2.46 a) Longitudinal, b) Lateral Pile Bending Moment Envelopes... 339 Figure 7.35 - Test Series 1.3 Pile Raft Foundation ...................................................... 341 Figure 7.36 - Test 1.37 Accelerometer/Strain Gage 5% Damped Response Spectra .... 342 Figure 7.37 - Test Series 1.4 Setup ............................................................................. 344 Figure 7.38 - Test 1.46 Accelerometer Time Histories ................................................ 345 Figure 8.1 - T-Bar Device Being Pulled Out of Soil at Conclusion of Test................... 349 Figure 8.2 - Phase I T-Bar and Vane Shear Test Results and Undrained Shear Strength Profile ........................................................................................................... 350 Figure 8.3 - Phase II T-Bar and Vane Shear Test Results and Undrained Shear Strength Profile ........................................................................................................... 351 Figure 8.4 - Model Soil UUTX Laboratory Test Results ............................................. 352 Figure 8.5 - Effect of Strain Rate on Laboratory Vane Shear Testing of Model Soil .... 353 Figure 8.6 - Test 1.13 Base Impact Shear Wave Velocity............................................ 355 Figure 8.7 - Test 2.10 Surface Impact Shear Wave Velocity Test; Stack 1 Blow 1 Unfiltered and Filtered Time Histories with Shear Wave Arrivals Identified...... 356 Figure 8.8 - Phase I Shear Wave Velocity Inferred Profile.......................................... 358 Figure 8.9 - Phase II Hammer Blow Test and Inferred Shear Wave Velocity Profiles .. 358 Figure 8.10 - a) Phase I ; b) Phase II Soil Peak Acceleration vs. Site Resonant Frequency Illustrating Trends of Soil Degradation and Recovery.................................. 359
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Figure 8.11 - Model Soil Modulus Degradation and Damping Curves ......................... 361 Figure 8.12 - Model Soil Container in Motion During Strong Shaking ........................ 363 Figure 8.13 - a) Test 2.13 and b) 2.14 Stack 1 Site Response vs. SHAKE91 Predicted Spectra......................................................................................................... 366 Figure 8.14 - a) Test 2.16 and b) 2.17 Stack 1 Site Response vs. SHAKE91 Predicted Spectra......................................................................................................... 367 Figure 8.15 - a) Test 2.24 and b) 2.26 Stack 1 Site Response vs. SHAKE91 Predicted Spectra......................................................................................................... 368 Figure 8.16 - a) Test 2.35 and b) 2.37 Stack 1 Site Response vs. SHAKE91 Predicted Spectra......................................................................................................... 369 Figure 8.17 - a) Test 2.44 and b) 2.46 Stack 1 Site Response vs. SHAKE91 Predicted Spectra......................................................................................................... 370 Figure 8.18 - a) Test 2.53 and b) 2.55 Stack 1 Site Response vs. SHAKE91 Predicted Spectra......................................................................................................... 371 Figure 8.19 - Static Lateral Load Tests 1.1 and 2.2 vs. COM624 Predicted Deflection and Bending Moments, with Secant Pile Head Stiffnesses ........................... 373 Figure 8.20 - Test 2.20e Pile S6 Head Impact Frequency Response............................. 376 Figure 8.21 - Test 2.20e Pile S6 Head Impact Test Free Vibration Response............... 376 Figure 8.22 - Test 2.20d Pile S5 Forced Vibration Spectral Analysis ........................... 377 Figure 8.23 - Test 2.20a Pile S1 Static Axial Load-Deflection and Failure Criterion .... 379 Figure 8.24 - Test 2.20a Pile S1 Static Axial Tip Pressure-Deflection (Q-z) Curve...... 379 Figure 8.25 - Test 2.20b Pile S3 Cyclic Axial Load-Deflection Response .................... 380 Figure 8.26 - Axial Load Cycling Effects for Test 2.20b Pile S3................................... 380 Figure 8.27 - Derivation of Pile S3 T-z Curves from Cyclic Axial Test Tensile Loading Segment......................................................................................................... 381 Figure 8.28 - Test 2.31 Pile Group Static Lateral Load Test Load vs. Strain Gage Response ............................................................................................................ 384
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Figure 8.29 - Test 2.31 Pile Group Average Head Load vs. Test 2.20g Single Pile Load-Deflection Curves and Secant Stiffnesses ..................................................... 384 Figure 8.30 - Longitudinal and Lateral Components of Free-Field Surface Ground Motion During 2-D Shaking Test 2.46 ............................................................ 387 Figure 8.31 - Gap Developed Around Single Pile S2 During 2-D Shaking Test 2.46.... 387 Figure 8.32 - Test 2.46 S2 Two Dimensional Shaking Response ................................. 388 Figure 8.33 - Test 2.46 S1Two Dimensional Shaking Response .................................. 388 Figure 8.34 - Test 1.11 Pile 6 Experimental vs. API Static P-Y Curves ....................... 392 Figure 8.35 - Test 2.20g Pile 6 Experimental vs. API Static P-Y Curves ..................... 393 Figure 8.36 - Test 1.15 Pile 1 P-Y Analysis Window................................................... 395 Figure 8.37 - Test 1.15 Pile 1 Experimental vs. API Cyclic P-Y Curves ...................... 395 Figure 8.38 - Test 1.18 Pile 1 P-Y Analysis Window................................................... 396 Figure 8.39 - Test 1.18 Pile 1 Experimental vs. API Cyclic P-Y Curves ...................... 396 Figure 8.40 - Test 1.15 Pile 1 System Identification .................................................... 401
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LIST OF TABLES Table 3-1 Criteria for Pile Rigidity (after Kulhawy and Chen, 1995).............................. 81 Table 4-1 Field Pile Group Lateral Loading Tests ....................................................... 158 Table 4-2 Field Pile Dynamic Loading Tests ............................................................... 166 Table 4-3 Model Pile Loading Tests............................................................................ 173 Table 4-4 Model Pile Dynamic Loading Tests ............................................................. 183 Table 4-5 Model Pile Centrifuge Tests ........................................................................ 189 Table 4-6 Model Pile Shaking Table Tests .................................................................. 201 Table 5-1 Identification of SSPSI Primary System Modes and Associated Variables.... 225 Table 5-2 Scaling Relations for Primary System Variables Expressed in Terms of the Geometric Scaling Factor λ ..................................................................................... 226 Table 5-3 Selected Properties of San Francisco Bay Mud............................................. 229 Table 5-4 Chemical Composition of Class F and Class C Fly Ashes.............................. 239 Table 5-5 Mechanical Properties of Candidate Model Pile Materials............................ 246 Table 6-1 Model Series 1.1 Instrumentation................................................................ 279 Table 6-2 Model Series 1.2 Instrumentation................................................................ 279 Table 6-3 Model Series 1.3 Instrumentation................................................................ 279 Table 6-4 Model Series 1.4 Instrumentation................................................................ 280 Table 6-5 Model Series 2.2 Instrumentation................................................................ 280 Table 6-6 Model Series 2.3 Instrumentation................................................................ 281 Table 6-7 Model Series 2.4 Instrumentation................................................................ 281 Table 6-8 Model Series 2.5 Instrumentation................................................................ 281 Table 6-9 Model Test Series 1.1 ................................................................................. 291 xxix
Table 6-10 Model Test Series 1.2 ............................................................................... 291 Table 6-11 Model Test Series 1.3 ............................................................................... 292 Table 6-12 Model Test Series 1.4 ............................................................................... 292 Table 6-13 Model Test Series 1.5 ............................................................................... 292 Table 6-14 Model Test Series 2.1 ............................................................................... 296 Table 6-15 Model Test Series 2.2 ............................................................................... 296 Table 6-16 Model Test Series 2.3 ............................................................................... 296 Table 6-17 Model Test Series 2.4 ............................................................................... 297 Table 6-18 Model Test Series 2.5 ............................................................................... 297 Table 8-1 System Identification Single Pile Flexible Base Frequency and Damping....... 402 Table 8-2 System Identification Pile Group Frequency and Damping............................ 403 Table 8-3 Estimates of Pile Lateral Dynamic Stiffness .................................................. 404 Table 8-4 Test Series 1.1 Single Pile Head Stiffness Estimates ..................................... 406 Table 8-5 Test Series 2.2 Single Pile Head Stiffness Estimates ..................................... 407 Table 8-6 Test Series 2.4 Single Pile Head Stiffness Estimates ..................................... 407
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Acknowledgments This research could not have been possible without the collaboration and support of a number of individuals, and I would like to extend my sincere thanks to them. My two coadvisers Dr. Michael Riemer and Dr. Raymond Seed provided a wealth of ideas and encouragement, and were always available to discuss this work. I would particularly like to thank Dr. Riemer for his hands on assistance with all aspects of the testing program. Dr. Seed’s mentorship and inquisitiveness will always be valued, and I greatly appreciate the opportunities he has given me to become involved with other aspects of his work. I have also enjoyed the insightful contributions of Dr. Lane Johnson to this research and greatly appreciate his efforts in reviewing this manuscript. Other members of the U. C. Berkeley Civil Engineering faculty were particularly helpful with specific areas of this work. Dr. Juan Pestana provided valuable input to both the analytical and experimental components of this project. Dr. Bob Bea granted early support, lent his pile expertise, and generously allowed the use of his private library. Dr. Greg Fenves assisted with a variety of problems relating to earthquake structural engineering. Dr. Steven Glaser reviewed and made positive suggestions to the signal processing and system identification portions of this research. Dr. Nicholas Sitar provided the inspiration to use Kevlar bands for the test container. In addition to the above mentioned individuals, I would also like to recognize Dr. Jon Bray, Dr. Richard Goodman, Dr. James Mitchell, Dr. Steve Mahin, Dr. Fahrang Ostadan, Dr. Norm Abrahamson, and Dr. John Lysmer for their contributions to my outstanding education and experience as a graduate student at U.C. Berkeley.
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I am grateful to the staff of the Pacific Earthquake Engineering Research (PEER) Center for helping to bring this project to realization. Dr. Andrew Whittaker, Mr. Don Clyde, Dr. Amir Gilani, Mr. Wes Neighbor, Mr. Changri Yin, and Mr. Kevin Mercer were an exceptionally professional and cooperative team to work with, and all made valuable contributions to the success of the experimental program. I particularly want to thank Mr. Don Clyde for his tireless efforts in operating the shaking table, and also allowing me to share his office. Dr. Gilani was of great assistance in the design and construction of the flexible wall test container. I am very grateful to Mr. Kevin Mercer for his hard work and dedication to the project, and without whom the testing would not have proceeded as smoothly as it did. Mr. Todd Merport and Mr. Bill McCracken in the Department of Civil Engineering also provided valuable assistance with early stages of the experimental work. Dr. Jon Stewart of the University of California Los Angeles was an initial collaborator on this project, and has been a source of continued advice and friendship, and a prime contributor to the system identification analyses made in this research. At the University of California Davis, Dr. Dan Wilson, Dr. Bruce Kutter, Dr. Ross Boulanger, and Dr. Doug Stewart provided input on various aspects of the experimental program.
Dr.
Stewart’s T-bar method proved very useful for model site characterization, and Dr. Wilson was especially helpful in sharing his work regarding the calculation of p-y curves from experimental data. The friendship and collaboration with a number of my fellow students has been invaluable. Mr. Thomas Lok has been a tremendous partner in this work, from mixing clay to deriving analytical expressions, and contributing his energy and good nature to every aspect of this research project. Dr. William Gookin provided critical input data for xxxii
the site response analyses by testing model clay samples with his cyclic triaxial device. Mr. Joseph Wartman performed a valuable study on the effects of fly ash on the model soil, and assisted with mixing clay for the experiments. Mr. Christopher Hunt and Mr. Carlton Grizzle also lent their efforts to the task of mixing clay soil for the tests. Ms. April Gruber conducted a series of laboratory tests that was instrumental in the development of the model soil. Ms. Giovanna Biscontin unraveled the mystery of shearing velocity with her vane shear testing work. Ms. Laurie Gaskins has been a helpful source of information regarding system identification and signal processing. The PEER Center library was an excellent resource for the prodigious literature review conducted as part of this dissertation, and Mr. Chuck James and Ms. Cecily Sobey were of great assistance in that regrard. I would also like to thank Dr. Eduardo Kausel of the Massachusetts Institute of Technology, Mr. Mark Lauby of the Electric Power Research Institute, Ms. Frances Brown of Shell Development Corp, Dr. Jose Roesset of the University of Texas at Austin, and the staff of the Earthquake Engineering Research Institute for their kind assistance in obtaining research materials. I would also like to thank Mr. Paul Scheller, Mr. Alfred Weinmann, and Mr. Detlef Menke of Bauer Spezialtiefbau for introducing me to the world of foundation engineering, and Dr. John Ting of the University of Massachusetts Lowell for his excellent coursework in soil mechanics and geotechnical engineering. I am also grateful to Mr. Noel Wong, Dr. Lelio Meija, and Dr. Bob Green of Woodward-Clyde Consultants, Oakland, for the opportunity to work as a geotechnical earthquake engineer. Support for this research was provided by the California Department of Transportation under contract number DOT-RTA59A130, which is gratefully xxxiii
acknowledged. In addition, a number of individuals provided valuable suggestions for this research, including Dr. Abbas Aghari, Dr. Cliff Roblee, Mr. Tom Shantz, Mr. Ken Jackura, and Mr. Dan Speer. Words are not enough to thank my family for the support they have given me during this long and sometimes difficult journey. My wife Alice has kept me going through it all, with her patience, encouragement, and love, and helping me to keep life in balance. Without her, I would not be able to achieve or enjoy these successes. Though they may not quite realize it yet, Emily and Leila are sources of great joy that sustain me and help keep life in perspective. Finally, I want to thank my mother for her love and support, and for instilling in me the value of learning and providing me outstanding opportunities to do so throughout my life.
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CHAPTER 1
STATEMENT OF RESEARCH
1.1 Introduction Deep foundations consisting of driven or drilled-in piles and piers are routinely employed to transfer axial structural loads through soft soils to stronger bearing strata at depth. These foundation elements may also be subject to transient or cyclic lateral loads arising from earthquake, wind, wave, blast, impact, or machine loading. The coincidence of major pile-supported structures sited on soft soils in areas of earthquake hazard results in significant demands on these deep foundations. Possible resonance effects between longer period soft soil sites, which may amplify ground motions, and large structures can exacerbate the problem. Liquefaction and/or strain-softening potential in these soft soils can impose additional demands on pile foundation systems. Historically, it has been common seismic design practice to ignore or simplify the influence of pile foundations on the ground motions applied to the structure. This is generally accepted as a conservative design assumption for a spectral analysis approach, as the flexible pile foundation results in period lengthening and increased damping, and consequent decreased structural forces relative to a fixed base case (see Figure 1.1). However, in extreme cases such as the 1985 Mexico City Earthquake, period lengthening can result in increased spectral values relative to current code specifications (see Figure 1.2).
1
Figure 1.1 - Effect of Soil-Structure Interaction on Seismic Coefficient for Base Shear (after Fenves and Serino, 1992) It is somewhat more common to evaluate pile integrity during seismic loading, though this too is accomplished with simplified and non-standardized analysis methods. However, in observations of pile performance during earthquakes, two principal facts emerge: pile foundations do affect the ground motions the superstructure experiences, and piles can suffer extreme damage and failure under earthquake loading. The purpose of this dissertation is to examine these two facets of this complex soil-structure interaction problem. 1.4
Acceleration (g)
1.2
1985 Mexico City SCT 1997 NEHRP Site Class D 1997 NEHRP Site Class E
1.0 0.8 0.6 0.4 0.2 0.0 0.01
0.1
1
10
Period (sec)
Figure 1.2 - Comparison of 1985 Mexico City Earthquake SCT Response Spectra with 1997 NEHRP Code Recommendations
2
Unfortunately, there is a lack of well-documented seismic soil-pile response case histories, and of these cases very few include piles that have been instrumented to record dynamic response.
This limited database of measured pile performance during
earthquakes does not provide a good basis for calibration and validation of the available analytical methods developed for seismic soil-pile-superstructure interaction problems. Centrifuge and shaking table model tests have therefore been used to augment the field case histories with laboratory data obtained under controlled conditions.
The vast
majority of centrifuge and shaking table model tests have studied soil-pile seismic response in cohesionless soils with liquefaction potential. But many pile foundations supporting critical structures are sited on soft clays, which have the potential for cyclic strength degradation during seismic loading. The San Francisco-Oakland Bay Bridge sited on San Francisco Bay Mud is a prime example. The principal characteristics of seismic soil-pile-superstructure interaction (SSPSI) for an individual pile are illustrated schematically in Figure 1.3. The system components include the superstructure, the pile cap, the pile(s), the soil (here idealized into near field and far field domains), and the seismic energy source. The modes of system interaction include kinematic, inertial, and physical interaction, and radiation damping, and are described below. •
Kinematic interaction is the seismic response of the soil profile transmitted to the pile foundation, which attempts to deform with the soil, and results in the superstructure experiencing a different ground motion than the “free-field” soil.
3
•
Inertial interaction consists of structural inertial forces being transferred to the pile foundation. These forces impose lateral loads which are concentrated near the pile head, and axial loads, if a rocking mode of the structure is present.
•
Important physical interaction between the pile and soil occurs before and during seismic loading. During initial pile installation and loading, soil displacement, load transfer, and downdrag forces set up a unique stress state in the pile and surrounding soil, upon which any seismically-induced stresses will be superimposed.
During
seismic loading, gaps may open between the soil and the pile near the ground surface; in cohesionless soils, the gap may fill in and be compacted; however in cohesive soils, the gap may stand open, resulting in a reduction of soil-pile lateral stiffness. If submerged, water alternately drawn in and ejected from the gap during each load cycle may scour the soil adjacent to the pile, resulting in a further reduction of stiffness. •
Radiation damping occurs due to the stiffness contrast between the soil and pile. Piles vibrate at much higher frequencies than the surrounding soil, but soil-pile contact forces the soil to also vibrate at these high frequencies, resulting in the transmission of high frequency energy away from the pile into the surrounding soil.
Radiation damping is most
pronounced at high frequencies and low levels of soil damping, and cannot propagate through “gaps” opened between the pile and soil. The pile cap can also be an important source of radiation damping.
4
Figure 1.3 - Schematic of Modes of Single Pile Seismic Response The high degree of system coupling between the modes and components of interaction illustrate the complexity of SSPSI; the seismic response of piles installed in group configurations add another layer of complexity. It is apparent that for systems with strong nonlinear response, a fully-coupled analysis technique may be desirable. Such an analysis can evaluate how the development of nonlinearity in one system component affects the demands on another, which may potentially contribute to more reliable and economical design practice.
This is in contrast to the commonly used dynamic substructuring
methods, which are more fully discussed in section 3.1, and can essentially be characterized as averting fully-coupled analysis of nonlinear system interaction.
5
1.2 Overview of Observed Pile Response During Earthquakes Many cases of damage to piles and pile-supported structures have been observed in earthquakes, and to a lesser degree, instrumented records of pile and pile-supported structural performance have been obtained.
Taken together, these qualitative and
quantitative observations have formed a framework for understanding SSPSI, albeit an incomplete one. Just as site response was accentuated in the Loma Prieta earthquake, individual earthquakes have imparted specific lessons about SSPSI, and no doubt future events will continue to incrementally advance the state of knowledge. Chapter 2 includes a review of observed pile seismic performance, but an overview is presented here to highlight modes of pile seismic response and failure. From instrumented case histories, it has been found that SSPSI commonly results in spectral deamplification of pile cap motions relative to free-field motions.
This
deamplification typically occurs at periods less than the period of the composite soil-pilestructure system, and varies greatly in amplitude. At low levels of shaking, kinematic interaction is seen to dominate the system response; period lengthening and increased radiation damping of the system are responsible for dissipating energy and deamplifying motions up to the resonant period. With the onset of stronger shaking, near-field soil modulus degradation and soil-pile gapping limit radiation damping, and structural inertial forces predominate, lessening the effects of spectral deamplification.
As system
components yield, the system period further lengthens and radiation damping is effectively suppressed.
6
STIFF SOIL PILE PULLOUT FROM CAP PILE FAILURE AT HEAD IN SOFT SOIL FLEXURE AND/OR SHEAR PILE FLEXURE/SHEAR FAILURE AT STIFFNESS CONTRAST
PILE CAP FAILURE BEARING CAPACITY OR TENSION PULL-OUT FAILURE
EXCESSIVE LATERAL DEFORMATIONS
Figure 1.4 - Potential Failure Modes for Pile Group Foundations Subjected to Seismic Shaking Particular modes of damage and failure include those related to both kinematic and inertial interaction (see Figure 1.4). Loss of lateral soil support has been observed to occur due to liquefaction of cohesionless soils or strain softening of cohesive soils near the pile head. When combined with large structural inertial loads, excessive displacements and bending strains concentrated near the pile head have developed and resulted in pile damage, frequently at the pile to cap connection. Another common liquefaction hazard arises from the large loads that laterally spreading soil deposits exert on piles, which has frequently resulted in pile and structural damage. When soils along the length of the pile soften due to liquefaction or strain softening, piles have experienced a loss of bearing capacity, and if combined with a rocking mode induced by superstructure inertial forces, the piles frequently undergo settlement, punching, or tensile pull-out failure. Piles may also be subject to damaging bending strains at interfaces between soil layers of strong
7
impedance contrast. This contrast may be provided by soft and stiff soil layers, or by soil layers that undergo liquefaction or strain softening under earthquake loading. Finally, battered (inclined) piles can form relatively stiff lateral resistance systems, and attract forces that the pile head and/or pile cap cannot sustain.
1.3 Research Needs and Research Objectives As will be shown in Chapter 2, there is a significant history of observed SSPSI effects, having often resulted in pile and/or structural damage or failure. Many of these case histories have been recorded in liquefiable cohesionless soils, but the potential for adverse performance of pile-supported structures founded on soft, strain sensitive cohesive soils is also of great concern.
The empirical case histories have provided
important qualitative data regarding SSPSI effects, but the paucity of quantitative data has not contributed to advancing the practice. To fill the gap, researchers have utilized an arsenal of field and laboratory test procedures to investigate SSPSI problems. As will be demonstrated in Chapter 4, these experimental procedures have primarily focused on individual segments of SSPSI, with varying degrees of rigor and success. Similarly, the disparate analytical tools that have been developed are generally uncoupled from the overall system response; these substructuring methods have historically been driven by the necessity of computational efficiency and by the artificial barrier between geotechnical and structural analysis. With this background, several research needs are clear with respect to SSPSI. With the great concentration of research effort on the performance of pile-supported structures in liquefiable soils, a strong need exists to examine SSPSI in strain-sensitive
8
cohesive soils. Shaking table experiments provide an excellent opportunity to augment the limited database of SSPSI in soft clays, and afford the ability to do so under controlled and varied conditions. Importantly, such experiments can be designed to simulate the fullycoupled behavior of the soil-pile-superstructure system, and fully-coupled analytical methods can be applied to the results. The development and calibration of advanced fullycoupled numerical tools is the subject of parallel work at U.C. Berkeley (Lok, 1999). The following topics are therefore identified as tractable by shaking table experiments, and constitute the focus of this research program: •
soil-pile-superstructure coupled response in soft clay during strong shaking,
•
elastic and nonlinear pile group interaction,
•
applicability of 1-D analysis to 2-D excitations,
•
pile cap embedment contribution to pile group impedance and group performance,
•
single pile and pile group stiffness derived from static and dynamic head loading tests compared with the seismic response of similar structures, and
•
degradation of soil resistance due to water scour in soil-pile gap during cyclic loading.
1.4 Organization of the Thesis Chapter 2 consists of a comprehensive survey of pile performance in earthquakes. The first section details observations from ten major earthquakes in the twentieth century that, together, manifested virtually all modes of pile damage and failure under seismic loading.
The second section reports case histories of measured seismic response of
instrumented pile supported structures, and in some cases, instrumented piles; both building structures and bridges are included. Taken together, the empirical observations and instrument records constitute an empirical framework for understanding SSPSI and potential failure modes.
9
The current state-of-the-art with respect to SSPSI is addressed in Chapter 3. First, a review of analytical methods for the static, cyclic, and dynamic response of single piles and groups under lateral loading is presented.
Second, a survey of building code
provisions is made to illustrate the lack of consensus on incorporating SSPSI effects into practice. To further illustrate this point, a third section details a number of case histories that take a variety of design approaches to account for SSPSI. Chapter 4 is a review of previous experimental work dealing with lateral pile response conducted in both field and laboratory settings. The test conditions range from small model piles to full scale shafts, and encompass a variety of soil conditions, and an assortment of loading schemes. The experimental work to date has focused on subcomponents of the overall SSPSI problem, and has done a great deal to validate and/or refine theoretical SSPSI models; however, true state-of-the-art test procedures are still emerging. Chapter 5 discusses the theory of scale model similitude and the development of scale modeling criteria for the shaking table testing program. Design, fabrication, and properties of the model soil and model piles used in the testing program are described, with commentary on the compromises inherent in the scale modeling process. Chapter 6 describes the shaking table test program, focusing on the development of the model container. Test parameters, instrumentation, and testing procedures are specified. Chapter 7 qualitatively reports the results of the shaking table test series. Soil and structure accelerations, displacements, and bending and axial strains measured in the model piles are contrasted for different model configurations.
Also included is a
discussion of the shaking table performance and the model container response.
10
Analysis of the results is presented in Chapter 8, which first establishes the in-situ soil properties and then examines model soil free-field site response. The suite of pile head loading test results is then compared to theoretical performance. Pile group effects are investigated through the results of the static lateral group test, and the effects of twodimensional shaking are analyzed.
System identification techniques are employed to
determine flexible base period and damping factors of the model structures, which are compared to the fixed base idealization. Pile performance is analyzed with respect to experimentally-derived static and cyclic p-y curves. Finally, Chapter 9 summarizes the experimental findings and makes recommendations for future research.
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CHAPTER 2 OBSERVED PILE SEISMIC PERFORMANCE
2.1 Observed Pile Damage During Earthquakes The following case histories are presented as a representative survey of observed pile damage and failure during major earthquakes.
It is comprehensive but not all-
inclusive, as a number of other case histories do exist for events worldwide. The cases are described here in some detail (and in the same units as originally reported), as they give an excellent indication of pile performance during strong shaking and insight into modes of behavior and failure.
2.1.1 The San Francisco Earthquake of April 18, 1906 In the 1906 San Francisco Earthquake, the most intense damage was concentrated at the margins of the historic shoreline, which during the 1850’s had been reclaimed with loosely dumped fill consisting of dune sand, silty sand, and other random rubble (Figure 2.1). Beneath this fill is soft Bay Mud, which in turn is underlain by much stiffer cohesive deposits. The strong shaking in this area of the city (Rossi-Forrel Intensity IX to X) resulted in widespread liquefaction of the sandy fill, and subsequent failure of numerous structures before they were consumed by fire (Seed, et. al., 1990).
Some of these
structures were pile-supported, and as noted in the 1908 Earthquake Commission report (Wood, 1908), in the vicinity of the Embarcadero, the concrete casing of piles was frequently broken. However, “first-class, modern” buildings founded on deep pilings, such as the Ferry Building, were not observed to suffer serious damage. A new U.S. Post Office, constructed at the margin of the Old Mission Bay on the corner of Seventh and
12
Mission Streets, was founded on piles driven “a considerable depth, but not as far as some had considered advisable” according to Wood.
The southwest corner of the
building was on the edge of the filled marsh, and experienced significant differential settlement due to massive ground failure, where “the streets are deformed into great waves, some with an amplitude of at least 3 feet, causing fissures and sharp compressional arches in the pavement and sidewalks” (Figure 2.2). Differential settlement was also apparent between the pile-supported cable car conduits on lower Market Street and the surrounding street, which settled as much as 2 ft below the tracks.
Figure 2.1 - Regions Most Intensively Damaged During the 1906 San Francisco Earthquake, and the Historic Shoreline (after Seed et al., 1990)
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Outside the city, a number of pile-supported bridges suffered damage.
In
Mendocino, the bridge across the Big River collapsed, reportedly due to the shifting north of the piles on the north side of the river, thus allowing the span to drop. Wooden piles 75 ft deep supporting the Gonzales bridge were undisturbed at the northeast end, but were torn loose and moved from plumb at the southwest end. The south pier of the two span Salinas bridge, “consisting of 26 piles incased in planking, was thrust to the south between 6 and 7 feet.” The piles were observed to be unbroken at ground level, but the entire pier was inclined as shown in Figure 2.3. At the Neponset county bridge, a pile-supported bent “moved at least 10 feet toward the river”. At Moss Landing, lateral spreading of the ground toward the Salinas River carried piles from beneath a railroad bridge and caused its collapse (Figure 2.4). At Inverness, two light wooden piers founded on timber piles were deformed as the underlying tidal mud was driven toward the shore in a ridge. The piles founded on the firm shore and the tidal mud experienced different inclinations, as shown in Figure 2.5.
Figure 2.2 - Ground Failure during the 1906 San Francisco Earthquake in the Vicinity of the U.S. Post Office at Mission and Seventh Streets (after Wood, 1908)
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Figure 2.3 - Failure of Pile Supported Pier of the Salinas Bridge during the 1906 San Francisco Earthquake (after Wood, 1908)
Figure 2.4 - Collapse of Timber Pile Supported Railroad Bridge at Moss Landing due to Lateral Spreading during the 1906 San Francisco Earthquake (after Wood, 1908)
Figure 2.5 - Deformation of Pile Supported Inverness Piers (exaggerated scale) due to Lateral Spreading during the 1906 San Francisco Earthquake (after Wood, 1908) 15
2.1.2 The Alaska Earthquake of March 27, 1964 The magnitude 8.3 Alaska Earthquake of 1964 caused extensive damage to highway bridges, though the damage intensity was not related to the proximity to the epicenter but rather to the susceptibility to liquefaction of the foundation soils. This was the conclusion of a comprehensive survey made by Ross, Seed, and Migliaccio (1969). Four bridges on the Seward Highway over the Snow River founded on timber piles in predominantly fine granular soils suffered varying degrees of damage. The piles for Bridge 603 were driven to bedrock, and the bridge suffered minor damage. Bridge 604 suffered considerable settlement of the abutments and approach fills. The timber piles for Bridge 605 were driven 40 - 60 ft through interbedded fluvial soil with an SPT blowcount of N = 5 - 10, and the bridge was destroyed, as the abutments were driven toward one another and the timber bents settled as much as 10 ft (Figure 2.6). The foundations for bridge 605A (next to Bridge 605) were under construction at the time of the earthquake, and they experienced liquefaction-induced failure, as heavy piers each supported by 21 concrete-filled steel pipe piles extending 90 ft deep experienced up to 8 ft of lateral displacement and 15 degrees of tilt (Figure 2.7). The timber bents for Bridge 606 were founded on bedrock on the eastern third of the span, and loose fluvial deposits on the western two-thirds of the span; the east end settled and the west end collapsed. An interesting contrast was provided by two Seward Highway bridges over the Resurrection River, both of similar construction and with similar silty sandy gravel (N = 30 - 60) foundation soils. Both bridges experienced lateral spreading of their abutment fills toward the channel, but Bridge 596 provided little clearance between the abutment and pier, and the displaced fill exerted high lateral loads on the pier resulting in serious
16
damage to the bridge. Bridge 598, constructed with greater separation between the abutments and piers, suffered only moderate superstructure damage.
Figure 2.6 - Collapse of Snow River Bridge 605 due to Liquefaction during the 1964 Alaskan Earthquake (after Ross et al., 1969)
Figure 2.7 - Liquefaction Induced 15 degree Tilt of Snow River Bridge 605A Foundations during the 1964 Alaskan Earthquake (after Ross et al., 1969) On the Seward Highway between Snow River and Turnagain Arm, 16 bridges suffered relatively minor damage, as the timber bent or steel rail pile foundations were driven into gravelly soils directly overlying bedrock, which showed no evidence of liquefaction. Of the 15 bridges on the Seward Highway in the Turnagain Arm area, many experienced severe damage and 10 wholly or partially collapsed (Figures 2.8 - 2.11).
17
These included the Placer River, Portage River, Twentyninemile River, Jim’s Creek, Virgin Creek, and Tidewater Slough bridges. The bridges that collapsed all consisted of concrete superstructures on timber pile bents founded on a surficial gravel layer over interbedded sands and silts, underlain by silt. SPT blowcounts ranged from N = 15 - 30 near the surface to N = 35 - 85 at the pile tips. Typical damage consisted of collapsed decks, twisted and shifted timber bents, and abutments shifted toward the channel.
Figure 2.8 - Collapsed Concrete Deck of Bridge 629 over the Placer River Penetrated by Timber Piles during the 1964 Alaskan Earthquake (after Ross, et al., 1969)
Figure 2.9 - Wreckage of Portage Creek Bridges, adjacent to Alaskan Railroad Grade and Bridges, during the 1964 Alaskan Earthquake (after Kachadoorian, 1968)
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Figure 2.10 - Collapsed Bridges over the Twentyninemile River during the Alaskan Earthquake of 1964 (after Ross et al., 1969)
Figure 2.11 - Collapsed Twentyninemile River Bridge with Timber Piles Punched through Deck during the Alaskan Earthquake of 1964 (after Ross et al., 1969) On the Sterling Highway, the Kenai River Bridge, supported on timber piles driven into silt and fine sand (N = 35 - 40), collapsed onto the stream bed (Figure 2.12). In the same area, the Quartz Creek Bridge was founded on timber piles driven into medium dense gravels, and experienced only minor damage. On the Copper Highway, 25 bridges spanned the Scott Glacier and Sheridan Glacier outwash plains, and experienced a range of damage directly related to liquefaction. Many brittle rail piles sheared near the head, as shown in Figure 2.13. The timber and rail pile bents in the Scott Glacier area were founded on loose to medium dense (SPT N = 10 -
19
20) stratified sands and silts with organic components.
The foundation soils in the
Sheridan Glacier area consisted of loose stratified sands and gravels (SPT N = 5 - 10) in the upper 20 to 25 ft, but were considerably denser (SPT N = 15 - 50) at depth.
Figure 2.12 - Collapsed Kenai River Bridge with Piles Punched through Concrete Deck during the Alaskan Earthquake of 1964 (after Ross et al., 1969)
Figure 2.13 - Sheared Rail Piles on Scott Glacier Bridge 6 during the Alaskan Earthquake of 1964 (after Kachadoorian, 1968)
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Also on the Copper Highway, most of the 19 bridges on the Copper River Delta sustained moderate to severe deformations, and at least 6 spans were reported collapsed. Foundation types ranged from massive caissons to timber pile-supported bents to steel rail pile bents. Although subsurface information was unknown at the time of Ross and Seed’s survey, considerable evidence of liquefaction in this area was noted. The famous Million Dollar Bridge collapsed due to abutment and streambed movements (Figure 2.14).
Figure 2.14 - Million Dollar Bridge Collapse during the Alaskan Earthquake of 1964 (after Kachadoorian, 1968) The Tasuna River Bridge was supported by piles driven into both gravels and sands, and portions of the bridge over the sandy soils collapsed. The Flagg Point Bridge was also founded on piles driven into both gravels and sands. The piles in sands settled as much as 10 ft and the differential settlement caused the bridge to collapse (Figure 2.15). Bridge 1121 crossing the Knik River exhibited liquefaction related damage, as four heavy pile-supported piers shifted as much as 2 ft toward the channel.
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Figure 2.15 - Collapsed Deck of Flagg Point Bridge 331 due to Liquefaction Induced Settlements during the Alaskan Earthquake of 1964 (after Ross et al., 1969)
A review of the railroad damage caused by the Alaska Earthquake is provided by McCullouch and Bonilla (1967). Of the 58 railroad bridges from Portage to Seward and Whittier built on unconsolidated sediments, 51 were either destroyed or rendered impassable; bridges built on bedrock in the same areas suffered almost no damage. Typical damage consisted of abutments laterally spreading toward the channel, resulting in compression of the span driving the stringers through the bulkheads, and arching the deck over the piers. In one case, it appeared that the deck repeatedly arched up and fell down on the piers during the earthquake, as evidenced by multiple impact holes caused by the piles on the underside of the deck. The bents, consisting of 5 piles and a pile cap driven up to 30 ft deep in the loose sediments, were translated both horizontally and vertically,
22
but with little rotation. This indicates that the depth of the liquefied layer was likely below the pile tips and a global flow failure took place in the channel. In summary, two general modes of liquefaction related bridge failure can be discerned from these examples. In the first case, liquefaction of the abutment fills caused span shortening and directly exerted damaging lateral loads on the bridge piers. In a second scenario, bridge decks were held in place while liquefaction in the channel caused settlement or lateral displacement of the bridge piers, which then broke away from the deck. Ross and Seed noted in their report the relatively good performance of piles in gravelly soils and on bedrock, but also observed that no cases of bridges founded in cohesive soils were known to exist on the routes surveyed. Margasson (1977) does provide evidence of the seismic performance of a pilesupported structure in cohesive soils in his review of waterfront dock damage in Anchorage.
The City Dock suffered extensive damage, although it was a modern
reinforced concrete structure supported on 16 to 42 in diameter steel pipe piles and 14 to 20 in diameter battered piles driven into stiff “Bootlegger Cove” clay (the Ocean Dock in Anchorage, founded on timber piles, was also damaged in the earthquake). Margasson estimated that the peak horizontal ground acceleration (MHA) at this site was 0.30 g, and observed that the added inertial loads due to the dock being heavily loaded with ice aggravated the seismic response. The dock was found to have settled nearly 4 ft, and translated outward 8 in at the south end and 17 in at the north end. Apparently the entire dock settled as the clay beneath the pile tips settled. In a report by TAMS to the City of Anchorage (1965), the pile damage is described as follows:
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“The batter piles battered to the west were bowed and buckled while those battered to the east were relatively straight. The evidence is that the displacement of the pier, both translational and rotational, was developed and retained by buckling of the batter piles in the west portion of the main pier. The working of these batter piles against the large horizontal seismic forces indicated vertical loads at the pile heads which were transmitted into concrete pile caps above. The seismic forces further caused a swaying of the pier in a rotational and east-west direction, inducing bending moments and shears at the tops of the vertical piles. These stresses in some cases caused shattering of the concrete cap and deck around the pile head. The effect of this displacement on the piles resulted in a stress condition which was one or a combination of the following: 1. At the top of the pile: a. The connection held rigidly, thereby inducing a bending moment at the cap. b. The connection held rigidly but the pile yielded, resulting in an indeterminable residual bending moment. c. The concrete cracked, causing the connection to rotate, resulting in very little or no bending moment at the top. 2. At the base of the pile: a. The soil held the base rigidly, thereby inducing a bending moment. b. The soil held the base rigidly but the pile yielded at some indeterminate point below the mudline, resulting in a residual moment. c. The pile rotated, relieving all or part of the bending moment. 3. Along the length of the pile: The pile yielded and deformed. The resulting loading pattern on the piles is complex and varied. Piles that lost their rigidity at their ends but retained their straightness still were able to carry their loads along the axis but now exerted a horizontal load on the dock. The horizontal load was transmitted through the deck to the other piles. Piles that retained their rigidity at one or both joints and piles that were deformed carried their loads by a combination of axial stress and bending stress. The effect of the bending stresses created in the piles is to reduce their load-carrying capacity as columns.” This highly detailed forensic investigation is an excellent analysis of the complex interaction of this soil-pile-structure system. The deficient response of battered piles is particularly evident in the manner they attracted horizontal load and transmitted these loads into the structure and other piles.
24
2.1.3 The Niigata Earthquake of June 16, 1964 The second major earthquake of 1964 was the magnitude 7.3 Niigata Earthquake, which caused widespread liquefaction related damage and numerous failures of pilesupported structures. Seed and Idriss (1966) summarized building damage patterns and related damage intensity to SPT blowcount of the foundation soil and the depth of foundation embedment (Figure 2.16). Kishida (1966) recounted several specific cases of liquefaction-induced pile damage at sites where piles were driven in loose sandy deposits with an SPT blowcount N = 5 - 10. At the Saiseikai Hospital, 7.2 m long concrete piles of 0.18 m diameter lost bearing capacity due to liquefaction, and the structure tilted and cracked. Similar concrete piles at the Ishizue Primary School also lost bearing capacity and differential settlement caused distress in the structure. Timber piles of 0.18 m
Figure 2.16 - Damage Intensity during the 1964 Niigata Earthquake Related to SPT Blowcount and Foundation Embedment Depth (after Seed and Idriss, 1966)
25
diameter under the Irifune Primary School were examined after the earthquake and found to be tilted and in some cases separated from the footing. The East Police Station did not suffer significant damage, although the foundation soil did liquefy and a post-earthquake foundation investigation revealed concrete piles cracked at the head and at the joint between the pile and cap. The failure of the 10 span 307 m long Showa River Bridge was a direct consequence of liquefaction of the upper loose sand layer, which in turn laterally flowed against and displaced the 60 cm diameter steel pipe pile-supported bents, unsupporting and dropping several spans (Figure 2.17). Fukuoka (1966) reports on the post earthquake failure investigation and recovery of the damaged piles; Figure 2.18 depicts approximately 1 m of permanent displacement at the pile head, maximum pile curvature at the transition from loose to medium dense sand, and local buckling at an intermediate elevation. He also notes the strong response of the structure due to resonance effects between the earthquake and bridge natural frequencies, which likely transmitted large inertial forces into the piles, causing the observed local buckling. 500 m downstream, both abutments of the Yachiyo Bridge moved up to 50 cm toward the channel, but the bridge did not collapse. Post-earthquake investigation of the 60 cm diameter precast concrete piles revealed horizontal cracks spaced continuously along the full length of the piles (Figure 2.19). Iwasaki (1973) reports on similarly cracked piles extracted from piers of the severely damaged Higashi-Kosenkyo Bridge, and destructive settlements and tilting of the timber pile-supported abutments of the Bandai Bridge. Kawakami and Asada (1966) describe 330 cm of liquefaction related settlement of the pile-supported Sakae-bridge over the Nikko River (Figure 2.20). Kawashima et al. (1988) recount the collapse of the main
26
span of the 229.5 m long East Over-Railway Bridge as a direct consequence of liquefaction-induced displacements of up to 58 cm of the 300 mm diameter 7 m long RC piles supporting the piers, which resulted in the main span girders becoming unsupported. Post-earthquake excavation revealed cracked and displaced piles, which directly correlated to surveyed permanent ground displacement in the vicinity.
Figure 2.17 - Liquefaction Induced Collapse of Showa Bridge during the 1964 Niigata Earthquake (after Iwasaki, 1972)
Figure 2.18 - Permanent Deformation of Pile Extracted from Showa Bridge Foundation during the 1964 Niigata Earthquake (after Iwasaki, 1972)
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Figure 2.19 - Cracked Precast Reinforced Concrete Piles from Yachiyo Bridge during the 1964 Niigata Earthquake (after Fukuoka, 1966)
Figure 2.20 - Liquefaction Related Settlement of Pile Supported Sakae Bridge during the 1964 Niigata Earthquake (after Kawakami and Asada, 1966) Another liquefaction related pile failure mechanism is presented by Hamada (1991), who estimated permanent ground displacements during the Niigata earthquake from aerial photographs and correlated these displacements to damage observed in piles excavated more than 20 years after the earthquake. The 11 - 12 m long 350 mm diameter concrete piles supporting the NHK Building were found to be broken at two positions, near the top of the pile and near the base, and consistently inclined in the direction of the permanent ground displacement (Figure 2.21). Similar damage was discovered during the reconstruction of the Niigata Family Courthouse; damage near the head of the 350 mm diameter concrete piles was more severe, and damage at the lower positions corresponded to the boundary between the liquefied and non-liquefied soil layers (Figure 2.22). Yoshida
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and Hamada (1990) contrasted liquefaction related pile damage to the Nigata Family Courthouse and the NHK building; the soil profile, pile deflection patterns, and pile crack patterns are shown in Figures 2.23a and b. Nishizawa et al. (1984) report that the three story branch office of the Daiyon Bank settled as much as 1.3 m, and tilted, but only experienced minor structural damage. After the earthquake, the building was jacked up and supported on newly driven H-piles. In 1984 this structure was demolished, and during the basement excavation the severely damaged original precast concrete piles were exposed; the piles were damaged both in the zone of maximum moment and also near the tip where a stiffness contrast in the soil layers occurred. The fact that these structures remained in service with no indication of the defective foundation condition vividly illustrates the difficulty of ascertaining pile performance and/or damage in earthquakes.
\ Figure 2.21 - Piles Supporting the NHK Building Sheared by Lateral Spreading during the 1964 Niigata Earthquake (after Hamada, 1991)
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\ Figure 2.22 - Damage Pattern to Foundation Piles Supporting the Niigata Family Courthouse during the 1964 Niigata Earthquake (after Hamada, 1991)
(a) (b) Figure 2.23 - Correlation of Pile Damage to Site Conditions at a) Niigata Family Courthouse and b) NHK Building during the Niigata Earthquake (after Doi and Hamada, 1992)
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2.1.4 The Off-Tokachi Earthquake of May 16, 1968 The magnitude 7.8 Off-Tokachi Earthquake and magnitude 7.4 aftershock caused substantial damage to a region of northern Japan, and in particular damaged the Anenuma bridge.
This 32 span structure was founded on end-bearing 16 in diameter precast
concrete piles, driven 65 to 105 ft through very soft peaty soils, with measured SPT N values of nearly zero. According to Tamura et al. (1973), post-earthquake inspection revealed cracks near the top of the piles, and over 2 ft of lateral displacement and as much as 4 in of settlement of the bridge. Forced vibration tests of the bridge were made and compared with similar test results conducted some time before the earthquake; it was judged from these tests that the bridge foundation strength had lowered, and subsequently steel pipe piles were driven beside and connected to the footings to augment the foundation capacity.
2.1.5 The San Fernando Earthquake of February 9, 1971 The epicenter of the magnitude 6.4 San Fernando Earthquake was less than 10 miles from four major freeway bridges. In all, some 15 bridges sustained major damage, with the Golden State Freeway/Foothill Freeway Interchange contributing the collapse of 7 concrete box girder spans. These spans were typically supported on single columns, which were lap spliced into single 6 ft diameter drilled piers. Soil conditions at this interchange consisted of dense silty sands. Failure was typically concentrated at the base of the columns, where the bond failed in the main reinforcing bars into the pile (see Figure 2.24). At the Roxford Street Undercrossing of the Foothill Freeway, no damage was observed on the deck or abutments, but in subsequent excavation to repair a wingwall, the
31
piles supporting one abutment were found to be heavily damaged. This reiterates the lesson from Niigata that seismic pile damage may be concealed by overtly undamaged structures.
Figure 2.24 - Failure at Connection Detail Between Drilled Shaft and Bridge Column at the Golden State Freeway/ Foothill Freeway Interchange during the 1971 San Fernando Earthquake (after Penzien, 1971) 2.1.6 The Off-Miyagi Prefecture Earthquake of June 12, 1978 The magnitude 7.4 Off-Miyagi Prefecture Earthquake resulted in a number of cases of damage to prestressed concrete piles, which were principally caused by earthquake-induced vibration of the superstructure, according to Sugimura (1981). In two instances, total structural collapse followed, and in others, minor to moderate structural damage was sustained. The soil conditions where pile damage occurred ranged from sands to silts to clays to peat, but liquefaction was not considered to be a contributing factor to these cases. The failure modes included bending-shear failure at the pile head, and complete crushing at the pile head. Notably, the most heavily damaged piles were found at the structure’s perimeters, suggesting that rocking due to inertial loads from the structure overstressed the piles.
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This experience motivated the Japanese to re-evaluate their pile seismic design criteria, and inspired Mizuno (1987) to compile a survey of 30 cases of pile damage in earthquakes in Japan from 1923 - 1983. Mizuno grouped the cases into five external causes: 1) lateral displacement of cohesive and/or organic soil in a plane deposit causing pile damage; 2) lateral spreading of embankment causing pile damage; 3) liquefaction of sandy soil in a plane deposit causing pile damage (most prevalent cause); 4) vibration effects of the soil causing pile damage; and 5) inertial forces of the structure causing pile damage. In addition, four damage patterns were described: 1) damage with subsidence of pile head (shear failure, compressive failure); 2) ring-type crack due to bending moment (no subsidence of pile head); 3) pile separation from pile cap; and 4) buckling failure of welded joint.
2.1.7 The Mexico City Earthquake of September 19, 1985 The epicenter of this magnitude 8.1 earthquake was some 400 km distant from Mexico City, but a convergence of site response factors focused massive damage on the “Lake Zone” of Mexico City. The seismic waves were effectively filtered to long period motions in traveling from the epicenter to the Mexico City region. In the Lake Zone, the intensity of shaking was greatly amplified by the deep soft clay deposits, with a resulting period of approximately two seconds. This long period motion came into resonance with many structures of intermediate height, resulting in a damage pattern closely focused on these long period structures.
Of these buildings, those supported by friction piles
experienced the most damage.
33
Before describing damage of pile-supported structures, it is useful to survey the types of pile foundations employed in this area (see Figure 2.25). Prime concerns of foundation design in the highly compressible Mexico City clays are limiting settlement and accommodating negative skin friction on deep foundations. Friction piles are employed without compensated foundations for light structures, and with compensation for medium weight structures. End bearing piles founded on Tarango sand at some 33 - 38 m depth are utilized for heavy structures. Additionally, many buildings are supported on end bearing piles with “control” devices on their heads; the pile freely penetrates the foundation slab, which is then allowed to settle at the same rate as the surrounding soil. The control devices are commonly provided by wooden blocks which compress at a predetermined rate, or hydraulically controlled jacks.
Figure 2.25 - Types of Foundations Used in the Soft Soil Deposits of Mexico City (after Mendoza and Auvinet, 1988)
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According to Girault (1986), 25 buildings on mat foundations supported by friction piles experienced large settlements (up to 130 cm) and tilting. The mechanism for these settlements was relaxation of the negative skin friction on the pile due to partial loss of shear strength during cyclic loading of the sensitive clays. Mendoza and Romo (1989) assert that low factors of safety and soil-pile stress states close to yielding with respect to static loading precipitated foundation failures under seismic loading.
Tilting and
overturning due to cyclic “rocking” may have been exacerbated by P-∆ effects associated with lack of plumbness of continually settling structures. In one instance a ten story building overturned entirely, as one corner sank 6 m into the soil and the other rose out of the soil 3 m, pulling piles out of the ground. The site profile and damage to this structure are shown in Figures 2.26a and b. Structures supported on end bearing piles performed better than friction piles, with smaller settlements and fewer structural
Figure 2.26 - Ten Story Pile Supported Building founded on Soft Soils during the 1985 Mexico City Earthquake: a) Elevation including Geotechnical Conditions; b) Overturned Structure (after Mendoza and Auvinet, 1988)
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failures. Slender buildings with control piles experienced tilting, as the wooden blocks were crushed and hydraulic jacks burst; these control devices were clearly not designed for the seismically-induced inertial rocking loads imposed on them. In summary, seismic overturning moments were the prime cause of failure of pile foundations, though perhaps some cyclic strength degradation contributed to a partial loss of soil-pile adhesion.
2.1.8 The Loma Prieta Earthquake of October 17, 1989 The magnitude 7.0 Loma Prieta Earthquake caused the dramatic failure of several pile-supported structures. The collapse of the Cypress Freeway killed 42 people, and though it was founded on piles along an alignment that transitioned from stiff to soft foundation soils, the site response and structural connection details were the principal failure mechanisms. A span of the San Francisco-Oakland Bay Bridge collapsed, and although this was primarily a structural failure, SSPSI constituted an important component of the bridge seismic response. Near Watsonville, the pile-supported Highway 1 bridge across the Struve Slough collapsed, as several of the piles punched through the roadway (Figure 2.27). It appears that soil liquefaction did not contribute to this failure, as the upper foundation soils consisted of soft clays and organics, with some alluvial sands present. The piles did not show signs of settlement, but there were gaps 30 to 45 cm wide opened around the piles, indicating inadequate lateral support (Figure 2.28).
This
inadequate lateral soil support resulted in excessive lateral pile deflections, and flexural/shear failures at the pile to bent connections (Figure 2.29).
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Figure 2.27 - Highway 1 Crossing Struve Slough near Watsonville Collapsed during the 1989 Loma Prieta Earthquake, with Pile Punching through Deck (after Seed et al., 1990)
Figure 2.28 - Formation of Gap Adjacent to One of the Piles Supporting the Collapsed Struve Slough Crossing during the 1989 Loma Prieta Earthquake (after Seed et al., 1990)
Figure 2.29 - Flexural Shear Failure of Pile to Bent Connection of the Struve Slough Crossing during the 1989 Loma Prieta Earthquake (after Seed et al., 1990)
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Yashinsky (1998) provides a comprehensive summary of damage to highway systems in the Loma Prieta Earthquake. In addition to the above-mentioned structures, he cites numerous examples of pile-supported bridge structures sited on soft soils that sustained damage in the earthquake. These include the Southern Freeway Viaduct, the China Basin Viaduct, the Embarcadero Viaduct, and the Terminal Separation Structure, all in San Francisco.
The Route 92/101 Separation Interchange in San Mateo, the Mococo
Overhead in Martinez, the Napa River Bridge in Vallejo, the Richardson Bay Bridge near Marin City, and the San Mateo-Hayward Bridge also sustained minor damage. None of these cases could be considered foundation failures, though the foundation performance obviously contributed to the structural response and consequent damage of these bridge structures. Port facilities and marine structures around San Francisco Bay experienced moderate pile damage in the earthquake (SEAOC, 1991). At the Port of Oakland, a MHA of 0.45 g was measured. The 7th Street Terminal Complex suffered extensive damage, as 16 in square prestressed concrete batter piles supporting the Public Container Wharf failed in tension at their connection to the deck (Figure 2.30). The inboard inclined piles were embedded in loose hydraulic fill which liquefied, settled, and laterally spread, exerting lateral and downdrag forces on the piles. The Matson Terminal Wharf at 7th Street suffered similar damage, but with additional damage to the back row of vertical piles. Reinforced concrete piles supporting the Charles P. Howard Terminal failed in bending at the transition from the piles to their capitals. At the Oakland Outer Harbor Pier 7, 16 in square prestressed concrete batter piles failed at or near the connection to the pile cap; again liquefaction and settlement of the supporting soil was observed. In San Francisco,
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the Ferry Plaza Pier experienced tensile failure at the connection of the deck to the prestressed concrete batter piles, with some of the piles punching the slab. Spalling and cracking of the bottom of the slab was found at over 100 pile locations. At Piers 27 and 29, similar damage as that experienced at the Ferry Plaza occurred to over 120 20 in square prestressed concrete batter piles (Figure 2.31).
Figure 2.30 - Damaged Batter Piles at Port of Oakland 7th Street Terminal during the 1989 Loma Prieta Earthquake (after SEAOC, 1991)
Figure 2.31 - Damaged Batter Piles at Port of San Francisco Piers 27 & 29 during the 1989 Loma Prieta Earthquake (after SEAOC, 1991)
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2.1.9 The Costa Rica Earthquake of April 22, 1991 The magnitude 7.5 Costa Rica Earthquake caused severe damage over a large area, including liquefaction related collapse of several pile-supported bridges. The three span Rio Banano bridge was located at a river crossing that showed extensive signs of liquefaction. The south abutment rotated about 9 degrees, causing movement of the 36 cm square precast concrete piles 66 cm toward the river (Figure 2.32). The front battered piles suffered flexural and shear damage, but the vertical piles at the rear showed less damage (Figure 2.33). Two of the three spans on the Rio Viscaya bridge collapsed due to severe abutment rotation, pile distress, and failure of one interior support, also resulting from extensive soil liquefaction (Figures 2.34a and b). The two span Rio Bananito bridge suffered collapse of the central pile-supported pier due to liquefaction, and both abutments experienced slumping and rotation toward the river (Figure 2.35). Liquefaction in the river channel caused rotation of 2.1 m diameter steel caissons supporting the Rio Bananito rail bridge (Figure 2.36), which tilted the bridge downstream (Figure 2.37). Steel caissons supporting the Rio Matina rail bridge experienced similar damage. At the Almirante port facility in Panama, concrete pilings supporting a railroad trestle were sheared at the head (Figure 2.38). In summary, Priestly et al. (1991) observe that inadequate pile penetration into stable materials contributed to structural failures, though this explanation ignores the lessons from 1964 that liquefaction solely in the upper soil layers can also result in structural failure.
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Figure 2.32 - Liquefaction Induced Rotation of Rio Banano Bridge Pile Cap during the 1991 Costa Rican Earthquake (after Priestly et al., 1991)
Figure 2.33 - Preferential Damage to Front Batter Piles of Rio Banano Bridge during the 1991 Costa Rican Earthquake (after Priestly et al., 1991)
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(a)
(b) Figure 2.34 - a) Failure of Rio Viscaya Bridge Piles during the Costa Rican Earthquake; b) Liquefaction Failure of Rio Viscaya Bridge (after Priestly et al., 1991)
Figure 2.35 - Rio Bananito Bridge Liquefaction Failure during the 1991 Costa Rican Earthquake (after Priestly et al., 1991)
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Figure 2.36 - Rotation of Caissons Supporting Rio Bananito Rail Bridge during the 1991 Costa Rican Earthquake (after Priestly et al., 1991)
Figure 2.37 - Tilting of Rio Bananito Rail Bridge due to Foundation Failure during the 1991 Costa Rican Earthquake (after Priestly et al., 1991)
Figure 2.38 - Sheared Concrete Piles Supporting a Railroad Trestle at the Almirante Port during the 1991 Costa Rican Earthquake (after Priestly et al., 1991)
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2.1.10 The Hyogoken-Nanbu (Kobe) Earthquake of January 17, 1995 The magnitude 7.2 Kobe earthquake was the most destructive earthquake to strike Japan in over 60 years, as it was a direct hit on a major metropolitan area, resulting in over 5500 deaths, damage to more than 200,000 houses, devastation of all modes of infrastructure, and losses exceeding 200 billion dollars (U.C. Berkeley, 1995). Liquefaction related damage to pile foundations was seen in a variety of settings, and several examples are presented here. The most dramatic structural failure during the Kobe earthquake was the collapse of an elevated section of the pile-supported Hanshin Expressway (see Figure 2.39). Gazateas and Mylonakis (1998) present an analysis suggesting that period lengthening due to foundation flexibility may have resulted in increased structural forces during the earthquake, as indicated by the response spectra from nearby instruments “Fukai” and “Takatori” shown in Figure 2.40.
Figure 2.39 - Collapsed Section of Hanshin Expressway
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Figure 2.40 - Response Spectra Recorded in Vicinity of Collapsed Hanshin Expressway Illustrating Effects of Period Lengthening due to Foundation Flexibility on Increased Structural Forces (after Gazetas and Mylonakis, 1998) A ramp structure at the Higashi-Kobe mainland ferry pier supported on pile foundations collapsed as the quay walls displaced outward (Figure 2.41).
Poor or
nonexistent connection details between the 30 and 35 cm diameter steel piles and cap are seen in Figures 2.42 and 2.43, with resultant failure at these connections. It is unlikely however, that sufficient connection details would have prevented the lateral displacement of the quay walls.
Figure 2.41 - Collapsed Pile Supported Ramp Structure at the Higashi-Kobe Ferry Pier during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995)
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Figure 2.42 - Nonexistent Connection Details Between Failed Piles and Pile Cap Supporting the Higashi-Kobe Ferry Pier (after U.C. Berkeley, 1995)
Figure 2.43 - Inadequate Connection Details Between Failed Piles and Pile Cap Supporting the Higashi-Kobe Ferry Pier (after U.C. Berkeley, 1995)
Figure 2.44 - Differential Settlement Between Pile Supported Roadway on Port Island and Surrounding Ground during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995)
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On Rokko and Port Islands, seismically-induced settlements of as much as 1 m were observed, and many pile-supported structures remained at the constructed elevation while the surrounding area settled around them. An example is provided by the piers supporting an elevated railway on Port Island (see Figure 2.44). In other locations, piles clearly underdesigned to resist lateral loads failed in shear, often due to lateral spreading (Figure 2.45). At the Port Island Ferry Terminal, large diameter 0.5 m diameter pier foundations resisted strong liquefaction and lateral spreading, and provided good structural performance. On Rokko Island, evidence of relative pile-soil movements was provided by gaps around a pile supporting a crane rail (Figure 2.46); the pile was found to be undamaged. Piles supporting bridge columns experienced two-fold liquefaction effects: a reduction of lateral resistance and loads imposed by lateral spreading, resulting in displacement, shifting, and tilting of bridge piers. The collapsed span of the Nishinomiya bridge provides such an example (Figure 2.47). Mizuno et al. (1996) surveyed more than 30 cases of pile damage observed in precast concrete, cast-in-place concrete, and steel pipe piles. Damage patterns consisted of separation between piles and pile caps, damage near the pile head, and damage at deeper portions of piles. The external causes were classified as due to inertial forces from the superstructure, lateral soil flow with liquefaction, and movements of natural deposits and fills.
At a site near Takatori station, the precast prestressed pile foundations
supporting three 12 story apartment buildings suffered shear and compressive failure near the pile head, and the buildings had to be demolished. No evidence of liquefaction was noted, and the damage was attributed to inertial forces from the superstructure.
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Figure 2.45 - Concrete Pile Sheared at Head on Port Island during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995)
Figure 2.46 - Relative Soil-Pile Movement Leaving Gap Around Pile on Rokko Island during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995)
Figure 2.47 - Collapsed Span of Nishinomiya Bridge during the 1995 Kobe Earthquake (after U.C. Berkeley, 1995)
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Matsui and Oda (1996) report on damage to foundations supporting the 6 major elevated highways in the Kobe area. A borehole television system was employed to directly inspect the condition of cast-in-place bored piles supporting these highway structures. On the Hanshin Expressway No. 5 Bay Route, 11 % of the inspected piles were classified as heavily damaged, and 37 % as lightly damaged; on the Hanshin Expressway No. 3 Kobe Route, 16 % of the inspected piles were classified as lightly damaged (other highways had lesser damage). Cracks were observed in the piles near the top (at the point of maximum moment), at positions where the density of steel reinforcement changed, and at interface zones between soft and hard soil layers. An interesting observation was that significant superstructure damage did not necessarily correlate to significant substructure damage, further suggesting that structures apparently undamaged in earthquakes may conceal damaged foundations. Matsui and Oda also recount case histories of waterfront steel pipe pile-supported structures subject to liquefaction and lateral spreading.
In one case, although the jetty revetment moved
laterally and was damaged, the piles were x-rayed and were found to be undamaged. In a second case, 70 cm diameter pipe piles supporting a landing pier were pulled out and found to be all indented at the same elevation corresponding to a replaced sand layer below the revetment.
Observations of precast concrete piles revealed cracking and
settlement and tilting of structures supported by these members. Matsui et al. (1997) describe pile load tests conducted to ascertain the serviceability of damaged piles on the No. 3 Kobe Route. They concluded that though the initial rigidity of the individual piles was degraded due to deformations past the yield
49
point, the pile group ultimate strength and displacement would be unaffected, with a slight decrease in initial rigidity. Sasaki et al. (1997) inspected the damaged Higashinada sewage treatment plant where liquefaction caused both lateral and vertical ground deformations of up to 2 m. Direct and non-destructive inspections of the 350 and 400 mm diameter prestressed concrete piles supporting the aeration tanks revealed extensive damage, mainly concentrated at 2 to 3 m from the pile head and at a depth corresponding to the bottom of the liquefied layer. They performed back analyses of the piles with a dynamic Winkler foundation model (see Chapter 3), and found that a failure mode that accounted for a combination of the superstructure inertial force, the lateral spreading force, and a reduced subgrade reaction due to liquefaction best replicated the observed pile damage. Tokimatsu et al. (1996) observed contrasting liquefaction effects in Fukaehama, where steel pipe pile-supported structures performed well, and precast concrete pilesupported structures experienced settlement and tilting.
They also observed good
performance of pile-supported structures in central Rokko Island, which they partially attributed to the fact that these buildings were constructed in accordance with newer building codes revised in the 1970’s and 1980’s to accommodate higher lateral forces acting on piles (i.e. in response to the Off-Miyagi Prefecture earthquake).
On the
shorelines of Kobe, and Port and Rokko Islands, liquefaction, lateral spreading, and ground subsidence damaged numerous piles and pile-supported structures. Both poorly and well connected precast concrete and steel pipe piles failed at the connection to the pile cap, or into the cap (Figure 2.48 and 2.49). Borehole television and non-destructive sonic tests revealed damage to precast concrete piles at various depths.
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Figure 2.48 - Lateral Spreading Damage to Pile during the 1995 Kobe Earthquake (after Tokimatsu et al., 1996)
Figure 2.49 - Pile Damaged by Superstructure Inertial Forces during the 1995 Kobe Earthquake (after Tokimatsu et al., 1996)
Figure 2.50 - Progression of Soil-Pile-Structure Interaction and Pile Bending Moments During Liquefaction (after Tokimatsu et al., 1998)
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Tokimatsu et al. (1997) used aerial surveys to quantify liquefaction-induced displacements of three 11 story buildings and excavated six pile caps to characterize the extent of the damage to the foundations supporting these structures. Two distinct pile damage patterns were detected, which were found to be directly related to the liquefaction-induced deformations of the surrounding ground. Tokimatsu et al. (1998) identified two buildings in Fukae in zones of large permanent ground deformations that did not suffer structural damage, and therefore hypothesized that serious pile damage due to lateral spreading may have occurred. This was confirmed by slope indicator and borehole camera investigations, and analytically modeled with a pseudo-static p-y method. The progression of soil-pile-structure interaction during liquefaction and the effects of uniform and non-uniform ground displacements on pile bending moments is shown schematically in Figure 2.50.
2.2 Measured Pile Response During Earthquakes In addition to qualitative observations, a limited amount of quantitative data of pile performance during earthquakes has been obtained and is to be reviewed here. This data consists of acceleration time histories recorded by seismographs at the pile cap, in the structure, and in the adjacent free-field, and in some cases bending and axial strain time histories recorded from strain gages fixed to the piles. The key features considered here are divergence between the acceleration time histories recorded at the pile cap and in the free-field, and the characteristics of the strain gage readings. The case histories published in the literature describe both building and bridge sites in a variety of site conditions and
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subject to a range of earthquake intensities; the cases which include instrumented piles have been limited to low intensity shaking however.
2.2.1 Building and Industrial Structures in Japan Esashi and Yoshida (1980) compared the response of instrumented pile foundations during recorded earthquakes and subsequent static and dynamic field tests. The 16 in diameter steel pipe piles were driven 33 ft deep into soft cohesive soils, and arrayed in a 1x2 pile cap partially embedded at the surface. Seismic recordings (MHA = 0.08 g) during the Matushiro earthquake swarm of 1966 showed similar free-field and pile accelerations at depth, but pile accelerations exceeding free-field ground motions near the ground surface. The predominant period of the pile motion during the seismic recordings matched the resonant period derived from independent vibration tests of the pile. In addition, the distribution of bending moment, shear, and soil reaction measured during the earthquakes, the dynamic tests, and a static head loading test all showed strong correlation. This study is unique in that it relates actual seismic performance with field test results, and partially validates the use of such tests for the characterization of the dynamic response pile foundations, albeit for low intensity shaking. Kawamura et al. (1977) monitored the response of a 7 story reinforced concrete apartment house subject to some 80 earthquakes between 1971 and 1977, with a MHA of 0.0076 g recorded. The structure was founded on 12 m deep precast piles driven through loose (SPT N < 10) into medium dense sands (SPT N > 30). With a building period of 0.2 seconds, and a site period of 1.2 seconds, 50 % deamplification of the pile cap motion
53
relative to the free-field motion was noted at periods less than 0.35 seconds for the particular event analyzed (Figures 2.51a and b).
(a)
(b)
Figure 2.51 - a) Apartment House Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Kawamura and Ikeda, 1981) Hagio et al. (1977) recorded the response of two petrochemical plant towers to 40 earthquakes between 1974 and 1977, with a MHA recorded at the site of 0.03 g. The 50 m and 30 m tall towers were supported on a common mat foundation, in turn supported by 45 m deep steel pipe piles driven through sands, silts, clays, and gravels into a dense sandy layer (SPT N > 50). The towers had first mode periods of 1.1 and 0.46 seconds, respectively, and the site period was estimated as 1.2 to 1.3 seconds.
Spectral
deamplification of 30 - 50 % was computed at periods less than 0.45 seconds at the base of both towers relative to the free-field for the particular earthquake studied (Figures 2.52a and b).
54
(a)
(b)
Figure 2.52 - a) Petrochemical Plant Towers Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Hagio et al., 1980) Hamada and Ishida (1980) report the response of a 37 m diameter pile-supported spherical tank structure to two large but distant earthquakes in 1978. The tank was supported by 56 steel pipe piles, 508 mm diameter and 30 m long, driven through soft soils (SPT N < 10) into a sandy gravel layer (SPT N > 50); shear wave velocities ranged from 140 to 470 m/sec through the soil profile. The period of the structure was estimated as 0.55 seconds, and the site period as 0.4 seconds. The MHA recorded at the site was 0.036 g, and 50 % spectral deamplification of the tank footing relative to the ground surface was recorded at periods less than 0.3 seconds (Figures 2.53a and b). Of particular interest is the strain gage data, which revealed axial strains in the piles two to three times the bending strains. This was partially due to the weak pile to footing connections, which Hamada and Ishida stated resulted in a hinged condition, thus limiting the bending forces
55
transferred from the structure into the piles. But the magnitude of the axial strains was also certainly related to the high center of mass of the structure, which would induce a rocking mode of deformation to the foundation, and alternating axial compressive and tensile stresses in the piles. In fact the predominant frequency of the axial strains near the pile head was 0.55 seconds, indicating these pile strains are directly related to the superstructure motion. The recorded bending strains were at a maximum near the pile head and decreased with depth, and generally correlated with the tank motions.
(a)
(b)
Figure 2.53 - a) Spherical Tank Structure Instrumentation Plan; b) Pile Cap to Free Field Transfer Function (after Hamada and Ishida, 1980) Ohta et al. (1980) studied the response of an 11 story composite frame apartment house supported by 1.3 to 1.5 m diameter cast-in-place concrete piles penetrating 22 m into an alluvial silt deposit. Shear wave velocities at the site ranged from 70 to 450 m/sec. The predominant period of the structure was reported as 0.45 seconds, and the site period as 0.71 seconds. Spectral deamplification on the order of 50 % was reported for periods
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less than 0.55 seconds for the seven earthquakes analyzed, which had a MHA of 0.06 g (Figures 2.54a and b).
(a)
(b)
Figure 2.54 - a) Eleven Story Apartment House Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Ohta et al., 1980) Abe et al. (1984) observed the response of a two story reinforced concrete rigid frame structure to 40 earthquakes between 1982 and 1983. The MHA recorded at the site was 0.075 g. The building was supported by 15 cast-in-place concrete piles 1.0 to 1.1 m diameter and 45 m deep installed through fill, sands, silts, clays (SPT N < 10) into a fine sand layer with an SPT N > 30. Shear wave velocities at the site ranged from 70 to 360 m/sec, with a site period estimated as 0.85 seconds. The first three modal periods of the structure were estimated by forced vibration tests to be 5.5, 8.0, and 9.5 Hz. Spectral deamplification on the order of 50 % was calculated at 5.1, 6.6, and 8.7 Hz for the suite of events analyzed (Figures 2.55a and b). The period shift from the first three modal periods estimated by forced vibration tests represents the period of the soil-pile-superstructure
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system, not period lengthening under these small levels of shaking. Strain gages fixed to the piles indicated that bending strains dominated at the pile head but decreased to equal axial strains at depth, which were constant over the length of the pile. In addition, the first and third vibration modes of the soil accelerations and the pile strain were correlated, indicating that the piles were moving in phase with the soil at these excitations.
(a)
(b)
Figure 2.55 - a) Two Story Reinforced Concrete Building Instrumentation Plan and Site Conditions; b) Pile Cap to Free Field Transfer Function (after Abe et al., 1984) Tsujino et al. (1987) described the response of a 58 m diameter above ground LNG storage tank supported on 546 steel pipe piles, of 60 cm diameter and 30 m length, to a series of earthquakes in 1984 - 85 that resulted in a MHA at the site of 0.02 g. The overall structural response and strain regime in the piles was found to be very sensitive to the height of liquid in the tank. At low liquid levels, the ground surface velocity spectra closely correlated to the spectra of the measured bending strains in the piles; at high liquid levels the bending strain spectra was amplified at the predominant site period (Fig 2.56). The measured axial strains in the piles also responded to the tank liquid height; at low
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liquid level the axial strains were small, and at high liquid levels they became relatively large (Fig 2.57). This clearly illustrates the relative effects of inertial interaction on the pile response. In addition pile group effects and spatial incoherence were apparent in the differential subgrade reaction computed at the edges and center of the pile group.
Figure 2.56 - LNG Storage Tank Pile Bending Stain and Ground Surface Velocity Spectra at Two Tank Liquid Heights (after Tsujino et al., 1987)
Figure 2.57 - LNG Storage Tank Pile Bending and Axial Stain Spectra at Two Tank Liquid Heights (after Tsujino et al., 1987) 2.2.2 Building Structures in California
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Housner (1957) published one of the first case histories observing soil-structure interaction with his analysis of the Hollywood Storage Company building performance during the 1952 Kern County earthquake.
The building was a 14 story reinforced
concrete structure, with a basement supported on 10 - 30 ft long piles driven into soft sandy clay. The building period was estimated as 1.2 seconds in the N-S direction, and 0.49 seconds in the E-W direction. Seismographs were stationed in the basement and the free-field, with MHAs of 0.06 g and 0.04 g recorded in the N-S and E-W directions. Response spectra computed from the accelograms revealed nearly identical basement and free-field spectra for the N-S direction, but 50 % deamplification of the basement motion relative to the free-field in the E-W component across the full frequency range. Crouse and Jennings (1975) analyzed the response of the same structure to the 1971 San Fernando earthquake, recomputed the building period as 1.05 and 0.5 seconds in the N-S and E-W directions, and reported the shear wave velocity in the upper 60 ft of the soil profile as approximately 800 ft/sec. MHAs were 0.15 g in the basement and 0.21 g in the free-field. Fourier amplitude spectra of the basement and free-field accelograms reveal up to 70 % deamplification of the basement motion relative to the free-field at periods less than approximately 0.3 seconds. They concurred with Housner’s conclusion that soilstructure interaction effects were present in the E-W response, but not evident in the N-S direction. Fenves and Serino (1992) studied the response of the same structure to the 1987 Whittier Narrows earthquake, but also revisited Housner’s work, asserting that their new analysis revealed no evidence of soil-structure interaction during the Kern County earthquake. They also re-analyzed the San Fernando earthquake records, and found only 20 – 25 % deamplification of the basement motion relative to the free-field, and at periods
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less than 0.3 and 0.5 seconds in the N-S and E-W directions, respectively. In the 1987 Whittier Narrows earthquake, Fenves and Serino computed an average reduction in acceleration at the base relative to the free-field of 46 %, which generally occurred at periods less than 0.3 seconds (Figure 2.58). Stewart (1997) analyzed the response of this structure to these three events and the 1994 Northridge earthquake, and found similar evidence of soil-structure interaction. It should be noted that the “free-field” station at this site is suspected to be contaminated by feedback interaction from adjacent structures, thus calling into question the overall accuracy of all of these results.
Figure 2.58 - Hollywood Storage Building Parking Lot/Basement Transfer Function during the 1987 Whittier Narrows Earthquake (after Fenves and Serino, 1992) The Imperial County Services Building was severely damaged in the 1979 magnitude 6.4 Imperial Valley earthquake, and eventually torn down. The original six
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story reinforced concrete structure was supported on 204 Raymond step-taper piles driven 14 m through soft to stiff sandy clay. Interestingly, a new structure was constructed on the old foundation, which was deemed to be undamaged. The predominant period of the structure was 0.61 and 1.75 seconds in the N-S and E-W directions respectively. As reported by Hadjian et al. (1990), the recorded pile cap motions exceeded the free-field motions, and spectral amplification of over 200 % was noted at periods less than 0.48 seconds (Figure 2.59). However, the strongly nonlinear and resonant response of the structure may have exerted a determining influence on the pile cap motion, in contrast to previously observed trends of pile cap deamplification relative to the free-field.
Figure 2.59 - Imperial County Services Building Ground Level to Free Field Transfer Function during the 1979 Imperial Valley Earthquake (after Hadjian et al., 1990)
Celebi (1993) investigated the response of adjacent instrumented structures during the 1987 Whittier Narrows earthquake. Building “A” was a 7 story rigid steel frame structure with a basement supported on concrete piles that varied in length from 25 - 35 ft; its first mode period was 1.53 seconds. Building “B” was a 7 story ductile moment resisting frame building with a basement resting on 30 ft deep caissons, with first mode periods of 1.2 and 1.31 seconds in the major and minor axes.
The site conditions
consisted of moderately dense to dense granular soils, with predominant site periods at
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0.55 and 0.83 seconds, respectively. In general, deamplification of basement motions relative to the free-field was noted for both buildings; Stewart (1997) presents a complete discussion of these cases. Kagawa et al. (1992) and Celebi and Safak (1992) studied the response of the 30 story Pacific Park Plaza building in Emeryville, California during the 1989 Loma Prieta earthquake. The building was founded on 828 14 in square precast concrete piles driven 100 ft through fill over Bay Mud. Predominant response modes of the structure at 2.5 and 1 second periods were identified from the strong motion recordings. Two free-field stations recorded peak accelerations of 0.22 and 0.26 g; at the ground floor of the structure, peak accelerations of 0.17 and 0.22 g were recorded. This lesser degree of deamplification of the structure relative to the free-field may be related to the stronger influence of structural inertial forces on the foundation, and the lesser effect of kinematic interaction, at this higher level of shaking. In his analysis, Stewart (1997) found some deamplification of ground floor motions relative to the free-field for frequencies < 3 Hz, and minor amplification from about 3 to 7 Hz. Using system identification techniques, he computed a flexible base damping ratio of 12 %, compared with an analytical value of 6 % that was based on a simple soil-structure interaction model that did not explicitly incorporate piles; Stewart concluded that the effect of the piles was to increase rocking stiffness and radiation damping relative to the surface foundation model, which failed to account for this difference. Stewart (1997) has recently published a comprehensive empirical assessment of soil-structure interaction effects using system identification techniques for 58 sites, mainly in California. The focus of this study was to quantify the effects of inertial and kinematic
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interaction on modal parameters of structures and foundation input ground motions. Thirty four of these sites consisted of pile-supported structures, and nearly all of these structures exhibited soil-structure interaction effects that manifested as period lengthening, increased damping, and spectral deamplification of the pile cap motion relative to the freefield. Flexible base period and damping factors derived from the system identification analyses were compared to a simplified soil-structure interaction model consisting of a circular flat disk bonded to a visco-elastic uniform halfspace (a shallow foundation model); in a number of cases the simplified models overpredicted period lengthening and underpredicted damping relative to the system identification results. These trends are indicative of the contributions to lateral and rocking stiffness and radiation damping made by the piles, suggesting that a more sophisticated model is appropriate in such cases.
2.2.3 Bridge Structures The Meloland Road Overpass was strongly shaken during the 1979 Imperial Valley earthquake, yet did not sustain visible damage.
Peak free-field horizontal
accelerations of 0.32 g were recorded during this M 6.4 earthquake. The structure was a two span concrete box girder type, supported by a single pier, in turn supported by 25 timber piles of 1 ft diameter and 50 ft length, driven into a medium stiff sandy clay with an average SPT N value of 14. A single row of seven 60 ft long piles supported each abutment. The response of the structure has been analyzed with system identification, finite element, and simplified methods by various researchers.
Werner et al. (1987)
reproduced Fourier amplitude spectra from the free-field and the pile cap; the motions are seen to be very similar with minor amplification between 0.3 and 0.6 second periods
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(Figure 2.60).
The system identification analyses identified the abutments and
embankments as dominating the transverse response of the bridge, with lesser contributions from the central pier, while the deck primarily affected the vertical response of the structure.
Figure 2.60 - Meloland Road Overpass Free Field and Base of Pier Fourier Amplitude Spectra during the 1979 Imperial Valley Earthquake (after Werner et al., 1987) A number of researchers have studied the response of the Ohba-Ohashi road bridge near Tokyo to a 1983 magnitude 6.0 earthquake that caused a MHA of 0.114 g at the site, and attempted to correlate their analytical models to the observed response, with varying degrees of success. The significance of this case is that the bridge and foundations were fairly well-instrumented, and the 1983 event represents the strongest shaking data for instrumented piles published in the literature. The Ohba-Ohashi bridge is 485 m long and is supported by 11 piers (Figure 2.61a). Published reports have concentrated on the performance of Pier 6, adjacent to the river, which is supported by 64 steel pipe piles of diameter 600 mm and length 22 m; half are battered. The soil conditions at Pier 6 consist of 22 m of extremely soft alluvial strata of humus and silt, with an SPT N value of nearly zero and a shear wave velocity of 40 to 65 m/sec. The underlying strata consists of
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diluvial deposits of clay and fine sand, with an SPT N > 50 and a shear wave velocity of 400 m/sec (Figure 2.61b). According to Ohira et al. (1984), large bending strains were observed at the upper and lower ends of the piles, and axial strains decreased with depth over the length of the piles.
Differences in strain distributions between vertical and batter piles were also
observed, especially for the piles battered parallel to the bridge axis. The power spectra of pile strains and pier accelerations were well-correlated, indicating that the pile response was dominated by inertial interaction with the superstructure. The alternating pattern of compressive and tensile stresses in the piles also corresponded to the observed rocking motion of the superstructure. Transfer functions between the surface and the base and the footing and the base indicate spectral deamplification of 50 – 80 % of the pier motion relative to the free-field up to a period of 1.4 seconds, which corresponds to the site period (Figure 2.61c). Tazoh et al. (1987) reported that the sign of axial strains in an instrumented vertical pile was opposite that of the adjacent instrumented battered pile for all seismic observations at this site, and used finite element models to investigate this phenomenon. Their models also discerned the relative contributions of inertial interaction to strains developed near the pile head, and kinematic interaction to strains near the pile tip. Gazetas et al. (1993) evaluated the Ohba – Ohashi case history with a dynamic
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(a)
(b)
(c) Figure 2.61 - Ohba Ohashi Bridge: a) Bridge Elevation and Soil Conditions; b) Instrumentation Plan (after Ohira et al., 1984); c) Pile Cap to Free Field Transfer Function (after Gazetas et al., 1993)
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substructuring analysis method. A central conclusion of their study was that determination of the free-field motion in this very high plasticity clay (PI = 100 - 250) and in this narrow alluvial valley (base dipping at 15 degrees) was no trivial matter. Complex basin effects may have influenced the free-field motion to the extent that the footing to free-field transfer function may not provide a clear basis for comparison. The Dumbarton bridge was the only major San Francisco Bay area bridge instrumented with strong motion seismographs at the time of the 1989 Loma Prieta earthquake. Fenves et al. (1992) evaluated the response of the bridge and compared it to a detailed analytical model. The 43 span Dumbarton bridge is 7300 ft long, consisting of prestressed concrete spans on the approaches and steel box girders over the main channel. The piers of the approach structures are supported by groups of 28 to 43 20 in diameter prestressed concrete piles or 22 in diameter steel pipe piles, with a length of 60 to 80 ft. The foundations of the main channel structure consist of either 21 to 32 54 in diameter prestressed concrete piles, or 52 22 in diameter steel pipe piles; both pile types are driven 50 ft below the mudline and also have 50 ft of free length from the mudline to the pile cap. The soil profile consists of approximately 50 ft of soft bay clays (only 10 ft in the main channel), underlain by stiffer old bay clays. The accelerometer array was comprised of 25 strong motion instruments at five piers and at two free-field stations at either end of the bridge (one of which malfunctioned during the earthquake). MHAs of 0.126 g (north) and 0.128 g (west) were recorded at the west free-field station.
But the amplitude of
longitudinal motions recorded at the base of piers 13 to 21 exceeded the transverse accelerations by 300 %. The duration of strong motion at the piers was roughly double the free-field strong motion duration. The motions at the piers were found to be in phase
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with the bent caps, indicating the pile caps were driven by inertial interaction from the superstructure. Vertical motions at the base of pier 21 were observed to be different from those at the piers of the approach structure, as pier 21 was situated over a shallower deposit of soft Bay Mud. Rocking of the piers was not significant. Fourier amplitude spectra showed the piers having peak response at approximately 0.5 Hz, the fundamental mode of the bridge.
The spectral analysis concluded that the free-field record was
contaminated by feedback energy from the bridge. In addition, the distance of the freefield station to the instrumented piers (over 1 mile) and poorly known site conditions at the station call into question the applicability of using that record as a point of comparison to the instrumented piers.
This points out the difficulty in properly instrumenting,
interpreting data, and modeling long bridge structures that have inherent spatial incoherence effects. The response of an elevated section of the BART commuter train during the Loma Prieta earthquake was reported by Tseng et al. (1992). This aerial structure located immediately north of the Hayward BART station consisted of a three span simplysupported prestressed concrete twin box girder, supported on four single column piers. The foundation for each pier consisted of 16 to 18 one ft diameter reinforced concrete vertical and battered piles, driven 40 to 50 ft deep into the underlying sandy clay and silty sand. A total of 18 channels of data was obtained from instruments at pier bases, tops of piers, at the deck level, and at a free-field station. The free-field MHA was 0.16 g, with MHAs measured at the bases of two piers of 0.14 and 0.15 g. Transfer functions for the pier base to free-field are shown in Figures 2.62a and b, indicating some deamplification of
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motion at higher frequencies, but amplification of motion at the superstructure period, indicating the dominance of inertial effects in this case.
(a)
(b) Figure 2.62 - a) Hayward BART Section Pier Base to Free Field Longitudinal Transfer Function; b) Transverse Transfer Function (after Tseng et al., 1992) Fenves and Desroches (1994) studied the response of the Interstate 10/215 Northwest Connector in the 1992 magnitude 7.6 Landers and magnitude 6.6 Big Bear earthquakes.
The connector is a 16 span 2540 ft long curved concrete box girder
structure supported by single column bents. The bents were originally supported by groups of 28 to 48 precast prestressed concrete piles, 1 ft square. These piles ranged from 21 to 50 ft in length, and were driven into slightly compact to dense clean sands and silty
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sands apparently not susceptible to liquefaction. A seismic retrofit and instrumentation program completed 6 months before the earthquakes upgraded the structure, with each footing receiving up to 30 additional 16 in diameter steel pipe piles approximately 60 ft long.
MHAs recorded at the free-field stations were 0.09 and 0.10 g in the two
earthquakes, respectively; the structure suffered only minor damage. MHAs recorded at the bent 3 footing were similar to the free-field, at bent 8 50 - 150 % higher than the freefield, and at the abutments several-fold greater than the free-field motions. Acceleration time histories and Fourier amplitude spectra showed great similarity between the free-field and support motions. Perhaps the most interesting conclusion from this study was that the fundamental period of the bridge lengthened from 1.56 seconds in the Landers event to 1.75 seconds in the Big Bear event. This softening of response the authors partially attributed to increased foundation flexibility in the latter event, as structural damage was not observed, and column yield forces not exceeded. It is postulated that soil-pile gapping occurred during the first earthquake, providing a larger compliance for the second event three hours later. Makris et al. (1996) analyzed the response of the Painter Street Bridge in Rio Dell, California to the 1992 magnitude 7.0 Petrolia earthquake. Although a MHA of 0.48 g was experienced at the site, with 0.92 g in the superstructure, the bridge suffered only minor damage. The bridge was a two span prestressed concrete box girder structure supported by a two column bent. Each bent was supported by 20 concrete piles driven into moderately stiff clayey/silty/gravelly sands with SPT N values varying from 8 near the surface to 34 at 10 m depth. Fourier amplitude spectra of the recorded motion at the pile cap, in the free-field, and near the abutments indicate spectral deamplification of the pile
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cap relative to the free-field motion, and spectral amplification of the abutment relative to the free-field. This latter effect is consistent with observed topographic amplification of ground motions at ridges, crests, embankments, etc.
2.3 Summary of Observed Pile Performance and Potential Failure Modes From observed pile damage during earthquakes, the following failure modes can be discerned, where failure is defined as the loss of structural capacity of the pile and/or degradation of the pile-soil load carrying capacity. These include the following: •
Loss of lateral soil support may occur due to liquefaction of cohesionless soils or strain softening of cohesive soils near the pile head. When combined with large structural inertial loads, excessive displacements and bending strains concentrated near the pile head can develop and result in pile damage, frequently at the pile to cap connection. Structural distortions may also be a consequence. This failure mode was observed in the San Francisco, Alaska, Niigata, Loma Prieta, and Kobe earthquakes.
•
A common liquefaction hazard arises from the large loads and displacements that a laterally spreading soil deposit (including a non-liquefied “crust”) exerts on piles, which often results in pile damage. The failures at Moss Landing in 1906, the Showa Bridge in Niigata, the collapsed bridges in Alaska and Costa Rica, and numerous harborside structures in Kobe are all illustrative of this phenomenon.
•
When soils along the length of the pile soften due to liquefaction or strain softening, the pile may experience a loss of bearing capacity. When combined with a rocking mode induced by superstructure inertia forces, the piles frequently undergo settlement, punching failure, and/or tensile pull-out failure.
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Cases where this mode was
particularly apparent were at the Anchorage City Dock and at a number of the observed failures in Mexico City. •
Piles may be subject to damaging bending strains at interfaces between soil layers of strong impedance contrast. This contrast may be provided by soft and stiff soil layers, or by soil layers that undergo liquefaction or strain softening under earthquake loading.
This is best evidenced by the foundations that have been excavated
subsequent to the Niigata earthquake. •
Inadequate (or nonexistent) structural detailing of pile to cap connections is a seemingly elementary design deficiency, but it resulted in pile head shear failures during the San Fernando, Loma Prieta, and Kobe earthquakes.
•
Batter piles are designed to accommodate large lateral loads, but they often attract forces that the pile heads and/or pile cap cannot sustain. Considerable damage at the Port of Oakland during the Loma Prieta earthquake provides evidence of this failure mechanism. From the instrumented cases, it can be seen that SSPSI often results in spectral
deamplification of pile cap motions relative to free-field motions. This deamplification was generally seen to occur at periods less than the period of the composite soil-pilestructure system, and varies greatly in amplitude. This phenomenon was observed for a number of case histories of building structures in Japan subjected to low intensity shaking, and several case histories (though not all) of buildings and bridge structures in the U.S. subjected to moderate to high levels of ground shaking. At low levels of shaking, kinematic interaction generally dominates the system response; period lengthening and increased radiation damping of the system are
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responsible for dissipating energy and deamplifying motions up to the resonant period. At higher levels of shaking, soil modulus degradation and soil-pile gapping can inhibit radiation damping, and structural inertial forces predominate, lessening the overall effects of spectral deamplification. When system components yield, the system period further lengthens and radiation damping may be effectively suppressed; such period lengthening may be towards or away from resonant response. The fact that SPSSI effects do not operate on a strict continuum further reinforces the notion that a fully coupled analysis technique is desirable to properly capture the range of system response from linear to nonlinear behavior. Analytical methods for SSPSI will be examined in the following chapter, with a review of building code provisions and selected design/analysis case histories relating to the seismic response of pile foundations.
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CHAPTER 3
SSPSI ANALYTICAL METHODS:
THEORY, CODE, AND PRACTICE
3.1 Analytical Methods The development of analytical methods for SSPSI has principally been driven by the demands of two sectors, offshore oil production activities, and to a lesser extent, the nuclear power industry. For offshore applications, where cyclic wave loading applies lateral loads to pile-supported marine structures, a limited series of field and model tests has established the empirically-based and widely accepted “p-y” method of laterally loaded pile analysis. This static loading analysis method has been modified and extended to cyclic loading conditions, and is also routinely applied to dynamic or earthquake loading cases. At the same time, dynamic soil-pile analysis methods have been developed for the idealization of piles embedded in a visco-elastic medium; these techniques have also found their way into practice. They are more theoretically grounded than the p-y method, and along with the finite element method, are an outgrowth of the considerable effort in the 1960’s and 1970’s to study the soil-structure interaction problem of partially embedded nuclear power plants. However, these methods generally do not allow for the adequate characterization of localized yielding at the soil-pile interface, and are therefore bettersuited to relatively low levels of seismic loading. In addition to these classes of analysis, four levels of progressively “complete” SSPSI analyses can be described. The basic level consists of a single pile kinematic seismic response analysis, normally incorporating nonlinear response and performed as a
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pile integrity evaluation. A pseudo-static method for pile integrity evaluation consists of transforming the horizontal profile of soil displacement (derived from a free-field site response analysis) to a curvature profile, and comparing peak values to allowable pile curvatures (see Figure 3.1). This method assumes piles perfectly follow the soil, and that no inertial interaction takes place. Alternatively, a displacement time history may be applied to nodal points along the pile in a dynamic pile integrity analysis. In a second level of analysis, pile head stiffness or impedance functions may be condensed from linear or nonlinear soil-pile analyses and assembled into a pile group stiffness matrix for use in a global response analysis (Figure 3.2). Secant stiffness values at design level deformations are normally proscribed from nonlinear soil-pile response analyses (Figure 3.3). Third, both inertial and kinematic interaction may be evaluated from a substructuring type analysis to determine pile head impedance and foundation level input motions (Figure 3.4). Finally, a fully coupled SSPSI analysis may be carried out to ascertain the complete system response.
Figure 3.1 - Pile Curvature Profile Derived from Site Response Analysis (after Margasson and Holloway, 1977)
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Figure 3.2 - Flexible Pile Stiffness Matrix (after Kriger and Wright, 1980)
Figure 3.3 - Selection of Secant Stiffness Value at Design Level Displacement from Nonlinear Soil-Pile Force-Displacement Curve (after Kriger and Wright, 1980)
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Figure 3.4 - Substructuring Concept: a) Definition of Problem; b) Decomposition into Inertial and Kinematic Interaction Problems; c) Two-step Analysis of Inertial Interaction (after Gazetas, 1984)
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It is instructive to recognize that each class of analysis may be applied to multiple levels of analysis. For example, a beam-on-Winkler-foundation analysis may be conducted as a pile integrity evaluation or to compute pile head stiffness terms. An elastic continuum analysis can be utilized to determine pile head impedance or applied in a substructuring fashion. Finite element methods have been employed to develop other classes of analysis as well as to perform complete SSPSI analyses. Static, cyclic, and dynamic loading are all considered in the SSPSI problem. Figure 3.5 depicts idealized soil-pile load-displacement diagrams for each of these various modes of loading.
Simplified methods for determining static pile head stiffness are
routinely used for dynamic response analyses, as it has been determined that pile head static stiffness is roughly equivalent to dynamic stiffness in the seismic frequency range of interest. Several caveats must be made for this simplifying assumption: 1) unlike stiffness, damping is frequency dependent over the range of interest, and it is therefore common practice to select impedance function values at the site and/or structural resonant frequencies; 2) static stiffness terms should be degraded to account for the effects of cyclic loading; 3) dynamic axial stiffness terms are not as well approximated by static stiffness as for lateral response; and 4) dynamic pile group efficiencies and load distribution are significantly different from static values. It is important to recognize that both lateral and axial stiffness terms are vital components of pile group impedance functions, as structural inertial response may induce a foundation rocking mode and mobilize axial pile resistance. Finally, pile group effects must be accounted for in the SSPSI analyses, and are more fully described in section 3.1.5. They may be implicit in a substructuring or complete analysis,
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but have to be separately accounted for with interaction factors when assembling a pile group impedance matrix from individual pile terms.
Figure 3.5 - Soil-Pile Load Displacement Diagrams for Various Modes of Loading (after Mosikeeran, 1990) Distinctions are commonly made between fixed head and free head (“pinned” connection) piles, and “rigid” and “flexible” pile behavior (see Figure 3.6) based on relative soil-pile stiffness. Flexible pile behavior is an underlying assumption of the beamon-Winkler-foundation analysis and is often intrinsic to elastic continuum analyses as a plane strain assumption. Rigid pile behavior requires that the cross-coupling stiffness terms associated with the additional modes of shaft resistance be accounted for in the analysis method (Figure 3.7). Various researchers have proposed criteria for rigid and flexible behavior, and they are summarized in Table 3-1.
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Figure 3.6 - Rigid Versus Flexible Pile Behavior (after Kulhawy and Chen, 1995)
Figure 3.7 - Rigid Pile Lateral Loading Resistance Components (after Kulhawy and Chen, 1995)
Table 3-1 Criteria for Pile Rigidity (after Kulhawy and Chen, 1995) Source
Criterion for Criterion for Note Rigid Behavior Flexible Behavior Broms (1964a) a βrD < 1.5 βrD > 1.5 Poulos & Davis (1980) Kr > 10-2 Kr < 10-5 b Bierschwale et al. (1981) D/B < 6 D/B > 6 c Dobry et al. (1982) SH < 5 SH > 5 d 0.36 0.36 Davies & Budhu (1986) D < 1.5 B K D > 1.5 B K e Budhu & Davies (1987) D < 1.3 B K0.222 D > 1.3 B K0.222 f 0.5 2/7 Carter & Kulhawy (1988) D/B < 0.05 (Ep/G*) D/B > (Ep/G*) g Poulos & Hull (1989) D < Dp/3 D > Dp h Note: B = pile diameter, D = pile depth, Ep = pile elastic modulus, Ip = pile moment of inertia, Es = soil elastic modulus, νs = soil Poisson’s ratio, Gs = soil shear modulus a - βr = (khB/4EpIp)0.25; kh = coefficient of subgrade reaction b - Kr = (EpIp/EsD4) = flexibility factor c - in some cases, may be rigid for D/B < 10 d - SH = (D/B)/(Ep/Es)0.25 = flexibility factor e - K = (Ep/Es) = stiffness ratio; for constant soil modulus with depth f - K = (Ep/mB); m is Es rate of increase; for linear variation of soil modulus with depth g - G* = Gs(1+3νs/4) = modified soil shear modulus h - Dp = 4.44(EpIp/Es)0.25 = critical pile depth
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The following sections will present a brief overview of four types of SSPSI analyses; these generally fall into the discrete and continuum classes of models. For a more complete review refer to Novak (1991), Gohl (1993), Pender (1993), or Gazetas and Mylonakis (1998).
3.1.1 Beam-on-Elastic Foundation Hetenyi (1946) originally presented beam-on-elastic-foundation solutions (also known as the subgrade reaction method) in the form of the governing fourth-order differential equation: 4
EI d y4 = p dx
(3.1)
with p = -Esy and where E and I are the pile modulus of elasticity and moment of inertia, y is the pile deflection, x is the depth below the soil surface, Es is the modulus of subgrade reaction, and p is the reaction of soil on the pile. As is the case with the elastic continuum method, analytical solutions are not available for arbitrary distributions of soil or pile stiffness. This method has mainly been applied to static lateral pile loading problems, and is therefore used for the determination of pile head stiffness terms in SSPSI analyses. Matlock and Reese (1960) presented a generalized iterative solution method for rigid and flexible laterally loaded piles embedded in soils with two forms of varying modulus with depth. Davisson and Gill (1963) investigated the case of a laterally loaded pile embedded in a layered soil system with a constant (but different) modulus of subgrade reaction in each layer. They concluded that the near surface modulus was the controlling factor for the pile response, and that soil investigations and characterization should be
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focused in this zone. In classic companion papers, Broms (1964a, b) described a method for analyzing lateral pile response in cohesive and cohesionless soils. His method for computing ground surface deflections of rigid and flexible fixed and free head piles was based on a modulus of subgrade reaction using values suggested by Terzaghi (1955). For undrained loading, he designated that a constant subgrade modulus be used with a value of 9 Su for the ultimate lateral soil resistance. For drained loading cases, a subgrade modulus linearly increasing with depth was specified and a Rankine earth pressure-based method was used for computing an ultimate resistance assumed equal to 3KpDpσ’v. Jamilokowski and Garassino (1977) provided a state-of-the-art discussion on soil modulus and ultimate soil resistance for laterally loaded piles. Randolph and Houlsby (1984) used classical plasticity theory to derive lower and upper bound values of the limiting pressure on an undrained laterally loaded pile that ranged from approximately 9 to 12 Su as a function of pile roughness. Hansbro (1995) revisited Brom’s computation of drained ultimate lateral resistance, and based on results of centrifuge tests conducted by Barton (1982) suggested that a drained ultimate lateral resistance of Kp2Dpσ’v is more appropriate for cohesionless soils. Kulhawy and Chen (1995) applied Brom’s concepts to drilled shafts, recognizing the components of resistance to lateral loading unique to drilled shafts, and noted the importance of conducting appropriate laboratory tests for laterally loaded pile and drilled shaft analysis.
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3.1.2 Beam-on-Winkler Foundation By accepting Winkler’s foundation assumption (1876) that each layer of soil responds independently to adjacent layers, a beam and discrete spring system may be adopted to model pile lateral loading. Although this assumption ignores the shear transfer between layers of soil, it has proven to be a popular and effective method for static and dynamic lateral pile response analyses. In this method, the soil-pile contact is discretized to a number of points where combinations of springs and dashpots represent the soil-pile stiffness and damping at each particular layer. These soil-pile springs may be linear elastic or nonlinear; p-y curves typically used to model nonlinear soil-pile stiffness have been empirically derived from field tests, and have the advantage of implicitly including pile installation effects on the surrounding soil, unlike other methods.
In advanced
applications, capabilities for soil-pile gapping, cyclic degradation, and rate dependency are also provided. A singular disadvantage of a beam-on-Winkler-foundation model is the two-dimensional simplification of the soil-pile contact, which ignores the radial and threedimensional components of interaction. For dynamic loadings, “free-field” soil acceleration time histories are usually computed in a separate site response analysis, double integrated to displacement time histories, and then externally applied to the soil-pile springs. The multi-step uncoupled approach has the disadvantage of potentially introducing numerical errors in the integration step, and artificially separates the overall soil-pile system response. Recently, investigators have begun to develop fully-coupled analyses wherein both soil and soil-pilesuperstructure response can be simultaneously evaluated (Lok, 1999).
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McClelland and Focht (1958) can be said to be the originators of the p-y method of laterally loaded pile analysis. They proposed a procedure for correlating triaxial stressstrain data to a pile load-deflection curve at discrete depths, and estimating the modulus of subgrade reaction at each layer. Of particular interest is the ensuing discussion provided by Peck, Matlock, and others to their paper, wherein Reese first presented his concept of a near surface wedge (see Figure 3.8) and deep plasticity flow failure models, with an ultimate undrained resistance of 12 Su. Penzien et al. (1964) were some of the first researchers to present a method for seismic pile response analysis, and focused their efforts on the problem of bridge structures supported on long piles driven through soft clays. They constructed a multidegree of freedom discrete parameter system for modeling the soil medium response initiated by seismic base excitation. This response then served as the input for the response analysis of the discrete parameter structural system. Bilinear springs afforded nonlinear hysteretic soil response, with parallel and series dashpots provided for soil damping and creep, respectively, and lumped masses to contribute soil inertial effects. The conclusions of their study regarding site response, pile curvature demands, and superstructure ductility, all remain valid to this day. In a series of reports to Shell Development Company, Matlock and his co-workers conducted static and cyclic field and laboratory tests of laterally loaded piles in soft clay (partially described in Chapter 4). He described the p-y concept as the relationship that relates the soil resistance “p” arising from the nonuniform stress field surrounding the pile mobilized in response to a lateral soil displacement “y” (see Figure 3.9). For a single pile, a family of p-y curves can be described (Figure 3.10), normally stiffer with depth.
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Figure 3.8 - Lateral Loading Near Surface Passive Wedge Geometry and Soil-Pile Forces (after Reese, 1958)
Figure 3.9 - Definition of P-Y Concept with a) Pile at Rest; b) Laterally Loaded Pile Mobilizing Soil Resistance (after Thompson, 1977)
Figure 3.10 - Typical Family of P-Y Curves, Progressively Stiffer with Depth (after Meyer and Reese, 1979)
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Matlock (1970) proposed p-y curves for static and cyclic loading of piles in soft clay which are shown in Figure 3.11a and b, with 0.33
p = 0.5 p u y yc
(3.2)
where: p = lateral soil resistance pu = ultimate soil resistance = Np c D Np = ultimate lateral soil resistance coefficient c = soil undrained shear strength D = pile diameter y = pile deflection yc = critical pile deflection = 2.5 εc D εc = strain at one-half maximum deviator stress in a UU triaxial compression test x = depth below ground surface xcr = critical depth where soil wedge failure transforms to flow failure
(a)
(b)
Figure 3.11 - Characteristic Shape of P-Y Curve in Soft Clay for a) Static Loading; b) Cyclic Loading (after Matlock, 1970) This method is codified in the API Recommended Practice (API, 1993) and is the established criterion for laterally loaded pile analysis in soft clays in the nearly ubiquitous computer program COM624P (Reese, 1984). Matlock also turned his attention to pile dynamics, and issued the beam-on-dynamic-Winkler-foundation analysis program SPASM
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8 (Matlock and Foo, 1978). In this approach, a discrete element linear elastic pile was linked to a fully nonlinear, hysteretic, degrading soil support model with gapping capability (Figure 3.12). The soil gapping model is shown schematically in Figure 3.13. The pile could be extended above the mudline where element stiffnesses and restraints would be introduced to simulate the characteristics of the superstructure. Separately computed lateral ground displacements are used as the input excitation at the ends of the soil support nodes. Note that nonlinear supports are specified near the pile head, and elastic supports are presented at depth, anticipating elastic response in this zone, and providing computational efficiency.
The solution method was a time domain finite difference
procedure that iterated on soil-pile tangent stiffness to ensure compatibility with computed deflections. A parallel array of elasto-plastic subelements provided for the nonlinear spring stiffness (see Figure 3.14), and linear dashpots attached directly to the pile effected radiation damping. Soil degradation was provided as a penalty method, incurred as an element experienced a full reversal in the direction of slip, with the ultimate resistance asymptotically approaching a user specified lower bound. In Matlock et al. (1981), a method for simulating soil-pile response in liquefiable cohesionless soils during earthquake shaking was presented. In this approach, the effective stress site response code DESRA II (Lee et al., 1978) was used as input to the SPASM 8 model, with degradation of the p-y backbone curve carried out in proportion to the excess pore pressure generation calculated by DESRA II. Matlock and Foo (1980) also described the computer code DRIVE 7, a model for axial loading of piles with similar features as
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Figure 3.12 - SPASM 8 a) Soil-PileSuperstructure Model; b) Variation in Load-Deflection Behavior versus Depth (after Matlock and Foo, 1978)
Figure 3.13 - SPASM 8 a) Soil-Pile Gapping Model; b) Force-Displacement Behavior (after Matlock and Foo, 1978)
Figure 3.14 - SPASM 8 Sub-element Nonlinear Spring Model (after Matlock and Foo, 1978) 89
SPASM 8, and suitable for static, cyclic, or dynamic loading, including pile driving simulation. The API recommended method for constructing p-y curves in sand was the result of work by Reese et al. (1974) from the results of static and cyclic lateral load tests. The curve consisted of two straight line segments joined by a parabolic segment (Figure 3.15). The ultimate soil resistance was determined from the lesser of two expressions reflecting shallow wedge failure and deep flow failure geometries, and modified for pile diameter, depth, and loading regime. Specific charts for determining the modulus of subgrade reaction were provided.
Reese et al. (1975) conducted lateral pile load tests in an
overconsolidated strain-softening stiff clay deposit and presented the characteristic p-y
Figure 3.15 - Characteristic Shape of P-Y Curve in Sand (after Reese et al., 1974)
Figure 3.16 - Characteristic Shape of P-Y Curve in Stiff Clay for a) Static Loading; b) Cyclic Loading (after Reese et al., 1975)
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curves shown in Figures 3.16a and b for static and cyclic loading; these too comprise currently recommended API design curves. Guidelines for computing the ultimate soil resistance pc, the static and cyclic stiffness parameters ks and kc, and the empirical A and B factors were given. It is important to recognize that water was impounded at the surface of this test site, and may have contributed to excess degradation of soil resistance due to near surface scour in the soil-pile gap. Perhaps Reese’s most influential contribution has been the introduction of the computer programs COM624P (Reese, 1984) and LPILE (Reese and Wang, 1989), first presented as COM622 in Reese (1977). These analytical tools provide highly efficient platforms for p-y analysis of static and cyclic laterally loaded piles in layered soils. Reese has also released codes describing axial pile response, and pile group behavior. Stevens and Audibert (1979) recast existing p-y curve formulations with a dependency on pile diameter. They noted that original p-y curve criteria were based on field load tests of relatively small diameter piles, and by reviewing a broader database of load test data they were able to derive an expression for pile deflection proportional to the square root of pile diameter. In addition, they proposed a modified profile of lateral soil resistance with an ultimate value of 11 SuB, as shown in Figure 3.17. O’Neill and Murchison (1983) carried out a systematic evaluation of p-y relationships in sands and compared the predictive accuracy of four methods against a set of pile load test data. The methods tested included the segmented curve of Reese et al. (1974), a modification suggested by Bogard and Matlock (1980), a bilinear representation proposed by Scott (1979), and a continuous hyperbolic tangent curve described by Parker
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and Reese (1970). The hyperbolic curve proved to be the most accurate for both static and cyclic loading, and relatively easy to implement. The form of the p-y curve is given by
p = η A pu tanh kz A y pu
(3.3)
where η = 1 for circular, prismatic piles, A is a factor for static or cyclic loading, k is the initial modulus of subgrade reaction, z is depth, and pu is determined from equations for wedge type and deep flow failure mechanisms. Ironically, Bogard and Matlock’s (1980) simplified method has found greater acceptance than this more accurate approach. In a similar vein, O’Neill and Gazioglu (1984) investigated p-y relationships in cohesive soils, and attempted to develop a unified method for both soft and stiff clay, but this method has not been widely adopted. Kagawa and Kraft (1980) developed a nonlinear dynamic Winkler model using the equivalent linear method, with input excitation applied as lateral ground displacements at the end of the near-field soil elements. The pile was modeled by a continuous beam with near field soil elements comprised of parallel springs and dashpots, and with superstructure elements that generated the inertial component of response. Soil spring stiffness values were determined from the hysteretic backbone curve as shown in Figure 3.18, and the radiation damping dashpot coefficient was computed as
c = 2 ρ S B (V P + V S )
(3.4)
In Kagawa and Kraft (1981), the nonlinear soil model was formulated as an effective stress model, and cyclic degradation of soil resistance was governed by pore pressure generation.
This model has been incorporated in the computer code NONSPS
(McClelland Engineers, 1983) which has achieved only fair performance in recent model
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simulation studies conducted at U.C. Davis (Chacko, 1993). These researchers have also investigated axial pile response, and presented a study of theoretical t-z load-deflection curves in Kraft et al. (1981).
Figure 3.17 - Lateral Bearing Capacity Factor Np with Respect to Normalized Depth (after Stevens and Audibert, 1979)
Figure 3.18 - Hysteretic Backbone Curve (after Kagawa and Kraft, 1981)
Bea has introduced several analytical methods dealing with SSPSI, particularly those relating to offshore structures. Bea and Audibert (1979) studied loading rate and load cycling effects on axial and lateral dynamic pile response.
In Bea (1990), an
advanced model for axial pile dynamic loading was presented, with guidelines for formulating t-z (soil-pile shaft load-deflection) and Q-z (soil-pile base load-deflection) curves, incorporating strain rate effects and cyclic degradation. Through a series of analytical models including INTRA (Arnold et al., 1977), SPSS (PMB, 1979), PSAS (Bea et al., 1984), and finally PAR (Bea, 1988), a three-dimensional, time domain, nonlinear, discrete element method for computing single pile dynamic response was developed. PAR is a hybrid model that performs site response analysis in the far field soil finite elements,
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and models soil-pile interaction with near field springs and dashpots (see Figure 3.19). Provisions for progressive gapping, cyclic degradation, and radiation damping are included, but pile group effects must be accounted for externally.
Figure 3.19 - PAR Analytical Model (after Bea et al., 1984)
Nogami also developed hybrid near field/far field soil-pile interaction models for dynamic loading, as shown schematically in Figure 3.20. He formulated solutions for single pile and pile group axial and lateral response in both the time and frequency domains, incorporating nonlinear soil-pile response, degradation, gapping, slip, radiation damping, and loading rate effects (Nogami et al., 1991; Nogami et al., 1992). In Nogami (1985) and Nogami and Konagi (1988), the transfer matrix approach was described that was used to solve the equations of motion for a pile subject to soil-pile interaction forces, functions of the near field and far field soil element properties. Nogami (1991) makes a detailed comparison of the features and performance of Matlock’s, Novak’s, and Nogami’s Winkler foundation models for lateral pile response. Nogami’s far field
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Figure 3.20 - Nogami’s Beam-onWinkler Foundation Soil-Pile Interaction Model (after Nogami et al., 1988)
Figure 3.21 - Nogami’s Far Field Soil-Pile Models for: a) Vertical Excitation; b) Horizontal Excitation (after Nogami et al., 1988)
(a)
(b) Figure 3.22 - Nogami’s Inner Field and Near Field Soil-Pile Models for: a) Vertical Excitation; b) Horizontal Excitation (after Otani et al., 1991)
95
element consisted of three Kelvin-Voigt parallel spring-dashpot pairs designed to simulate an infinite elastic plane strain medium, and a shear element in series to simulate interaction of adjacent soil layers (Figure 3.21). The near field element was a nonlinear spring, with mass to simulate near field inertial effects (Figure 3.22). Gapping was provided by an elasto-plastic interface element. Nogami’s models can be used to compute pile head impedance functions, or input excitations can be directly applied to the discrete end nodes of the model. As will be described in section 3.3.9, WSDOT favorably evaluated a Nogami soil-pile interaction model in a SSPSI study they conducted; this represents the sole example in the literature of Nogami’s model being coded for computer applications. Makris and Badoni (1995a) introduced a so-called macroscopic model based on the Bouc-Wen model of visco-plasticity, which used distributed nonlinear springs to approximate the soil-pile reaction. Limits of soil resistance were based on the work of Broms (1964), Randolph and Houlsby (1984), and Matlock (1970). Radiation damping was provided by a frequency dependent viscous dashpot that attenuated at large pile deflections.
The model accommodated pile head loading, and required that two
parameters be fit by experimental data. Validation against five case studies was provided. Makris (1994) has also presented an analytical solution for pile kinematic response due to the passage of Rayleigh waves, applicable to near field earthquake response. Pender and Pranjoto (1996) updated a nonlinear soil-pile interaction model originally proposed by Carter (1984) to include the effects of gapping. Compression-only springs were attached to both sides of the pile, preloaded to reflect the effects of pile installation, and provided with the ability to detach and form a gap when the spring force reached zero. A hyperbolic form of the nonlinear spring stiffness was adopted, defined by
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initial stiffness and ultimate resistance parameters. The model very well demonstrated progressive gapping with depth and with the number of load cycles, and the consequent reduction in pile head lateral stiffness. The authors acknowledged the need to extend the model to dynamic loading.
3.1.3 Elastic Continuum The elastic continuum analytical method is based on Mindlin’s (1936) closed form solution for the application of point loads to a semi-infinite mass. The accuracy of these solutions is directly related to the evaluation of the Young’s modulus and the other elastic parameters of the soil. This approach is limited in the sense that nonlinear soil-pile behavior is difficult to incorporate (the equivalent linear method is available), and it is more appropriately applied for small strain, steady state vibration problems. In addition, layered soil profiles cannot be accommodated, and only solutions for constant, linearly increasing, and parabolically increasing soil modulus with depth have been derived. True continuum models do have the advantage of intrinsically modeling the effects of radiation damping, whereas discrete models must artificially simulate this energy dissipation mode. Tajimi (1966) was the first to describe a dynamic soil-pile interaction solution based on elastic continuum theory. He used a linear Kelvin-Voigt visco-elastic stratum to model the soil and ignored the vertical components of response. His basic method has been modified and extended by Tazoh et al. (1988) and other researchers to include superstructure inertial effects. Poulos has been a major progenitor of elastic solutions for soil and rock mechanics, and has worked extensively on all aspects of pile foundation response to axial
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and lateral loads. In Poulos (1971a, b) he first published elastic continuum solutions for laterally loaded single piles and groups under static loading. Poulos and Davis (1980) presented a comprehensive set of analysis and design methods for pile foundations based on elastic continuum theory. Poulos (1982) described a procedure for degradation of soilpile resistance under cyclic lateral loading and compared it to several case studies. In a different approach, Swane and Poulos (1984) proposed a subgrade reaction method that provided for progressive soil-pile gapping with bilinear elasto-plastic springs and friction slider blocks. In the 29th Rankine Lecture, Poulos (1989) presented a compendium of his work on axial pile loading. In 1974, Novak published the first of many papers dealing with pile dynamics, where he adopted a plane strain, complex transmitting boundary adjacent to the pile for solution of pile stiffness and damping coefficients. The plane strain condition is equivalent to incorporating the Winkler assumption into the continuum model, and formed the basis for his future work. Axial response of floating piles was considered in Novak (1977), and the particular sensitivity of response to the pile tip condition, i.e. end-bearing or floating, was noted. Novak and Aboul-Ella (1978) improved this model by considering layered soil media, imperfect fixity of the pile tip, and material damping of the soil. Nogami and Novak (1976) and Novak and Nogami (1977) formulated more rigorous solutions for axial and lateral pile response, respectively, in a linear visco-elastic medium in a similar fashion as Tajimi (1966). To account for the development of soil nonlinearity adjacent to the pile, Novak and Sheta (1980) proposed a cylindrical boundary zone around the pile that was characterized by decreased modulus and increased damping relative to the freefield, and with no mass to prevent wave reflections from the fictitious interface between
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the cylindrical zone and the outer region. Novak and his co-workers have issued the computer code DYNA4 (Novak, et al. 1993), which implemented their studies of single and pile group lateral and axial dynamic response. Gazetas and Dobry (1984) derived a method for substructuring the SSPSI problem into kinematic and inertial components from a parametric finite element study based on the work of Blaney et al. (1976). For the inertial interaction component, they described the pile head dynamic stiffness by a complex valued impedance function of the form
K + iω C = po y d
(3.5)
where K is the soil-pile stiffness, ω is the excitation frequency, C is the coefficient of equivalent viscous damping, po is the amplitude of the forcing function, and yd is the complex amplitude of the horizontal motion. Constant, linearly varying, and parabolically varying soil modulus with depth cases were studied for single piles subjected to vertically propagating shear waves. Kinematic interaction factors were graphically presented as functions of D, B, Ep, Es, ω and site frequency f; these curves are multiplied against freefield response spectra to yield design pile head response spectra.
The authors also
considered the problem of dynamic pile response in layered soil profiles and described a method whereby a static pile head stiffness was “corrected” to account for profiling, and the overall damping value was obtained from a weighted average of dashpot coefficients developed along the length of the pile. They also included a discussion of radiation damping models and proposed a simplified plane strain version as a function of B, ρs, Vs, and ω (see Figure 3.23). This model for radiation damping emanating from a laterally oscillating pile consisted of zones of waves traveling at the soil shear wave velocity Vs, and at Lysmer’s analog velocity VLa, where 99
V La =
3.4 VS π (1 − ν )
(3.6)
The authors made the important note that at frequencies less than the natural frequency of the system, there is no radiation damping. Gazetas (1991) made a complete survey of foundation vibration problems and included detailed design charts and equations for direct computation of pile head lateral and axial stiffness and damping coefficients in the three above mentioned soil profiles. These expressions were a function of D, B, ρp, Ep, ρs, Es, Vs, ω and soil damping β.
Figure 3.23 - One- and Two-Dimensional Radiation Damping Models (after Gazetas and Dobry, 1984) Davies and Budhu (1986) and Budhu and Davies (1987, 1988) used the boundary element method to develop convenient design equations for the analysis of static laterally loaded fixed and free headed piles.
They utilized an elastic continuum model that
accounted for nonlinear soil response with yield influence factors in profiles of both
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constant and linearly varying soil modulus with depth. Application of this method to cyclic or dynamic loadings was not made by these authors.
3.1.4 Finite Element Methods The finite element method potentially provides the most powerful means for conducting SSPSI analyses, but is has not yet been fully realized as a practical tool. The advantages of a finite element approach include the capability of performing the SSPSI analysis of pile groups in a fully-coupled manner, without resorting to independent calculations of site or superstructure response, or application of pile group interaction factors. It is of course possible to model any arbitrary soil profile, and to study 3-D effects.
Challenges to successful implementation of this technique lie in providing
appropriate soil constitutive models that can model small to very large strain behavior, rate dependency, degradation of resistance, and still prove practical for use. Special features to account for pile installation effects and soil-pile gapping should also be implemented. Yegian and Wright (1973) implemented a finite element analysis with a radial soilpile interface element that described the nonlinear lateral pile response of single piles and pairs of piles to static loading. Based on work by Kausel et al. (1975), Blaney et al. (1976) used a finite element formulation with a consistent boundary matrix to represent the free-field, subjected to both pile head and seismic base excitations, and derived dynamic pile stiffness coefficients as a function of dimensionless frequency. Desai and Appel (1976) presented a three dimensional finite element solution with interface elements for the laterally loaded pile problem. Emery and Nair (1977) studied an axisymmetric finite element model that incorporated non-symmeteric free-field acceleration boundary
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excitations from wave propagation analyses. Randolph and Wroth (1978) modeled the linear elastic deformation of axially-loaded piles. Kuhlemeyer (1979a) offered efficient static and dynamic solutions for lateral soil-pile elastic response; Kuhlemeyer (1979b) used a finite element model of dynamic axially loaded piles to verify Novak’s (1977) solution and a simplified method presented by the author. Angelides and Roesset (1981) extended Blaney’s work with an equivalent linearization scheme to model nonlinear soil-pile response. Force-deflection relations were developed and compared favorably with p-y curves suggested by Stevens and Audibert (1979). Randolph (1981) derived simplified expressions for the response of single piles and groups from a finite element parametric study. Dobry et al. (1982) made a parametric study of the dynamic response of head loaded single piles in uniform soil using Blaney’s method and proposed revised pile stiffness and damping coefficients as a function of Es and Ep. Kay et al. (1983) promoted a site-specific design methodology for laterally loaded piles consisting of pressuremeter test data as input to an axisymmetric finite element program. Lewis and Gonzalez (1985) compared field test results of drilled piers to a 3-D finite element study that included nonlinear soil response and soil-pile gapping. Trochianis et al. (1988) investigated nonlinear monotonic and cyclic soil-pile response in both lateral and axial modes with a 3-D finite element model of single and pairs of piles, incorporating slippage and gapping at the soil-pile interface. They deduced a simplified model accommodating pile head loading only. Koojiman (1989) described a quasi-3-D finite element model that substructured the soil-pile mesh into independent layers with a Winkler type assumption. Brown et al. (1989) obtained p-y curves from 3-D finite element simulations that showed only fair comparison to field observations. Wong
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et al. (1989) modeled soil-drilled shaft interaction with a specially developed 3-D thin layer interface element. Bhowmik and Long (1991) devised 2-D and 3-D finite element models that used a bounding surface plasticity soil model and provided for soil-pile gapping. Brown and Shie (1991) used a 3-D finite element model to study group effects on modification of p-y curves. Urao et al. (1992) contrasted results from a dynamic 3-D finite element analysis of a composite pile/ diaphragm wall foundation with an axisymmetric model. Cai et al. (1995) analyzed a 3-D nonlinear finite element subsystem model consisting of substructured solutions of the superstructure and soil-pile systems. In companion papers, Wu and Finn (1997a, b) presented a quasi-3-D finite element formulation with relaxed boundary conditions that permitted: a) dynamic nonlinear analysis of pile groups in the time domain, and b) dynamic elastic analysis of pile groups in the frequency domain.
These methods showed good comparison to more rigorous
techniques, but at reduced computational cost. Fujii et al. (1998) compared the results of a fully-coupled 2-D effective stress SSI model to measured performance of a pilesupported structure in the Kobe earthquake.
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3.1.5 Pile Group Effects The results of single soil-pile interaction analyses must be extended to reflect the group configurations piles are typically installed in for accomplishing full SSPSI analyses. This is in contrast to substructuring or complete analysis methods which inherently consider the entire group response. If piles are arrayed in groups with large pile-to-pile spacings (greater than 6 - 8 pile diameters), pile group interaction effects are normally ignored for static loading (see Figure 3.24). But this may be an inaccurate approach for dynamically loaded piles, as much of the pile group interaction effects arise from wave energy reflected between neighboring piles, which does not attenuate as rapidly as static loading pile group interaction. Pile group dynamic response is also a function of load level; many of the group analysis methods that will be described address small strain elastic response, and few researchers have investigated nonlinear pile group interaction. There is evidence however to suggest that pile group effects lessen with increasing soil-pile nonlinearity, which inhibits wave energy transmission between piles.
Figure 3.24 - Pile Group Interaction as Function of Pile Spacing (after Bogard and Matlock, 1983)
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The behavior of a pile group subjected to lateral loading and overturning moment is shown in Figure 3.25, which illustrates the components of pile group response. These components include: •
group rotation, inducing axial tensile/compressive forces, most severe at end piles,
•
group translation and relative pile translations,
•
individual pile head rotations at pile to cap connections, and
•
individual pile deflections and consequent bending moments.
The factors that influence the group response consist of: •
individual pile response: small strain elastic or nonlinear behavior,
•
loading: static, cyclic, or dynamic; transient or steady state,
•
soil properties, particularly as modified by pile group installation,
•
relative soil-pile stiffness; more flexible piles experiencing greater interaction,
•
group geometry, including individual pile cross sections and group spacing,
•
head fixity, idealized as free head or fixed head, but in actuality an intermediate case,
•
tip condition, either floating or end-bearing,
•
superstructure mass and flexibility, which impart inertial loads to the pile group, and
•
pile cap embedment depth, stiffness and damping characteristics.
The objectives of conducting a pile group analysis are to determine the following: •
pile group and individual pile deflections,
•
individual pile head shear forces and moment distributions, and
•
modifications to the input ground motion for superstructure analysis. The manner in which this is accomplished relates to the level of single pile analysis.
Single pile kinematic response analyses can be modified to approximate group effects and superstructure influence. Single pile impedance functions can be assembled into group impedance functions with a group interaction theory. The group impedance function is then used in a global structural analysis, which produces forces and deflections on the pile
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group. These forces and deflections can then be distributed to the individual piles with group interaction theory, and individual pile head forces can be checked not to exceed the pile to cap connection capacity. Then the most critically loaded pile(s) in the group can be assessed in a single pile integrity analysis mode to determine whether pile moment distributions exceed capacity. To determine the effect of the pile group on modifying ground motions input to the superstructure, the analysis must be either conducted in a true substructuring fashion; or alternatively, this effect can be captured in a complete SSPSI analysis.
Figure 3.25 - Components of Pile Group Response Under Lateral Loading (after O’Neill and Dunnavant, 1985)
In the following sections, static and dynamic pile group response theories will be presented, defined as one of two categories: 1) pile group interaction methods, used in relating single pile analysis results to group behavior; 2) pile group complete dynamic analyses, where the entire group response is analyzed in one step. Reviews of pile group dynamic response are provided by Roesset (1984) and Novak (1991).
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3.1.5(a) Pile Group Interaction Methods Poulos (1971) introduced the concept of pile group interaction factors. He used Mindlin’s elasticity equations to solve for stresses and displacements between pairs of piles due to horizontal point loads applied in an elastic half space. Poulos described interaction factors as: α=
additional displaceme nt (rotation) due to adjacent pile (3.7) displaceme nt (rotation) of pile due to its own loading
He presented charts of α factors for both fixed and free head piles subject to lateral and moment loadings as functions of pile flexibility Kr (see Table 3-1), pile spacing, pile diameter, pile length, and departure angle (angle between piles and direction of loading). Analysis of groups was accomplished by superposition, calculating each pile’s interaction with all other piles in the group, and ignoring the presence of intervening piles. Subsequently, his method has proved to underestimate pile group interaction at small pile spacings and overestimate interaction at large spacings. Poulos elaborated this method to include soil limit pressures, soil-pile axial slip, variation of soil modulus with depth, and batter piles in the computer code DEFPIG (Poulos, 1980). Randolph and Poulos (1982) presented a simplified flexibility matrix method for pile group response based on Poulos’ axial interaction factors and Randolph’s (1981) lateral interaction factors. In Poulos and Randolph (1983), these two methods are compared. Randolph (1986) also issued the pile group analysis program PIGLET, based on parametric finite element analyses. Focht and Koch (1973) combined Poulos’ elastic interaction factors with nonlinear p-y analysis in a hybrid model to predict group deflections and shear load distributions. They conceived of pile group interaction to consist of two components, nonlinear soil
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response close to the piles, and an elastic component at intermediate ranges between piles. The analysis procedure consisted of first computing a single pile mudline deflection from conventional p-y analysis, then computing a Poulos interaction factor-derived deflection at the mudline, the latter based on a low stress level in the soil. Individual pile deflections and shear forces were then estimated from integrating the plastic and elastic deformations, and the total group response was solved for. The variations of deflection and moment with depth on individual piles was then constructed from conventional p-y data modified by “Y” factors, accounting for the elastic components of interaction.
The authors
recognized the uncertainty in selecting values of soil modulus for elastic interaction, but it has proven to be a viable tool for pile group analysis under static and cyclic loading. Reese et al. (1984) suggested modifications to the relative stiffness factor R in this procedure. Bogard and Matlock (1983) introduced the modified unit transfer load method, which developed p-y curves for group piles by considering an imaginary pile with a diameter equal to the pile group diameter. As shown in Figure 3.26, the group pile p-y curve is constructed by summing the single pile deflection with the pile group soil mass deflection at a given soil pressure. This method was developed for static and cyclic loadings of a circular pile group in soft clay, and its extension to other group geometries and conditions is unproven. O’Neill and Dunnavant (1985) surveyed static laterally loaded pile group interaction analyses, and compared the hindcast performance of four methods against a database of 16 pile group load tests. The methods evaluated included the Focht-Koch hybrid analysis, the Bogard-Matlock modified unit load transfer method, a plane strain
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interaction procedure (Hariharan and Kumarasamy, 1982), and the PILGP2R hybrid method, proposed by the authors. The plane strain interaction procedure consisted of analyzing stresses and displacements in an elastic layer produced by the displacement of a rigid embedded disk. The PILGP2R hybrid model overcame a limitation of the FochtKoch model, providing for a variation in Y-multipliers over the pile depth, rather than a single value applied to the entire pile. Overall, the study showed the PILGP2R model to provide the best estimates of average behavior of group piles, of initial group lateral stiffness, and load distribution, but it was found to underpredict deflections and moments at high load levels.
Figure 3.26 - Pile Group Unit Load Transfer Method (after Bogard and Matlock, 1983) Brown et al. (1987) performed cyclic lateral load tests on 3x3 pile groups in stiff clay and sand (see Chapter 4), and proposed the concept of p-multipliers to account for group effects. The p-multipliers are reduction factors applied to the p-y relationship computed for an individual pile of the group. These reduction factors are a function of pile spacing and orientation to loading, and are implemented in the pile group analysis program GROUP (Reese et al., 1994).
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Ooi and Duncan (1994) presented the group amplification procedure for laterally loaded pile groups, which was derived from single pile analyses by the characteristic load method (Duncan et al., 1994) and group interaction using the Focht and Koch (1973) procedure. Their parametric studies yielded a deflection amplification factor
N C y = A + pile
B ((S D )+ (Ps CPN ))
0.5
(3.8)
where A, B, and C are factors for clay and sand soils, Npile is the number of piles, S is the average pile spacing, D is the single pile diameter, PS is the total lateral load on the pile group, and PN = SUD2 for clay and KPγD3 for sand. A simplified procedure was also presented for estimating the maximum bending moment in the most critically loaded pile in the group. The method applied to statically loaded, vertical, uniformly spaced, fixed head, flexible piles embedded in a homogeneous soil. Validation against several case histories was provided, with reasonable accuracy attained. Kaynia and Kausel (1982) derived dynamic interaction factors for floating pile group interaction analysis by combining a numerical integration for the evaluation of the influence coefficients with an analytical solution for the pile stiffness and flexibility matrices. This boundary element formulation computed Green’s functions from imposed barrel and disk loads in a homogeneous soil medium, and used a consistent stiffness matrix to account for the far field. Their interaction factors were presented as complex-valued frequency dependent ratios of the dynamic displacement of pile i to the static displacement of pile j, due to a unit harmonic load on pile j. Vertical and horizontal interaction factors are shown in Figure 3.27, demonstrating positive and negative group efficiencies. Normalized dynamic stiffness and damping of a 4x4 pile group for different spacings is
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shown in Figure 3.28, indicating the strong frequency dependence of dynamic group response. They also derived expressions for the distribution of forces over the pile group (see Figure 3.29), which was shown to vary from static loading force distributions. Other important conclusions from this study were that the superposition technique is valid for dynamic pile group solutions (in homogeneous soil), pile groups are less influenced by near-surface ground conditions than isolated piles, group interaction effects are stronger for softer soil, and radiation damping increases with foundation size.
Figure 3.27 - Vertical and Horizontal Dynamic Pile Interaction Factors (after Kaynia and Kausel, 1982)
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Figure 3.28 - Normalized Horizontal and Vertical Dynamic Stiffness and Damping of 3x3 Pile Group in Soft Soil (after Kaynia and Kausel, 1982)
Figure 3.29 - Distribution of Horizontal and Vertical Forces in 4x4 Pile Group in Soft Soil Medium (after Kaynia and Kausel, 1982)
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In companion reports, Sanchez-Salinero (1982, 1983) investigated single pile and pile group dynamic response. Using static and dynamic axial and lateral single pile head stiffness coefficients as indices, he compared the values computed by the methods of Poulos (1971), Penzien (1964), Kuhlemeyer (1979), Novak (1974), Blaney et al. (1976), and Novak and Nogami (1977). For static lateral loads, Poulos’ method was found to give lower stiffnesses and Kuhlemeyer’s approach was found to give higher stiffnesses, with the other methods yielding similar intermediate values. For dynamic loads, Novak’s Winkler assumption produced results comparable to Blaney’s more sophisticated formulation.
Sanchez-Salinero therefore extended the Winkler concept to an
elastodynamic boundary element formulation for developing pile group interaction factors. He contrasted point and disk pile approximations, and verified the validity of the superposition technique.
The strong frequency dependence of pile group stiffness
coefficients was noted, with the author concluding that the effects of soil nonlinearity on pile group response may significantly affect the results. Dobry and Gazetas (1988) presented a simplified method for calculating dynamic pile interaction factors in homogeneous soil by assuming that cylindrical wave propagation governs vibration of source piles and displacement of neighboring piles. Fan and Gazetas (1991) studied pile group kinematic interaction effects, and as shown in Figure 3.30, the generalized pile head to free-field transfer function illustrates the pile group effect in filtering out high frequency components of motion.
They found that pile group
configuration and spacing have little influence on kinematic response, as pile head fixity and relative soil-pile stiffness play a stronger role. Gazetas and Makris (1991) and Makris and Gazetas (1992) developed simplified methods of analysis for pile group axial and
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lateral dynamic response, respectively (see Figure 3.31). Using a dynamic Winkler model, they found pile group effects to be more pronounced for inertial than kinematic loading. The substructuring approach unifying the kinematic and inertial analyses is described in Gazetas et al. (1992), and is shown schematically in Figure 3.32. Mylonakis et al. (1997) applied this substructuring approach in an equivalent linear method to analyze pilesupported bridge piers.
Figure 3.30 - Generalized Pile Head/Free Field Transfer Function for Kinematic Interaction (after Fan and Gazetas, 1991)
Figure 3.31 - Schematic of Three-Step Procedure for Computing Pile-Soil-Pile Interaction (after Makris and Gazetas, 1992)
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Figure 3.32 - Substructuring Method for Seismic Soil Pile Superstructure Interaction Analysis (after Gazetas et al., 1993)
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3.1.5(b) Pile Group Complete Dynamic Analyses Wolf and von Arx (1978) generalized the solution of Blaney et al. (1976) to publish the first pile group complete dynamic response analysis method. They considered a horizontally layered visco-elastic soil deposit with piles of equal diameter and length, either floating or endbearing, in any group configuration. They used an axisymmetric finite element model to calculate the Green’s functions producing the displacements at any point in the soil mass given a ring load applied at a discrete layer. The Green’s functions were then used to compute the flexibility matrix of the soil at each frequency, and the dynamic stiffness matrix of the complete system was then assembled.
The results
displayed strong dependence on frequency, number of piles, and pile spacing. Wolf (1980) detailed procedures for calculating the dynamic stiffnesses of groups of battered piles. Most recently, Wolf et al. (1992) described simplified but reasonably accurate cone models for single pile and pile group dynamic response. Waas and Hartmann (1981) analyzed pile groups arrayed in concentric rings, and assumed that the radial, vertical, and tangential components of displacement were proportional to the direction of applied loading. They substructured the problem (see Figure 3.33) and determined the flexibility matrix of the visco-elastic soil deposit with applied point and ring loads, for coupling to the structure/pile stiffness matrix. They suggested that nonlinear soil behavior could be modeled by an equivalent linear analysis, and that rectangular pile groups could be transformed into equivalent circular groups amenable to their analysis technique. Their analysis clearly demonstrated the effects of kinematic and inertial interaction as shown in Figures 3.34a - d.
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Figure 3.33 - Separation of SSPSI Analysis into Kinematic and Inertial Interaction Components (after Waas and Hartmann, 1981)
(a)
(b)
(c)
(d)
Figure 3.34 - a) Definition of Transfer Function; b) Transfer Function without Building Mass for Soft Soil; c) Transfer Function without Building Mass for Stiff Soil; d) Transfer Function for Different Building Masses in Stiff Soil (after Waas and Hartmann, 1981)
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Kagawa (1983) used elastic wave propagation to compute soil displacements and reactions between pairs of piles for the derivation of pile group stiffness and damping coefficients. Both vertical and lateral interaction were considered, as well as pile head fixity condition. These values were found to be dependent on pile spacing, departure angle, and frequency. Dynamic pile group impedance efficiencies both in excess of and less than one were calculated. Kagawa (1991) adopted a substructuring approach to the pile group dynamic response problem, as shown in Figure 3.35. In this method, the stiffness of the superstructure with piles was calculated by conventional means, and the load displacement relations for the cylindrical cavities obtained from a flexibility analysis. The flexibility analysis consisted of applying ring loads to one cavity, and computing displacements in the neighboring cavity (Figure 3.36); Kagawa noted that compatibility conditions are often relaxed in this type of analysis for computational efficiency. By formulating a more rigorous method, Kagawa was able to demonstrate a moderate loss in analytical accuracy when using relaxed compatibility conditions. Sheta and Novak (1982) investigated the effects of soil nonlinearity on pile group axial dynamic response by means of including a cylindrical weak zone surrounding floating or endbearing individual piles. Figure 3.37 demonstrates that group interaction effects elevate the response peaks, while the inclusion of a weak boundary zone serves to dull the peaks, but not eliminate them. El Sharnouby and Novak (1984) described a method of analysis of pile group interaction under static axial and lateral loading that yielded interaction factors, and was found to compare reasonably well with other accepted analyses (This method was updated by the authors in 1990).
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Figure 3.36 - Soil Displacements due to Ring Loading (after Kagawa, 1991)
Figure 3.35 - Example of Substructuring Approach (after Kagawa, 1991)
Mitwally and Novak (1987) presented complex, frequency dependent interaction factors for dynamic pile group response of offshore structures, with the recommendation that the equivalent linear method be employed to simulate nonlinear soil-pile response. The authors evaluated the effects of including pile group interaction effects on the response of a pile-supported platform subjected to wave loading; the results shown in Figure 3.38 illustrate the frequency dependence of group interaction. El-Marsafawi et al. (1992) derived pile group dynamic interaction factors from a boundary integral formulation for floating and end-bearing piles in homogeneous or non-homogeneous soil deposits.
They also verified the applicability of the superposition approach for the
conditions studied, with some limitations.
A set of translation, rotation, translation-
rotation coupling, fixed head, and vertical interaction factors were described in terms of
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amplitude and phase angle, a more convenient form for interpolation than real and imaginary stiffness terms. The authors concluded that the superposition method worked well except for cases of vertical response of stiff end-bearing piles, and the high frequency range for nonhomogeneous soils.
Figure 3.37 - Dynamic Response of Pile Supported Foundation Indicating Influence of Group Effects and Weak Zone (after Sheta and Novak, 1982) El Naggar and Novak (1994a) described a nonlinear model for dynamic axial pile response that consisted of a slip zone, inner field, and outer field (see Figure 3.39) that simulated a variety of field test results with great success. El Naggar and Novak (1994b) presented chart solutions for pile group interaction factors derived from this model. Most recently, El Naggar and Novak (1995) described a dynamic nonlinear time-domain Winkler soil-pile interaction model that allowed for both axial and lateral pile group response. The axial model consisted of a linear outer region and a nonlinear inner field connected to the pile by a plastic slider allowing for soil-pile slip. The lateral response mode also consisted of inner and outer fields with formulations by Novak and Aboul-Ella
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Figure 3.38 - Platform Response to Wave Loading with Pile Group Interaction both Considered and Neglected (after Mitwally and Novak, 1987)
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Figure 3.39 - Nonlinear Model for Dynamic Axial Response of Single Pile (after El Naggar and Novak, 1994b)
Figure 3.40 - Nonlinear Model For Dynamic Lateral Response of Pile Groups (after El Naggar and Novak, 1995) 122
(1978) and Novak and Sheta (1980) but with the addition of a directional gapping model. Interpile springs were used to model lateral and axial pile group effects (see Figure 3.40). They found that nonlinear foundation response is more pronounced for nonhomogeneous soil profiles than homogeneous ones, and that the nonlinear foundation behavior decreases the structural damping ratio, but this is more than offset by the increase in foundation damping.
They also concluded that dynamic pile group effects increase foundation
damping, significantly for linear conditions, but to a lesser extent for nonlinear conditions. Nogami (1979) presented solutions for the dynamic axial response of pile groups in homogeneous soil profiles. Nogami and Konagi (1987) studied nonlinear pile group axial response by incorporating slip at the soil-pile interface in a dynamic Winkler model. They found this nonlinearity to reduce wave interference effects and suppress the frequency dependence of dynamic group response. Nogami et al. (1988) and Otani et al. (1991) extended the dynamic Winkler pile group model to lateral loading, and included slip, gapping and inelastic soil behavior. Their nonlinear near field model was found to dull the peaks of computed pile head impedance functions. Unfortunately, Nogami has not presented his work in a form convenient for use by the profession, and it remains underutilized and not well validated. In addition to studying pile group interaction under static loading, Banerjee has also researched pile group dynamic interaction effects.
Banerjee and Davies (1980)
compared the results of a boundary element formulation pile group analysis method with static loading field case histories. Banerjee and Sen (1987) reported on boundary element formulations for pile group dynamic response. They also investigated the effects of a ground contacting massless pile cap, and found a marginal increase in pile head impedance
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of small floating pile groups, most pronounced for the damping component.
Mamoon
(1990) conducted an extensive study of cap effects on dynamic group response. He accounted for pile cap inertia, but ignored the shear stress in the mat base. An important conclusion from this study was that pile cap inertia can reduce the sharp peaks in the dynamic response. Makris and Badoni (1995b) followed their earlier work with a simplified method for analysis for pile groups subject to obliquely incident shear and Rayleigh waves, with spring and dashpot coefficients evaluated from the techniques described in Makris and Gazetas (1992).
The method consisted of computing the difference between single
“source” piles and free-field response, and propagating it to neighboring “receiver” piles. By superposition, the pile group displacement, rotation, and individual pile head forces were obtained, incorporating both kinematic and inertial sources of loading. The results from this approximate method were found to compare very favorably to methods by Mamoon and Banerjee (1990), and Kaynia and Novak (1992). In a comprehensive report encapsulating Badoni’s Ph.D. dissertation work, Badoni and Makris (1997) summarize numerical analysis methods for structures incorporating nonlinear axial and lateral soil-pile group interaction, as well as structural nonlinearity and pile yielding. The complex response method finite element computer programs FLUSH (Lysmer et al., 1975) and SASSI (Bechtel, 1991), through principally designed for soil-structure interaction analyses, do have the capability of modeling SSPSI as a complete analysis, but are not well equipped to deal with strong soil-pile nonlinearity, gapping, etc.
The
generalized finite element code DRAIN2D-X (Prakash et al., 1993) has also been used by a number of researchers as a platform for SSPSI analyses.
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3.2 Building Code Provisions This section will examine the myriad of building code recommendations for conducting soil-structure interaction design and analyses, and provisions for dealing with the seismic performance of pile foundations. Although many of these codes incorporate simplified soil-structure interaction analysis methods, they acknowledge the need for sitespecific studies for structures on soft soils subject to strong levels of shaking. First, codes dealing with building structures will be reviewed, followed by those pertaining to bridges.
3.2.1 Uniform Building Code / SEAOC Recommendations The 1997 Uniform Building Code (ICBO, 1997) and the companion Blue Book Recommended Lateral Force Requirements and Commentary (SEAOC, 1996) do not provide any overt requirements for consideration of soil-structure interaction. Chapter 18 of the UBC, “Foundations and Retaining Walls”, provides minimal design guidance for foundation construction in seismic zones 3 and 4, but emphasizes consideration of the potential for soil liquefaction or strength loss. Specific requirements for steel pile width to thickness ratios and concrete pile transverse reinforcement are given. An emphasis is also placed on the capacity of the foundation to sustain the base shear and overturning forces transmitted from the superstructure and for the adequacy of superstructure to foundation connections. The SEAOC recommendations call general attention to cyclic degradation, pile group effects, pile cap resistance, pile flexure and ductility, and kinematic loadings, but offer no specific requirements for design. Chapter 16 of the UBC, “Structural Design Requirements”, provides for both response spectrum and time history analyses for
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earthquake design; however there are no provisions to account for soil-structure interaction in either method. In essence, the UBC partially addresses pile integrity under kinematic and inertial loading, but does not explicitly account for the influence of the pile foundation on the ground motions imparted to the superstructure.
3.2.2 National Earthquake Hazard Reductions Program The 1997 NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (BSSC, 1997) includes detailed procedures for incorporating the effects of soil-structure interaction in the determination of design earthquake forces in the structure. Incorporating these effects has the direct result of reducing the base shear applied to the structure, and consequently the lateral forces and overturning moments, but may increase lateral displacements (due to rocking).
The
maximum permissible base shear reduction factor is 30 %, and it is computed as a function of flexible base period and damping factors. The flexible base period is a composite of fixed base, flexible rocking, and flexible translational periods, the latter two computed from foundation stiffnesses. The accompanying Commentary presents a procedure for deriving the foundation stiffness factors from a simple model of a rigid mat bonded to an elastic halfspace. The model can take into account foundation shape, embedment, and soft soil over stiff layer, but the Commentary acknowledges that its application to pile foundations is more tenuous. This is the type of model that Stewart investigated (see chapter 2), and his findings echoed this conclusion. The Commentary states that individual pile stiffness factors may be determined from field tests or beam-on-elastic-subgrade analyses, but
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provides scant details. Perhaps unconservatively, the Commentary recommends summing individual pile stiffness factors to compute pile group stiffness, without reduction factors. The 1997 NEHRP Guidelines for the Seismic Rehabilitation of Buildings (BSSC, 1997) provides simplified expressions for pile axial and rocking stiffness and the influence of pile caps on pile group seismic response.
For cases where the piles may significantly
contribute to lateral stiffness (i.e., soft soils, battered piles), the Provisions recommend that a beam-column analysis be performed. In promoting an elastic model of soil-structure interaction, the NEHRP Provisions do not directly incorporate nonlinear effects, but attempt to overcome this limitation by recommending that foundation stiffness factors be selected based on anticipated strain levels in the soil response. The NEHRP foundation design requirements primarily focus on assuring adequate pile cap connections, transverse reinforcement, and the ability to withstand maximum imposed curvatures resulting from seismic loading. These curvatures are observed to potentially arise from: 1) soil settlement beneath the pile cap, leaving an unsupported pile length in the zone of maximum inertial forces; 2) large deformations and/or reduction in soil strength as a result of liquefaction; and 3) large deformations in soft soils, particularly at soft/stiff soil interfaces.
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3.2.3 Mexico City Building Code The 1987 Mexico City Building Code carries with it lessons from the 1985 Mexico City Earthquake (see Chapter 2). The Complementary Technical Norms (Gomez and Garcia-Ranz, 1988) includes a simplified method for considering the effects of soilstructure interaction. The objective of the procedure is to obtain a flexible-base period of the structure for use with the response spectrum method, which is a weighted function of the rigid base, flexible rocking, and flexible translational periods of the structure. Methods for computing the rocking and translational stiffnesses of slabs, footings, friction, and end bearing piles is included. Minimum spacing between structures is recommended as large rocking displacements are possible. Foundation elements are to be designed “taking into account a horizontal inertia force, acting on that volume of soil beneath them that potentially would move during a shear soil failure... subject to a horizontal acceleration of (0.04 - 0.15) g.” In summary, the Mexico City building code contains the basic elements of the NEHRP provisions, specifically tailored for the longer period deep clay sites under its jurisdiction, and is unique in that it attempts to differentiate the particular response of pile foundations.
3.2.4 People’s Republic of China Aseismic Building Design Code The 1989 People’s Republic of China Aseismic Building Design Code (PRC, 1989) states that “influences of soil-structure interaction may be disregarded in aseismic structural analyses. When the soil-structure interaction is taken into account for highrise reinforced concrete buildings with box-shaped or stiff raft foundations and constructed on the Type III or IV site (softer soils), the seismic loads evaluated on the basis of the rigid-
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foundation assumption may be diminished by 10 to 20 percent, their interstory drifts being determined under the resulting reduction of story shear forces.” What this means is that the code recognizes the beneficial effects of soil-structure interaction in period lengthening and increased damping for longer period structures, thereby decreasing design forces, but does not consider the potentially unconservative force increase for very short period structures whose period lengthens on the ascending part of the response spectrum; nor does it recognize potentially greater displacements due to rocking. With respect to piles, the code requires piles in liquefiable layers to have minimum embedment in more stable layers, but this requirement ignores the damage potential arising at zones of soil stiffness contrast.
3.2.5 American Petroleum Institute Recommended Practice The offshore oil industry has been a driving force behind the development of analysis methods for the response of pile foundations under lateral cyclic loading, primarily due to wave loading of pile-supported offshore drilling platforms.
The API
Recommended Practice 2A-WSD (API, 1993) codifies the p-y type analysis method, which is directly based on field tests conducted by Reese and Matlock in sands and clays. Reduction factors for cyclic loading cases are given for both sands and clays, and the sensitivity of axial capacity to cyclic lateral loading is also noted. With the enormous investments and lack of redundancy in offshore drilling platforms, it is universal practice to perform site-specific analyses, and not rely on published codes. A type of analysis known as a “static push-over analysis” is commonly performed, which consists of building a finite element model of the entire structure including the foundation piles and soil, and laterally
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displacing the platform until yielding occurs in a component of the system; in this manner, the designer can direct the system response. This formulation is convenient for offshore platforms, which have a limited number of piles and structural elements, and the soil-pile interaction is commonly modeled by p-y curves or a finite element mesh. Such a method does not however capture the dynamic features of SSPSI, but it does succeed in coupling the substructure and superstructure components of the system.
3.2.6 Improved Seismic Design Criteria for California Bridges The 1996 ATC-32 Improved Seismic Design Criteria for California Bridges: Provisional Recommendations (ATC, 1996) is a companion document to the current Caltrans Bridge Design Specifications (BDS), and includes specific recommendations for the seismic design of pile foundations. These recommendations are refinements of the BDS, and take the form of presumptive values and simplified charts. ATC-32 defines four types of bridges, two categories of seismic evaluation, and four levels of analysis to be applied. Equivalent static analysis, conducted only for small ordinary bridges, does not account for SSPSI. Elastic dynamic analysis, for which the seismic design of most bridges is carried out, consists of a modal spectral analysis of a finite element “stick model” of the bridge.
The soil-pile rotational and translational
flexibilities are represented by linear elastic springs with secant stiffnesses based on maximum load levels anticipated.
The commentary cautions that development of
nonlinearity in the soil and other components of the structure are possible, but that the elastic model can give good insights into system response. Inelastic static analysis is a higher level evaluation required for important bridges and is used to examine inelastic
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response of the bridge when subject to lateral displacements generated during the design earthquake. This type of analysis, also known as a static push-over analysis, is intended to capture the nonlinear response of the entire system, including nonlinear soil-foundation interaction.
Inelastic dynamic analysis may be performed in place of inelastic static
analysis; the type of soil-pile model for these inelastic analyses is not specified by ATC-32. The commentary does make the interesting point that the seismic demand on the foundation is an artifact of the analysis method; it also acknowledges that the methods recommended only account for inertial loading from the superstructure into the piles, and does not consider the effects of kinematic loading on the overall response of the structure. The specifications require that pile foundations have sufficient capacity to resist loads transmitted from the superstructure, while accounting for ductility developed in the structure in the computation of these loads; adequacy of structural and connection details is emphasized.
Loads generated by ground movements and settlement should be
accounted for. The desired structural action is such that plastic hinges develop in elements above the ground surface for inspection and repair accessibility, or that a sufficient load path exists that directs failure into the soil, rather than the pile. ATC-32 provides information on assigning foundation stiffness values based on linear elastic response.
It is important to emphasize that these stiffness values are
developed from static (or at best, cyclic) loading patterns, and are not true dynamic stiffnesses. Lateral resistance is provided by piles and in some cases by passive pressure on the sides of embedded pile caps, while bending stiffness is attributed only to the piles. At stable soil sites, the resistance of the pile cap can contribute a significant lateral stiffness to the pile footing, but at poor soil sites (liquefiable sands and soft clays), such
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resistance is to be ignored. As axial capacity is provided by soil resistance at depth and lateral capacity by shallow soil resistance, there is very little cross coupling between the resistances and soil-pile interaction can be evaluated independently for the two modes of loading. A table of presumptive lateral pile stiffness values is given, and is supplemented by a series of simplified pile head stiffness charts based on a beam-on-elastic subgrade reaction model; these charts provide stiffness values for a variety of pile head embedment and boundary conditions. The specifications also define presumptive values for standard Caltrans pile types for lateral capacity, tolerable foundation displacements up to 3.0 in, and angular distortion up to 0.008 radians. With respect to nonlinear soil-pile interaction, the capacity of piles to resist both axial compressive and tensile loads while accounting for the effects of cyclic degradation of bearing capacity is addressed, particularly for friction piles, piles at soft soil sites, and piles subject to skin friction shear stress reversal induced by superstructure rocking. The commentary recommends that a site-specific analysis be undertaken to determine pile stiffness and shear capacity at poor soil sites (liquefiable sands and soft clays), cautioning that fully liquefied sands have a residual strength of only about 10 % of the initial p-y curve resistance. At such sites, a number of design strategies to resist the shear load are given, including the use of stronger connection details and more ductile pile types. In general, the seismic response of bridge structures is most sensitive to the rotational component of stiffness of pile groups. According to the Commentary, pile group effects for rotational response can be ignored for groups consisting of less than 20 piles at standard spacing, as their response is not in phase; relatively small group effects are noted for translational response. Group effects are mitigated under cyclic loading at
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soft soil sites, as the remolded soil is less effective in transferring stresses to neighboring piles. However, group effects can become very important for large pile groups, and special analyses are warranted in these cases. The effects of radiation damping dissipating energy in the system are not accounted for. The use of batter piles must be accompanied by proper understanding of their performance and adequate detailing of connections and transverse reinforcement. At poor soil sites subject to lateral ground movements, stiff batter piles tend to attract very large forces compared to more compliant vertical piles, and their use is to be avoided. The pile shaft, a continuous extension of the column into a foundation element, also has special design guidelines, including a recommendation to increase the value of the modulus of subgrade reaction used in computing p-y curves for shafts of diameter greater than 2 feet. In summary, the ATC-32 guidelines provide a comprehensive and efficient method for evaluating seismic response of bridge structures. They do not represent the state-ofthe-art for SSPSI, as a detailed nonlinear foundation model can be uneconomical for complex bridge structures; but they do consider in a simplified fashion the principal modes of SSPSI, and provide a very practical approach for bridge designers.
3.2.7 FHWA Seismic Design of Highway Bridge Foundations The Federal Highway Administration has published a series of design manuals addressing SSPSI for bridge structures, including Seismic Design of Highway Bridge Foundations (1986). The lead authors of this manual, Lam and Martin, also participated in the ATC-32 document, and the content is quite similar. Again, a simplified approach is taken, which includes the use of equivalent linear frequency independent static pile head
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stiffness terms, while ignoring radiation damping, pile group effects, and kinematic loading. Nonetheless, due attention is given to nonlinear soil-pile interaction (p-y curve method), liquefaction hazard, influence of rotational stiffness, load transfer, batter piles, head fixity, pile cap stiffness, and special design procedures for drilled shafts.
3.2.8 Japanese Seismic Design Specifications for Highway Bridges Kawashima and Hasegawa (1994) trace the history of seismic damage to highway bridges in Japan and the consequent evolution of Japanese building codes. According to the authors, the 1971 and 1980 specifications provided countermeasures against damage of substructures caused by liquefaction and lateral spreading, and subsequent earthquakes did not manifest damage in structures built to these standards. The 1990 specifications included revisions that addressed the classification of ground conditions, the inertia force applied to substructures, providing ductility in columns, and improvements in evaluating the resistance of sandy soils to liquefaction (which has historically been the major pile seismic hazard in Japan - see Chapter 2). Unjoh and Terayama (1998) published a translation of the complete Seismic Design Specifications of Highway Bridges, issued by the Japanese Public Works Research Institute in 1996 to reflect the lessons of the Hyogo-ken nanbu earthquake. Clearly, Kawashima and Hasegawa’s conclusion regarding newer building codes “eliminating” liquefaction hazards was nullified by the experience in Kobe. Consequently, the 1996 code provides detailed guidelines for the design of foundations at sites vulnerable to soil instability.
These guidelines include the assessment of liquefaction potential, the
calculation of forces arising from lateral spreading, and the decrease in bearing capacity of
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weak cohesive soils. An entire chapter is devoted to ductility design of foundations, recognizing the fact that it is not always possible to ensure purely elastic foundation response, particularly at sites subject to soil instability. Ductility is allowed to develop in foundation elements under conditions where the performance limits of the superstructure and the foundation are not exceeded, but at the same time limiting yielding of the pile members and/or the pile-soil resistance.
3.2.9 New Zealand Bridge Design Specifications Specifications for the seismic design of bridge foundations promulgated by the New Zealand National Society for Earthquake Engineering in 1980 (Edmonds et al., 1980) are among the most extensive dealing with SSPSI. The document begins by stating: “In assessing the response of a bridge structure to earthquake excitation, the foundation flexibility resulting from the interaction between the bridge foundation and the soil should be taken into account.” The overall design philosophy is stated that it is desirable for pile foundations to remain elastic, but that ductility is permissible if yielding is unavoidable. Several classes of seismic soil-pile interaction methods are noted to be available, including: equivalent cantilever, beam on an elastic foundation, soil medium as an elastic halfspace, discrete soil-pile springs, and finite element models. The point is made that for any analysis method the soil stiffness should be strain compatible with the pile deflections produced by the design loading.
Design loadings are given for capacity design,
development of ductility in the piles, and axial loading due to rocking of the foundation. The specification also recommends that special consideration be given to the performance of batter piles, pile group effects, liquefaction hazards, soil-pile gapping, and cyclic
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degradation of soil strengths.
With respect to pile caps, it is noted that frictional
resistance of the underside should be disregarded due to settlement, but that passive lateral resistance of caps embedded in cohesive soils may be incorporated. As a final note, the commentary to the specification observes: “The use of a more refined soil foundation interaction model for pile foundations will not necessarily lead to a more reliable prediction of foundation behaviour as the accuracy of the prediction will depend as much on the reliability of the soil data as upon refinement of the model. Confidence in the soil data implies knowledge of the following: •
Modification to the undisturbed characteristics of the soil caused by the change in the stress state of the soil during and subsequent to the installation of the foundation.
•
Time dependent changes in the soil properties depending on the number of cycles of loading and the amplitude of each cycle.”
These are very difficult properties to know, and yet we use sophisticated SSPSI models...
3.3 Current State-of-Practice SSPSI Design and Analysis Applications Due to the complexity of the problem, the unavailability of standardized and validated analysis techniques, and the perception that doing so is conservative, designers routinely ignore or greatly simplify the presence of pile foundations in their analyses. A special challenge of soil-structure interaction problems are that they span two disciplines, geotechnical and structural engineering, and the analysis is frequently broken into parts rather than addressed in a holistic manner. Where a geotechnical engineer may idealize a complex multimode superstructure as a single degree of freedom oscillator, the structural engineer will often represent the potentially nonlinear soil-pile interaction with a simple
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linear spring. In this manner, nonlinear system interaction between the superstructure and substructure is artificially prevented. The following case histories are presented as a survey of design applications for SSPSI for bridge structures indicative of advanced stateof-practice. The diverse and non-standardized design approaches are intended to illustrate the lack of professional consensus and the gap between the current state-of-practice and the current state-of-the-art; they can also be considered creative applications of limited tools to complex problems.
3.3.1 National Survey Hadjian et al. (1992) conducted a national survey of design professionals to ascertain the state-of-practice with respect to the seismic response of pile foundations. The respondents, both geotechnical and structural engineering firms, often ignored SSPSI effects and at most considered them in a simplified fashion. Typically a geotechnical designer would provide load-deflection and -moment diagrams to the structural engineer, who would in turn select a foundation spring value to be used in the structural analysis. Although the load-deflection and -moment diagrams are routinely developed with nonlinear soil-properties in a “p-y” type analysis, this nonlinearity is lost when the structural engineer ignores the strain and frequency dependence of the loading. Few respondents indicated consideration of pile inelasticity, radiation damping, or soil-pile gapping.
Group effects were treated based on empirical or elastic/static interaction
solutions, and did not account for the dynamic nature of the problem. The effect of pile foundations modifying foundation input ground motions was not identified by the respondents as a common engineering consideration. Hadjian identified the uncoupling of
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the analysis between the geotechnical and structural engineer as a prime limitation on advancing the state-of-practice in this field.
3.3.2 ASCE Workshop At an ASCE Technical Workshop on the Lateral Response of Pile Foundations conducted in San Francisco in 1994, representatives from major geotechnical engineering firms gave presentations indicative of the local state-of-practice. A variety of methods for analysis of lateral loading of single piles were presented ranging from simplified chart solutions to the advanced computer code PAR (Bea, 1988). Group effects were treated with Poulos’ elastic/static interaction factors and empirical results from Reese (1990). Finally, the lateral response of piles in liquefaction susceptible soils was addressed with a method for degrading the p-y curve based on soil index properties. To analyze earthquake and liquefaction-induced pile curvatures, two methods were outlined: the first, consisting of using a site response analysis (i.e. SHAKE91) to determine the soil response with depth, and imposing that on the pile to generate moment and shear distribution along the pile; the second, consisting of using a nonlinear dynamic 2-D or 3-D finite element analysis (i.e. SASSI) that models both piles and soil. The first approach is conservative in that it does not account for soil-pile interaction, and the second approach is complex, costly to implement, and does not capture important soil-pile interface nonlinearities.
3.3.3 San Francisco-Oakland Bay Bridge Under contract to Caltrans, G & E Engineering Systems recently performed an earthquake assessment for the east span of the San Francisco-Oakland Bay Bridge (1994).
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They studied four structural models of increasing complexity and concluded that the most sophisticated model, incorporating dynamic nonlinear analysis with multiple independent support motions, considering soil-structure interaction and local soil conditions, gave superior results and the added cost of the analysis was justified. Methods not considering local soil conditions and the influence of foundation flexibility were judged inadequate. Although this higher level analysis provided for superstructure nonlinearity, the foundations were modeled by elastic springs. 18 bridge piers of the east span of the San Francisco Oakland Bay Bridge are supported on groups of Douglas Fir timber piles, from 184 to 625 in number, driven through fill, soft clays, sands, and stiff clay deposits. The foundation impedances were computed for each pier as 6 x 6 stiffness and damping matrices, generally ignoring the cross coupling terms. Lateral stiffness terms for individual piles were computed by the method of Kuhlemeyer (1976), as a function of the pile radius and relative soil-pile stiffness, as represented by the ratio of soil-pile elastic moduli. Damping terms were computed as a function of pile radius and soil shear wave velocity in the vicinity of the pile. Single pile vertical impedance factors were computed as a function of pile and soil elastic properties by the method of Novak (1976). The individual pile impedances were then assembled into group impedance function for each pier using a group efficiency factor of 0.2, in accordance with recommendations of Gazetas et al. (1992) and El-Marsafawi et al. (1992). The final analysis results predicted longitudinal motions would be damaging to the piles and pile caps, and it was observed that such damage would soften the rocking stiffness of the bridge, thereby increasing superstructure forces. In summary, SSPSI effects are seen to be crucial in properly modeling this structural response, though in this case implementation of foundation impedance functions
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based on frequency independent elastic soil-pile properties may be inaccurate under strong levels of shaking.
3.3.4 San Diego-Coronado Bay Bridge Sykora et al. (1995) developed foundation impedance functions for a seismic vulnerability study of the San Diego-Coronado Bay Bridge. 22 of the 30 bridge piers are supported by groups of 10 to 44 54 in diameter prestressed concrete pipe piles, ranging from 32 to 111 ft in length, driven/jetted into hydraulic fill and young bay deposits. The foundation idealization was based on the assumption that the point of connection between the superstructure (including the upper segment of the piles and cap) and the substructure was the mudline, and therefore the foundation was condensed at this point and an equivalent static spring stiffness computed at this elevation; free head conditions were therefore used for all single pile evaluations. Lateral load deflection relationships were calculated using the p-y based computer code COM624P (Reese, 1984), and secant stiffness values selected based on conservative pile head deflection and rotation limits. The authors acknowledged that this is preferably an iterative process between the foundation and structural analysis, but project limitations precluded this approach. With individual pile lateral and axial stiffness values, the pile group stiffness was assembled with the computer code GROUP (Reese et al., 1990) and reduced with empirical data to account for group effects. The resultant stiffness matrix was then available for use in global structural analyses. Unfortunately, the authors did not comment on the selection of the damping component of the foundation impedance functions. This overall approach is
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very common for bridge design (it is promoted by ATC-32), but is limited in that secant stiffnesses do not truly provide for the nonlinear response of the foundation system.
3.3.5 Continuous Column-Shafts Conner and Grant (1995) presented a method for the seismic analysis of typical bridge bents consisting of concrete columns on single drilled shafts. The authors observed that a single drilled shaft foundation has a great deal more flexibility (especially rotationally) than a pile group, and thus moderate variations in shaft stiffness can have substantial effects on the magnitude and distribution of column forces. In addition, where cross coupling terms of pile group stiffness matrices are typically ignored, these effects are significant for drilled shafts and should be accounted for. The method employed consisted of using the p-y based computer code LPILE (Reese and Wang, 1989) to determine loaddeflection relationships, from which secant stiffness values were selected; cracked section properties (50 %) were selected for the shaft. The higher flexibility of single drilled shaft foundations relative to pile groups demanded that soil-pile nonlinearity be treated by fully iterating pile head secant stiffness values with the superstructure analysis. Deflections and rotations reported by the foundation model were converged with those calculated from the stiffness used in the dynamic analysis. Formation of plastic hinges in the column or shaft was determined by a static inelastic analysis or from the dynamic elastic analysis at locations where computed moments exceed the plastic hinge moment. Finally, the forces in the drilled shaft were determined from a separate foundation model. Overall, this method is an extension of the basic “local-inelastic global-elastic” method promoted by
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ATC-32, sensibly tailored for this special foundation type, but still subject to previously described limitations.
3.3.6 Caltrans Simplified Method Abghari and Chai (1995) attempted to couple the substructure and superstructure components of the SSPSI problem in an efficient manner by modeling a single pile extracted from a pile group and including the superstructure contribution to that pile. Their analysis was made for the Napa River Bridge, a 1000 m long structure supported by prestressed concrete piles driven into Bay Mud. A SHAKE91 (Idriss et al., 1991) site response analysis was made, and the resultant free-field displacement time history was applied to nodal points of the dynamic soil-pile interaction code PAR. This approach was contrasted with a pseudo-static approach, in which maximum free-field soil displacement loads were combined with increasing load levels of superstructure inertial forces (0, 25, 50, 75, and 100 %).
The authors concluded that the success of the pseudo-static
approach is highly dependent on the site-specific soil properties.
Additionally, by
extracting one pile for both analyses, important group effects influencing load distribution, rocking, and radiation damping are absent.
3.3.7 Alemany Interchange Retrofit Fowler et al. (1994) described the design procedures for the foundation retrofit of the I-280/101 Alemany interchange in San Francisco. The double deck viaduct was originally founded on a variety of driven piles in variable soil conditions. To upgrade the foundation capacity, drilled shafts were selected to augment both lateral and axial capacity
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of the pile groups.
The authors recognized that no established methods existed for
analyzing the seismic response of this complex hybrid foundation system, and adopted a pseudo-static approach. Trial foundation groups were developed by adding drilled shafts to the existing group in progressive length, diameter, and number, until a condition of fixity or no lateral deflection at the pile tip was predicted by the computer model. Load and moment combinations were generated at the base of the columns for input into the foundation analysis, and lateral loads were reduced to account for pile cap passive resistance. The p-y and t-z based computer programs APILE2 (Reese and Wang, 1990), SHAFT1 (Reese and Wang, 1989), LPILE (Reese and Wang, 1989), and GROUP (Reese et al., 1990) were utilized to analyze axial, lateral, and group performance, with an allowance made for cyclic degradation of soil resistance. Limit states for acceptable foundation design consisted of pile bending moment, axial and uplift capacity, and pile cap rotation and translation. Given the complex structure, foundation, and site conditions, this pseudo-static approach appears to be an efficient and reasonable approximation, although it ignores the true dynamic nature of the problem.
3.3.8 Mercer Slough Motivated by the failure of the Struve Slough Bridge in the Loma Prieta earthquake, Kramer (1993) performed an investigation for the Washington State Department of Transportation (WSDOT) into the seismic behavior of bridge foundations for I-90 crossing the Mercer Slough in Bellevue, Washington. The Mercer Slough Bridge is a 2800 ft long 85 span bridge supported on pile-founded, five column, reinforced concrete bents; the pile foundations consist of four 50 ft long timber piles at each cap,
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notable for their lack of mechanical connection to the caps. The site is underlain by a very soft, thick deposit of peat, known to provide little lateral pile resistance, and also poorly characterized in terms of dynamic properties. A series of field static and dynamic pile head loading tests was conducted to evaluate the in-situ impedance of the soil-pile system. The dynamic tests produced impedance values which varied with both load magnitude and frequency. The results from the static tests were extrapolated using the method of Scott (1981) to compute individual pile horizontal stiffness terms, which were simply summed to obtain the pile group stiffness for use in a global structural analysis. McLean and Cannon (1994) performed dynamic analysis of the bridge with the baseline and + 33 % baseline foundation stiffness cases; structural response was found to be moderately sensitive to the foundation stiffness case used. To investigate pile bending, 3-D finite element analyses were performed, recognizing that the commonly held assumption that piles move in phase with the surrounding soil is not reasonable for the very soft peat deposits, and that estimating pile curvatures from site response soil strain profiles was inappropriate. In the finite element analyses, the soil deformation patterns were applied statically and corresponded to the times at which the maximum soil profile curvature had developed in the site response analysis; inertial forces and P-∆ effects contributed by the superstructure were not considered. The results indicated that pile curvatures were significantly reduced relative to free-field curvatures.
3.3.9 WSDOT Study Cofer et al. (1994) also studied modeling of foundations for seismic analysis of bridges for WSDOT. Their approach was to develop a discrete foundation element for use in the
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nonlinear seismic bridge analysis computer code NEABS, and conduct a parametric study with this element on two bridge structures containing shallow and deep foundations. Following the work of Nogami (1992), the discrete foundation element was formulated with bi-linear spring stiffness and a linear viscous damping dashpot, with options for strain degradation or hardening, and soil-pile gapping. The stiffness and damping in each of the local six degrees of freedom was independently specified, and the foundation damping was independent of the global structural Rayleigh damping scheme. A parametric study was made of the Mercer Slough Bridge studied by Kramer (1993) using the discrete foundation element in four flexible base models, and contrasted with a fixed base assumption. The structural discretization consisted of a single bent supported by five columns, each with a common support model: •
The first discrete pile cap model used a linear lateral spring with properties based on Kramer’s experimental work. This model also included a rotational spring derived from calculating the resistance to rotation of the center of the pile cap which was afforded by the eccentric axial reaction of the piles, assumed to be elastic and endbearing; this rotational spring was used for all four flexible foundation models.
•
The second discrete pile cap model used a hysteretic bilinear lateral spring in conjunction with a viscous lateral damper.
The bilinear spring stiffness was
determined by first conducting a Winkler foundation analysis based on the modulus of horizontal subgrade reaction, calibrating the results to Kramer’s experimental data, and scaling the spring properties to account for the pile group effect. The damping coefficient was also based on the results of Kramer’s field tests.
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•
The third discrete pile cap model used an elastic lateral spring, with a secant stiffness based on the results of an analysis conducted using the second model; no damper was included.
This model corresponds to the commonly used secant stiffness “local
inelastic global elastic” approach favored by many practitioners. •
Finally, a Winkler-type pile foundation was employed as the fourth flexible foundation model with the four pile group represented by a single pile element; the soil reaction springs were based on Nogami’s (1988) far field submodel incorporating elastic stiffness and damping features. The performance of these elements was evaluated by subjecting the bent model to a
suite of earthquake excitations, and compiling column drift, column top internal moment, and column top plastic rotation as indices of the structural performance. For filtered motions (derived from site response analyses) applied to the foundation models, the structural response quantities progressively increased for the flexible foundation model cases above the fixed base response case, with the Winkler foundation producing the most severe response. It is important to recognize that these analyses predicted that structural forces, not only displacements, may be increased by SSPSI. Unfiltered records were also applied to the foundation models, and although the flexible foundation model responses exceeded the fixed base model, an opposite trend was observed for the filtered records, i.e., structural response quantities decreased with increasing foundation flexibility. An important conclusion, therefore, is that SSPSI effects may exhibit an important frequency dependence.
3.3.10 Alaskan Way Viaduct
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Kramer (1995) studied seismic vulnerability of the Alaskan Way Viaduct in Seattle for WSDOT, a structure of similar design, construction, and age as the Cypress Freeway in Oakland, California, which catastrophically collapsed in the 1989 Loma Prieta earthquake. The viaduct is a 2.2 mile long double deck reinforced concrete structure founded on cast-in-place, precast concrete, composite timber/concrete, and steel H piles. The alignment is underlain by soft sediments, historically a tideflat area later reclaimed by hydraulic filling, and susceptible to liquefaction. The computer code DYNA4 (Novak et al. 1993) was used to evaluate foundation stiffness and damping coefficients for use in a dynamic structural analysis, not considering liquefaction; the analysis was conducted at the assumed primary response frequency of the structure. Interestingly, pile group interaction was not considered with the rationale that using soil parameters from samples recovered at a distance from the actual piles would be compensated for by the intergroup densification due to piledriving (?!). To account for soil-pile nonlinearity, static nonlinear p-y pile analyses were performed using a modified version of COM624, and the pile deflectioncompatible soil moduli recorded at each lateral load level were used to compute soil modulus reduction factors to be used in the DYNA4 analysis. The overall structural response using this foundation model was found to be similar to a fixed base assumption. With respect to liquefaction, the viaduct foundations were judged to be subject to potential loss of lateral support and bearing capacity. But the critical liquefaction failure mode was governed by lateral spreading and failure of the timber pile-supported seawall retaining the reclaimed shorefront on which the viaduct was constructed. Four typical pile-supported seawall sections were modeled with the finite difference computer code FLAC (Itasca, 1993) in a pseudo-static manner, using post-liquefaction residual soil
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strengths. The analysis predicted large ground instabilities and damaging lateral spreading, thereby necessitating remediation and ground improvement measures.
3.3.11 Caltrans Liquefaction Mitigation Jackura and Abghari (1994) recount methods for analysis and mitigation of liquefaction hazard at three pile-supported bridge structures in San Diego and the San Francisco Bay Area. Both loss of lateral pile support and loads imposed due to lateral spreading were identified as design concerns in these cases, and the analyses focused on the survivability of the substructures. A common design approach consisted of selecting liquefied p-y curve criteria based on site specific information, and applying peak superstructure inertial force contributions computed from SHAKE91 and SUMDES (Li et al., 1992) -derived site specific acceleration response spectra to a single pile analysis code BMCOL76 (Matlock et al., 1981). Where judged a hazard, additional loads from lateral spreading were applied to the pile. Group and/or dynamic effects were not considered. Pile failure was predicted under the design loadings for the three sites studied. Stone columns and ductile piles were employed to mitigate the liquefaction hazard at these sites and improve foundation capacity.
3.3.12 Port Mann Bridge Another case involving liquefaction hazard is reported by Chang et al. (1995) in their study of the seismic vulnerability of the Port Mann Bridge near Vancouver, British Columbia. A number of the bridge pier locations were originally densified with ground improvement methods, but this analysis indicated that at several piers flowslides and loss
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of bearing capacity remained a possibility. Extensive site investigation and laboratory testing was performed to provide suitable parameters for the geotechnical analyses. At the main span pier N1, supported by 164 24 in diameter steel pipe piles each 144 ft deep, arrayed in a sheetpile cofferdam filled with densified sand and a concrete cap, a flowslide of the surrounding loose sands was studied. A 2-D finite element model of the piles, cofferdam, sheetpiles, cap, and surrounding soil was analyzed with pre- and postliquefaction soil strengths using the computer code SSCOMPPC (Boulanger et al., 1991), subject to the lateral flowslide loads applied to nodes of the sheetpiles. Pile lateral loaddeflection curves were calibrated against a simultaneous GROUP (Reese et al. 1990) analysis. The results indicated formation of plastic hinges in the piles at the base of the densified sand and below the tip of the sheetpiles. Foundation stiffness factors for use in a global structural analysis were developed using GROUP, with no adjustments made for group interaction (due to large pile spacings) or for cyclic degradation (based on laboratory and field test observations). Further ground improvement was recommended to mitigate the discerned liquefaction hazards.
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3.4 Summary of SSPSI Analytical Methods A comprehensive survey of analytical methods dealing with SSPSI has been made. Techniques for the analysis of single piles and pile groups under static, cyclic, and dynamic loading have been described. It has been shown that the nonlinear dynamic response of pile groups, with coupled superstructure response, has not been adequately resolved by the profession. Instead, approximate methods for extending static and single pile analyses to this complex problem is the norm, which ignores significant characteristics of SSPSI including nonlinear response, degradation of resistance, frequency dependence, dynamic load distribution, and group effects.
A review of building code requirements and a
representative sampling of design case histories further this conclusion, i.e. the state of practice for SSPSI is fragmented and falls behind the state-of-the-art. Efforts to expand the database of case histories and to validate analytical models for SSPSI are recounted in the following chapter dealing with previous experimental work.
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CHAPTER 4
PREVIOUS EXPERIMENTAL WORK
4.1 Introduction A wide range of field and laboratory experiments has been performed by researchers attempting to provide parameters for and to validate SSPSI analytical methods. These experimental methods have been concerned with the load-deformation behavior of soil-pile systems both singly and in groups, at small to large strains, loaded statically, cyclically, dynamically, or seismically, by exciting the pile head or the soil mass, and covering a variety of pile types and soil conditions. In-situ tests have the advantage of providing “correct” soil and pile stress conditions, whereas laboratory tests offer the flexibility and economy of making parametric studies in a controlled environment.
Taken together, field and laboratory tests of soil-pile interaction
complement each other and provide a valuable body of data where recorded SSPSI response is lacking. The following sections provide a comprehensive survey of soil-pile experimental research published in the literature; the purpose of such a review is to understand the adequacy of previous work and the dimensions of further research needs. Attention is particularly focused on experimental work applicable or directed to SSPSI in soft clays.
4.2 Full Scale Pile Test Programs Pile load test programs conducted in the field offer the distinct advantages of utilizing real soil, real piles, and realistic soil-pile stress conditions. They are limited in the sense that loading is applied in a “top down” fashion, concentrating the effects of
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inertial interaction and ignoring the effects of kinematic interaction.
This section
recounts selected case studies of single pile lateral load tests, as well as a complete survey of pile group lateral load tests and pile dynamic tests reported in the english language literature.
4.2.1 Field Single Pile Lateral Load Tests Of the innumerable field load test programs performed, three are particularly notable in that they exert a disproportionate influence on engineering practice, as they have been codified in API design recommendations and are programmed as default soil properties in the COM624P and LPILE computer programs (which are universally used for the design of laterally loaded piles).
These field load tests were performed by
Matlock (1962) in soft clay, Reese et al. (1975) in stiff clay, and Reese et al. (1974) in sands. A typical example of the setup for a pile lateral load test is shown in Figure 4.1; the American Society for Testing Materials publishes standardized procedures for conducting such load tests under specification ASTM D-3966 (ASTM, 1996).
Figure 4.1 - Example of Pile Load Test Set Up for Combined Lateral and Axial Load (after ASTM, 1996)
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Matlock (1962) performed an integrated field and laboratory study that included static, cyclic, and post-cyclic lateral head loading of 12.75 in diameter steel pipe piles embedded 42 ft deep at two different soft clay sites at Lake Austin and Sabine, Texas. The undrained shear strength of the soils at these two sites ranged from 300 to 800 psf in the upper soil layers. The principal conclusions of his study were: •
The soil resistance-pile deflection (p-y) relationship is highly nonlinear and inelastic, with characteristic pile bending moment patterns (see Figure 4.2).
•
Static and cyclic nonlinear soil-pile response is most severe at shallow depths, and approaches linear response at greater depths.
•
For engineering purposes, the fundamental p-y relationship is independent of pile head fixity (although pile forces are strongly related to fixity).
•
After a large number of cycles of loading and degradation of resistance, the soil-pile system tends to stabilize (a condition known as “shakedown”).
•
An important effect of cyclic loading is gapping, with high transient pile forces developed while traversing the gap.
•
Response during reloading after cycling is governed by soil resistance being reduced for deflections smaller than those previously attained.
This seminal work has guided the field of laterally loaded pile research, and has also exerted due influence on SSPSI analyses. In their similarly conducted tests, Reese and his co-workers (1975) drove 6 and 24 in diameter steel pipe piles into a stiff, fissured, overconsolidated clay deposit near Austin, Texas; their site had been pre-excavated 3 ft, and water impounded at the surface to simulate conditions that exist at the ocean floor. Unconfined compressive strengths of
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Figure 4.2 - Characteristic Fixed Head Laterally Loaded Pile Bending Moment Pattern (after Matlock, 1962) 2 to 4 tsf were found at this site in the upper 20 ft. Reese found a much greater degree of cyclic degradation of soil resistance in his tests than Matlock found in soft clay; the impounded water was thought to have contributed to scour of the soil in the soil-pile gap that opened during each cycle of loading, thereby further degrading resistance. It is important to consider that the period of cyclic loading in these tests was in excess of 15 seconds, and the observed scour effect could be expected to vary with loading rate. P-y curves for a series of depths in static and cyclic loading are shown in Figure 4.3, with results presented for a series of depths; they reflect the tendency for the p-y relationships to become linear at depth.
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Figure 4.3 - P-Y Curves Developed from Static and Cyclic Lateral Load Tests on 24-in Diameter Pile in Stiff Clay (after Reese et al., 1975) Gill (1968) conducted a series of field tests on 4.5 to 16 in diameter steel pipe piles driven into San Francisco Bay Mud at Hamilton Air Force Base in Novato, California. The field tests consisted of lateral head loading tests and segmental pile tests, the latter accomplished by horizontally loading small (4 – 12 in tall) detachable segments of the pile which had been driven to a predetermined depth of interest. The tests were conducted in both flooded and dry areas, where the undrained shear strength measured insitu by vane shear ranged from 600 - 1200 psf in the flooded area, and up to 2600 psf in the top dessicated zone of dry sites.
Figure 4.4 depicts Gill’s experimental results
superimposed with groundline deflections computed for this study by COM624P, the latter using pile and soil properties provided by Gill; the analysis was conducted as a “blind” prediction, with no iteration on input parameters to optimize the results. The analysis very well predicts deflections recorded in the field for the two smaller pile types,
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20 Test P-2 Flooded
Test P1 - Flooded Experimental COM624P
0
Lateral Load (K)
20 Test P-3 Flooded
Test P-4 Flooded
Test P-5 Dry
Test P-6 Dry
Test P-7 Dry
Test P-8 Dry
0 20
0 20
0 0
0.5
1
1.5
2
Groundline Displacment (in)
0
0.5
1
1.5
2
Groundline Displacement (in)
Figure 4.4 - Static Lateral Load Test Results for Piles at Dry and Flooded Bay Mud Sites, Superimposed with COM624P Predicted Response (after Gill, 1968)
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but overpredicts the stiffness of the two larger diameter piles. In fact the pile EI values published by Gill for the two larger diameter piles in particular seem 30 % high, given standard pipe sizes and steel properties, but reducing these EI values to a reasonable range has only a moderate effect on reducing lateral pile stiffness. These trends also run counter to the diameter effect observed by Stevens and Audibert (Section 3.1.2). The overall conclusion is that the lateral response of piles in Bay Mud at this site is inconsistently (and potentially unconservatively) captured by the default Matlock and Reese p-y curve criteria, and could possibly be improved with site specific p-y curve construction. After the 1985 Mexico City earthquake, Jaime et al. (1989) conducted cyclic axial load tests on friction piles driven in Mexico City clay, and concluded that the performance of these foundations during the earthquake was a function of the initially applied static load. In these tests, when the total applied cyclic load Pmax did not exceed the ultimate static capacity Pult, the piles behaved elastically, with rate-dependent stiffness and strength increasing under dynamic loading. As Pmax ranged from 1.0 to 1.2 Pult, permanent displacements ensued, and when Pmax exceeded 1.2 to 1.3 Pult, large permanent displacements and a loss of capacity occurred. The results of a parallel finite element study were in agreement with the field test results, and indicated that interaction between group piles would be greatly reduced due to nonlinearity arising from soil-pile slippage.
4.2.2 Field Pile Group Lateral Load Tests Several field load tests on pile groups are reported in the literature, and are summarized in Table 4-1. These tests have been conducted on a variety of pile types,
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pile type Reference (B= some battered piles) Feagin (1937) timber (B) Wagner (1954) timber Peck (1961) step-taper (B) Matsumoto et al. (1962) reinforced concrete (B) Kim and Brungraber (1976) steel HP (B) Bartolomey (1977) prestressed concrete Kim et al. (1979) steel HP (B) Stevens et al. (1979) timber Matlock et al. (1980) steel pipe Matlock et al. (1980) steel pipe Schmidt (1981) drilled shaft Holloway et al. (1982) timber Schmidt (1985) drilled shaft Meimon et al. (1986) steel HP Brown et al. (1987) steel pipe Brown et al. (1988) steel pipe Abacarius (1991) concrete fill steel pipe Abacarius (1991) concrete fill steel pipe Kobayashi et al. (1991) steel pipe Kimura et al. (1993) drilled shaft Ruesta and Townsend (1997) prestressed concrete Rollins et al. (1998) concrete fill steel pipe Weaver et al. (1998) concrete fill steel pipe
pile diameter (in) 12 - 14 16 13 18 10 12 10 12 - 14 6 7 47 14 47 12 10.75 10.75 12 12 6 39 30x30 12.75 12.75
pile length (ft) 30 34, 39 40 49 40 16, 40 40 43 - 45 45 45 52, 92 35 28 25 43 43 60 15 22 82 46 30 30
pile pile pile head group spacing fixity 6, 8, 9 3d cast 1x2 ? cast 3 4 - 8d cast 1, 4, 6 2.4 - 2.9d cast 3x3 3.6, 4.8d cast 4, 6 3d, 4d cast 3x3 3.6, 4.8d cast 8, 12 3d cast 5 3.4d fixed 10 1.8d fixed 1x2 1.3, 2.4d free 2x4 3d cast 2, 3 3d free 2x3 3d free 3x3 3d free 3x3 3d free 11, 17 3d cast 10, 12 3d cast 3x3 3.3d free 1x2 2.8d cast 4x4 ? ? 3x3 3d free 3x3 3d free/fixed pile cap above grade above grade at grade above grade partial embed above grade above grade above grade load frame load frame load frame above grade load frame load frame load frame load frame partial embed partial embed load frame above grade above grade load frame partial embed
Table 4-1 Field Pile Group Loading Tests
pile installation soil conditions driven sand driven glacial till driven sandy silt driven peat, clay driven silty clay driven clay driven silty clay jetted/driven clay, sand driven soft clay driven soft clay cast in place silt, marl jetted/driven alluvium cast in place med. dense sand driven clay driven stiff OC clay backfilled med. dense sand driven bay mud driven sandy silt driven sandy clay cast in place soft silt driven sand driven clayey silt driven clayey silt
test loading static static static static cyclic load static cyclic load static cyclic displ. cyclic displ. static static to failure cyclic load cyclic load cyclic defl. cyclic defl. static to failure static to failure static cyclic static to failure static statnamic
max. # of cycles 1 1 1 1 3 1 3 1 100's 100's 1 1 40 10000 900 900 3 2 3 3 1 3 1
generally of smaller diameter and shorter length, driven in a gamut of soil conditions, and loaded both statically and cyclically. The size of the pile groups has been limited by the capacity of external loading equipment, so small pile groups at close to intermediate spacing have been the norm. The first pile group lateral load tests reported in the literature are by Feagin (1937), who performed field tests on groups of 32 ft long timber piles at Lock and Dam No. 26, Alton, Illinois. The soil conditions at this site were sandy alluvium, and the piles were installed by a combination of jetting and driving. The focus of the test program was to investigate the relative lateral resistance of vertical and battered piles, in all conceivable combinations and orientations to the direction of loading. The superior performance of battered piles under lateral load was clearly evident. Kim and Brungraber (1976) drove 2x3 groups of vertical and battered H-piles in cohesive soil, and aroused much discussion with the reporting of their test results. They compared the pile group per pile performance (fixed head condition) to single (free head) reference piles driven nearby, and computed pile group efficiencies in excess of unity, contrary to conventional notation. The group piles were joined by a pile cap, the bottom of which was cast against the ground surface, which introduced a potential for pile cap base frictional contribution to lateral resistance. In response to their critics, Kim et al. (1979) published the results of a second series of tests where 4 in of soil beneath the pile caps had been excavated to relieve any potential frictional resistance. They concluded that the pile cap base friction contribution was negligible for battered pile groups, but significant for vertical pile groups.
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Figure 4.5 - Field Pile Group Load Test Results Indicating Preferential Load Distribution to Leading Piles (after Holloway et al., 1982) The first field pile group load test program that clearly delineated group effects was performed by Holloway et al. (1982), who revisited Lock and Dam No. 26 in a study of rehabilitation schemes for the facility. They installed timber piles with the same construction techniques as originally used in the 1930’s, and tested a 2x4 pile group to failure. One of the key results was experimental evidence of pile group “shadowing”, i.e. the preferential load carrying capacity of piles in front of the line of loading, thereby reducing load on piles at the rear of the line of loading.
This load distribution is
illustrated in Figure 4.5. Brown et al. (1987, 1988) performed cyclic lateral load tests on 3x3 pile groups in stiff clay and sand, and provided detailed evidence of pile group effects.
Their
conclusions can be summarized as follows, and are reflected in Figures 4.6a and b. •
Pile group deflections exceed single pile deflections under equivalent per pile load.
•
Pile group bending moments exceed those for single piles, and are shifted deeper.
•
Pile group maximum soil resistance is reduced relative to single piles under both static and cyclic loads, and is most pronounced at depth.
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•
The greatest portion of shear on the pile group is distributed to piles in the front row, and variations in load within the group are approximately 20 %.
Pile group cyclic loading effects were found to contribute to degradation of soil resistance at the stiff clay soil site, but densification at the sand soil site prevented any loss of capacity.
(a)
(b) Figure 4.6 - Field Pile Group Load Test Results Depicting; a) Cyclic Degradation of Resistance; b) Distribution of Load by Row (after Brown et al., 1987) Abacarius (1990) statically loaded pile groups to failure that supported two bents of the then demolished Cypress Freeway that had catastrophically collapsed in the 1989 Loma Prieta earthquake. The two bents were founded on 60 ft long concrete filled steel
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pipe piles in Bay Mud, and 15 ft long piles in sandy silt, respectively. The pile groups ranged in size from 10 to 17 piles, and the pile caps were partially embedded. The basic conclusion of the test program was that the Caltrans presumptive lateral resistance of 5 kips for this pile type at ¼ in deflection was extremely conservative, as experimental values ranged from 17.7 to 32.9 kips. This however did not take into account the passive resistance offered by the pile cap, which may be significant, and the report does not provide sufficient information to evaluate those effects. Rollins et al. (1998) investigated pile group effects with field lateral load testing of a 3x3 group (and a single pile) consisting of 12.75 in diameter concrete filled steel pipe piles spaced at 3d and driven 30 ft into lightly overconsolidated layered silts, clays, and sands.
They found that pile shadowing resulted in the maximum load being
distributed to the front row of piles, and that more load was distributed to the back row than the interior piles, in contrast to Brown’s findings. Rollins and his co-workers also observed higher bending moments in group piles than in the single pile at the same average load level, particularly at higher load levels. As they note, this has important implications for the common engineering practice of extrapolating single pile test results to group behavior. They simulated the single pile response with the computer code LPILE, and found that using a detailed soil profile rather than an averaged one produced good results. They also proposed p-multipliers for this soft soil site ranging from 0.6 for the front row piles to 0.4 for the interior and back piles, which are lower values than those proposed by other researchers. Weaver et al. (1998) followed Rollins’ work by conducting statnamic lateral loading tests on the same 3x3 pile groups, in both fixed and free head conditions, and
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with and without pile cap embedment. They found that the dynamic resistance was 30 to 50 % higher than the static resistance for a free head pile and for the fixed head group without cap embedment, and 100 to 125 % higher for the fixed head group with cap embedment.
They attributed the increased resistance mainly to damping and
acknowledged that further work needs to be done in interpreting statnamic test results.
4.2.3 Field Pile Dynamic Tests In order to ascertain pile stiffness under dynamic loads, researchers have conducted three classes of tests on full-scale piles and pile groups in the field. In all three types of tests, a mass is commonly fixed to the pile head to accentuate the resonant response and damping characteristics of the pile. Ringdown tests consist of quickly releasing the pile from some imposed, initial lateral displacement, and measuring the ensuing free vibrations of the pile as it attempts to rebound to its original position. Pile stiffness and damping values can be derived from measurements of the free vibrations of the pile by the logarithmic decrement method. Impact tests are an even smaller strain version of a ringdown test, where a blow to the pile generates free vibrations in the pile to be measured. Forced vibration tests involve mounting an eccentric mass shaker to the pile head, whose motors spin eccentrically fixed masses, thereby inducing vibrations into the pile head. By adjusting the orientation, motor speed, and fixed mass, this test offers the flexibility of generating horizontal, vertical, or rocking vibrations over a range of frequencies and amplitudes. Electrodynamic oscillators are also employed in forced vibration tests, and can deliver much higher frequencies to the pile head than the mechanical type, which is limited to about 100 Hz. Soil-pile stiffness and damping can
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be interpreted directly from the test data resonance curves with the half-power bandwidth method. Comparisons of observed and predicted behavior are good when the response remains linear and soil elastic properties are well-characterized.
Conversely, when
higher load levels generate nonlinear soil-pile response, models of predicted response are less accurate. Cases of field pile dynamic tests reviewed are summarized in Table 4-2, with the following general observations followed by comments on selected test programs: •
Soil-pile dynamic response is highly site dependent.
•
Soil-pile dynamic response is frequency and load level dependent.
•
Soil-pile vertical stiffness exceeds soil-pile horizontal stiffness.
•
Pile cap embedment increases soil-pile dynamic stiffness and damping.
•
Soil-pile nonlinear response decreases both stiffness and damping.
•
Pile group effects are frequency, pile spacing, and site dependent, and are more pronounced for stiffness than damping.
•
Elastic continuum analytical models incorporating a “weak zone” around the pile, soil-pile gapping, and a parabolic variation of modulus with depth appear to provide a reasonably good level of accuracy for the cases studied. Petrovski and Jurokovski (1973) dynamically tested single piles and four pile groups
of drilled shafts in loose sandy soil, with different conditions of pile cap embedment. The contrast between linear and nonlinear response is shown in Figures 4.7a and b, which depict stiffness and damping degradation at increasing load levels in the latter figure as a result of pile cap resistance removed relative to the first case. In a unique approach, the Soviet researcher Grib (1975) reports on field piles excited by a series of explosive charges timed to have “earthquake-like” characteristics. Grib’s
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results and analysis were not especially impressive, but his experimental method does hold promise as it overcomes the limitation of applying dynamic loads directly to the pile head, rather than through the free-field soil. This explosive excitation method has also been performed for soil-structure interaction tests (no piles) in the SIMQUAKE experiments in the 1970’s and in centrifuge experiments by Zelikson et al. (1982).
(a)
(b)
Figure 4.7 - Dynamic Pile Response from Forced Vibration Tests: a) Linear Response; b) Nonlinear Response due to Removal of Supporting Soil Near Pile Head (after Petrovski and Jurokovski, 1973) Scott et al. (1982) conducted horizontal forced vibration and ringdown tests on an instrumented steel pipe pile driven into silty sand, and in a parallel study modeled the observed field response in centrifuge tests.
The extensive field instrumentation
monitored pile bending moments, pile head displacement and acceleration, pore pressures in the surrounding soil, and ground surface velocity in the free-field (Figure 4.8).
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pile pile diameter length Reference pile type (in) (ft) Hayashi et al. (1965) steel pipe 47 ? Hayashi et al. (1965) steel HP 12 ? Ishii and Fujita (1965) steel pipe 42, 59 109 Maxwell et al. (1969) concrete fill steel pipe 14 46 Maxwell et al. (1969) steel HP 14 52 - 88 Maxwell et al. (1969) steel HP 14 52 Alpan (1973) reinforced concrete 12 15 Hakuno (1973) steel pipe 24 197 Petrovski and Jurokovoski (1975) drilled shaft 20 49 Grib (1975) concrete, steel pipe 6 - 12 11 - 16 Gyoten et al. (1980) steel pipe 24 47, 87 Gyoten et al. (1980) concrete 24 47 Scott et al. (1982) steel pipe 24 40 Scott et al. (1982) steel pipe 24 40 Gle and Woods (1983) steel pipe 12.75, 14 50 - 160 Jennings et al. (1984) steel pipe 18 22 Mizuhata and Kusakabe (1984) steel pipe 26, 32 142 Blaney and O'Neill (1986) steel pipe 10.75 44 Blaney et al. (1987) steel pipe 10.75 43 Crouse and Cheang (1987) concrete fill steel pipe 12 38 Blaney and O'Neill (1989) steel pipe 10.75 43 Wakamatsu (1989) cast-in-place barette 28x5, 14x5 16 Hakulinen (1991) reinforced concrete 12x12 23 Hakulinen (1991) concrete fill steel pipe 10.75 23 Kobori et al. (1991) drilled shaft 23.6 24.6 Kobori et al. (1991) drilled shaft 23.6 24.6 Kobori et al. (1991) drilled shaft 23.6 24.6 Fuse et al. (1992) steel pipe 59 164 Han and Vaziri (1992) drilled shaft 12.5 25 Mizuno and Iiba (1992) steel pipe 16 20 Mizuno and Iiba (1992) prestressed concrete 14 20 Mizuno and Iiba (1992) steel pipe 4 20 Puri and Prakash (1992) reinforced concrete 18 56 Puri and Prakash (1992) reinforced concrete 18 56 Puri and Prakash (1992) reinforced concrete 18 56 Sy and Siu (1992) drilled shaft 20 27 Sy and Siu (1992) drilled shaft 20 27 Sy and Siu (1992) drilled shaft 20 27 Tuzuki et al. (1992) prestressed concrete 24 95 Kramer (1993) steel pipe 8 49 Kramer (1993) steel pipe 8 49 Kramer (1993) steel pipe 8 49 Carrubba and Maugeri (1996) drilled shaft 47 190 Han and Cathro (1996) drilled shaft 12 25 Imamura et al. (1996) precast concrete 18 49 pile group n.a. n.a. n.a. n.a. n.a. 2x2 n.a. n.a. 1, 4 2x2 1, 5 1, 6 n.a. n.a. n.a. n.a. n.a. n.a. 3x3 8, 16 3x3 n.a. 2x2 n.a. 2x2 2x2 2x2 7x8 2x3 1, 2, 4 1, 2, 4 2x2 n.a. n.a. n.a. n.a. n.a. n.a. 1, 2, 4 n.a. n.a. n.a. n.a. 2x3 1, 2x2
pile spacing n.a. n.a. n.a. n.a. n.a. ? n.a. n.a. ? ? ? ? n.a. n.a. n.a. n.a. n.a. n.a. 3d 4.6d 3d n.a. 5d n.a. ? ? ? 2.6d 2.8d 3.8, 4.3d 3.8, 4.3d 3.8, 4.3d n.a. n.a. n.a. n.a. n.a. n.a. 2.8, 5.6d n.a. n.a. n.a. n.a. 2.8d 6.7d
pile head fixity ? ? ? cast cast cast fixed ? cast ? ? ? free free ? free cast free cast cast cast cast ? n.a. cast cast cast cast cast cast cast cast free free free free free free cast free free free free cast cast pile cap soil conditions test loading n.a. silty clay horizontal FV n.a. sand horizontal FV n.a. soft clay horizontal FV n.a. fat clay, sand vertical FV n.a. fat clay, sand vertical FV above grade fat clay, sand vertical FV n.a. plastic clay ringdown n.a. fine sand horizontal FV embed / above loose sand horizontal FV ? silty dense sand explosive n.a. sand FV / ringdown n.a. sand FV / ringdown n.a. silty sand horizontal FV n.a. silty sand ringdown n.a. sand, clay FV / ringdown n.a. silty sand horizontal FV n.a. sand, clay horizontal FV n.a. stiff OC clay horizontal FV above grade stiff OC clay vertical FV embedded loose sand ringdown above grade stiff OC clay horizontal FV above grade fill, loam, gravel horizontal FV above grade sand, clay horizontal FV n.a. sand, clay horizontal FV above grade sand horizontal FV at grade sand horizontal FV embedded sand horizontal FV partial embed clay, gravel, sand horizontal FV above grade silty clay horizontal FV embed / above loam, sand, clay horizontal FV embed / above loam, sand, clay horizontal FV embed / above loam, sand, clay horizontal FV n.a. clayey silt horizontal FV n.a. clayey silt vertical FV n.a. clayey silt ringdown n.a. fill, silt, sand horizontal FV n.a. fill, silt, sand vertical FV n.a. fill, silt, sand rocking FV above grade sand horizontal FV n.a. peat horizontal FV n.a. peat ringdown n.a. peat horiz. impact n.a. peaty clay horizontal FV above grade silty clay horizontal FV above grade sand horizontal FV
Table 4-2 Field Pile Dynamic Loading Tests freq. range (Hz.) 0.5 - 1.5 1-9 0.7 - 1.3 2 - 16 2 - 16 2 - 16 n.a. 3 - 10 2 - 40 n.a. ? ? 1.5 - 8.5 n.a. 5 - 55 2 - 14 2 - 60 1 - 15 5 - 95 n.a. 2 - 50 0.2 - 20 2 - 20 2 - 20 1 - 20 1 - 20 1 - 20 2.8 - 15 5 - 50 2 - 25 2 - 25 2 - 25 6 - 20 n.a. n.a. 6 - 30 10 - 110 20 - 55 1 - 20 1.8 - 2.9 n.a. n.a. 0 - 25 0 - 40 1 - 20
max. resonant accel. freq. damping (g) (Hz.) (%) ? 1 ? ? 5.8 ? ? 1 - 1.1 5 ? 8-9 5 ? 6-9 4-9 ? 8-9 10 ? 12.2 5.4 ? 4-5 7 0.066 13 - 18 10.5 - 39 ? 2-5 ? ? 4.2 -12.1 4 - 14 ? 5.1 - 16.2 9 - 12 0.265 1.7 - 2.9 1.5 - 7 ? 4.1 - 4.3 1.4 - 2.8 ? n.a. ? ? 8.1 7.7 ? 7.5 - 10 ? 0.1 2.1 - 2.3 10 - 11 ? 68 26 ? 3.8 - 6.3 5 - 15 ? 7.5 12 1.00 3 - 12 4 - 15 ? 13.8 - 15.8 10 - 25 ? 6 - 20 2 - 15 ? 7 ? ? 8.2 ? ? 9.8 ? ? 1.4 - 3.2 20 ? 22 ? ? 10 - 14 ? ? 10 - 15 ? ? 9 - 13 ? ? 10.3 ? ? 32.2 ? ? 11.5 ? ? 6.5 - 7.1 4 ? 46.5 - 50.4 5 ? 38.5 - 40.8 3 ? 10 - 13 ? 0.5 n.a. 15 - 20 0.15 2.3 - 5.5 25 - 33 ? 5.27 30 - 35 ? 12.5 ? ? 16 - 24 20 - 34 ? 3.2 - 6.3 4.1 - 12.8
Maximum pile head accelerations reached 0.265 g, which unlike many smaller amplitude tests, is representative of seismic loading. At higher loading levels, partial liquefaction was observed around the pile head, considerably reducing pile stiffness. Damping values were relatively small (1 - 7 %) and were observed to increase with the amplitude of pile motion, until the onset of liquefaction. Resonant frequencies observed in low level forced vibration and ringdown tests were considerably different, 2.3 to 2.9 versus 4.1 to 4.3 Hz, respectively.
Ting (1987) computed p-y curves from the test results and
compared them to API recommended curves, which were found to overestimate the observed stiffness due to the nonlinear response, gapping, and partial liquefaction that occurred. In a recent publication, Lam and Cheang (1995) released cyclic load test data from a second test program conducted at the same site in order to compare dynamic p-y curves with cyclic p-y curves; this proprietary information had remained unpublished for a number of years. Tests were made on a pile newly installed, and on a pile previously subjected to vibratory loading; the load-deformation measurements of the two piles were nearly identical, indicating that the prior vibratory load did not result in permanent changes to the soil-pile system. Free-head resistance to lateral loading was found to be greater than fixed-head resistance, due to the mobilization of additional frictional resistance in the free-head rotational deformation mode; the authors assert this mechanism contributes to the “diameter effect” observed by Stevens and Audibert (1979). The soil-pile stiffness under cyclic loading compared very favorably to the low amplitude dynamic loadings, but nonlinear response under large amplitude dynamic loads reduced the apparent stiffness by 80 %. This was attributed to drained versus undrained soil behavior in the two types of tests.
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Figure 4.8 - Field Pile Forced Vibration Test Set Up (after Scott et al., 1982) Crouse and Chang (1987) performed ringdown tests on vertical and battered concrete filled steel pipe pile-supported transformers with pile caps embedded in surficial loose, sandy, saturated soils. Observed resonant frequencies and damping values were less than those predicted by simplified numerical models by 10 – 30 %, and the low damping values in particular suggested suppressed pile cap-soil interaction. The authors observed that the site experienced peak ground accelerations of 0.06 - 0.1 g during the 1965 magnitude 6.5 Puget Sound earthquake, which may have induced settlement of the loose sandy soil away from contact with the pile cap. When ignoring cap embedment contact effects, predicted and observed values showed excellent agreement. Blaney et al. (1987) and Blaney and O’Neill (1989) dynamically tested a 3x3 group of steel pipe piles driven into overconsolidated clay. The two publications report the results of vertical and horizontal forced vibration tests, respectively. A prime conclusion from the first study was that the average group pile frequency response was stiffer and
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more damped than that of an equivalent single pile. This was concluded to be related to wave interference in the group, but was cautioned not to be taken as a universal result, but one highly dependent on the soil properties and pile spacing at this site. In contrast, under horizontal vibration, the average group pile frequency response was more flexible and less damped than that of an equivalent single pile. Numerical models incorporating the observed soil-pile gapping were found to more accurately capture the measured response. Kobori et al. (1991) conducted an extensive series of tests on a pile group with different pile cap contact/embedment conditions that consisted of horizontal forced vibration tests and earthquake observations, in order to evaluate both inertial and kinematic interaction effects. The pile group was composed of four drilled shafts, and is shown schematically in Figure 4.9a. The three pile cap conditions included no contact, grouted contact with the soil surface, and complete backfilled embedment. The forced vibration test results are shown in Figure 4.9b, indicating the strong influence of backfill embedment on group stiffness; damping values were not tabulated. At the completion of the forced vibration tests, the earthquake observations commenced; the maximum observed MHA at the site was 0.08 g. Transfer functions of pile cap to free-field ground surface motions are shown in Figure 4.9c, with decreasing amplitude at resonant frequency with pile cap contact/embedment. Impedance functions for the three pile cap conditions were derived, and using SHAKE (method A) and a finite element method (method B) to compute free-field input, motion at the top of the block was computed and compared favorably with the observed records, as shown in Figure 4.9d.
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(a) Figure 4.9 - Field Pile Forced Vibration Test and Earthquake Observation: a) Test Set Up and Seismometer Arrangement; b) Forced Vibration Tests Results Illustrating Influence of Lateral Support Condition; c) Structure to Free Field Transfer Function for Three Backfill Cases; d) Observed and Computed Response Spectra for Seismic Event (after Kobori et al., 1991)
(c)
(d)
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As part of a foundation investigation for a pile-supported bridge spanning a peatfilled slough near Seattle, Kramer (1993) performed forced vibration, ringdown, and impact tests on an 8 in diameter steel pipe pile. Unfortunately, the test results of different methods were inconsistent and in some cases ran contrary to expected trends of behavior, partially echoing Scott’s findings; the lack of uniformity between test results could perhaps be attributed to shakedown effects. Radiation damping in excess of 25 % was recorded in the free vibration tests, and average horizontal stiffness was interpreted from the forced vibration test results. The latter value correlated reasonably well to static lateral load test results, and was therefore used in deriving the design dynamic stiffness of the pile groups. Finally, brief reference is made to other noteworthy experimental programs including Fuse et al. (1992) who dynamically tested a 7x8 pile group (the largest full scale group reported in the literature), and Mizuno and Iiba (1992) who reported on a welldocumented parametric study of pile cap embedment, pile spacing, number of piles, and soil nonlinearity on soil-pile dynamic response.
4.3 Model Scale Pile Test Programs Model pile tests have offered a wealth of information for SSPSI studies, but they must be carefully considered in the context of the particular scale model testing method and its inherent limitations. Scale model tests are economical, versatile, and conducive to parametric studies and repeatability tests. A technique known as “modeling of models” can improve the confidence of the modeling methodology. Both kinematic and inertial interaction effects may be studied, and pile groups with attached superstructures can be
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readily constructed and tested. Principal limitations of scale model testing include the difficulty in fully satisfying all relevant scale modeling criteria, adequately replicating realistic soil-pile stress fields, and the boundary effects of test containers. This section will report on a wide variety of scale model testing programs dealing with SSPSI published in the literature; a small number of studies published in Japanese and as dissertations in England have not been reviewed here.
4.3.1 Model Pile Head Loading Tests A large number of tests on model piles are reported in the literature, and those tests consisting of static and cyclic lateral pile head loading are summarized in Table 4-3, with the inclusion of selected cases of axial head loading of model piles in clays. Wen (1955) was the first to report tests on model piles instrumented with strain gages in the literature, and focused his investigation on small groups of vertical and batter piles to ascertain distribution of axial and lateral loads. His findings regarding lateral load resistance of symmetric and asymmetric battered pile groups and the preferential distribution of load to front piles in the group were similar to Feagin’s (1937) test results on full scale pile groups tested in the field. As part of an integrated project investigating the lateral loading of piles in cohesive soils, Matlock and Ripperger (1957) conducted a suite of basic research tests. To appreciate the development of stress fields around a rigid cylinder laterally translating through an elastic medium, photoelastic studies of cylinders in gelatin were made and are shown in Figure 4.10. In stage (d) of the loading sequence, the rear face of the cylinder has separated from the gelatin and the resultant gap has lowered the stress in this zone;
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pile pile pile diameter wall length Reference model pile material (in) (in) (in) pile group Tschebotarioff (1953) wood rod - dolphins 1.625 - 2 n.a. 29 3, 7 Wen (1955) wood rod 1.5x1.5 n.a. 45 1x3 Matlock and Ripperger (1957) steel rod 1 n.a. 1-9 n.a. Gaul (1958) aluminum pipe 2.375 0.15 96 n.a. Shinohara et al. (1960) steel bar/steel pipe 0.7 - 11.8 ? 55.1 - 94.5 n.a. Matlock (1962) steel rod 0.375 n.a. 2 n.a. Prakash (1962) aluminum pipe 0.5 0.035 21 1, 2x2, 3x3 Kubo (1965) steel pipe/steel tube 0.7 - 4 ? 55.1 - 94.5 n.a. Davisson and Salley (1970) aluminum pipe 0.5 ? 21 1, 6, 96, 99, 245 Singh and Prakash (1971) aluminum tube 0.5x0.5 0.06 24 1, 2x2 Holmquist and Matlock (1976) aluminum pipe 1 0.03 40 n.a. Ranjan et al. (1977) aluminum pipe 0.4 - 0.8 ? 18.5 - 37.8 n.a. Allen and Reese (1980) aluminum pipe 1 composite 25 n.a. Georgiadis and Butterfield (1982) aluminum pipe 0.25 - 1 ? 24 n.a. Matlock et al. (1982) aluminum pipe 1 0.03 40 1, 6 Cox et al. (1983) stainless steel 1 0.03 2-8 1, 3x5 Franke and Muth (1985) PVC, PC, PE pipe 0.7 - 10.2 ? ? n.a. Kishida et al. (1985) acrylic resin pipe 0.8 ? 15.7 n.a. Maung (1985) PVC pipe 8.5 0.16 39.4 n.a. Meyerhof and Purkayastha (1985) steel pipe 0.5 ? 7.5 1 / 2x2 Meyerhof and Sastry (1985) steel pipe 2.9 0.28 43.3 n.a. Selby and Poulos (1985) aluminum pipe 0.6 0.05 20.5 2-9 Williams and Parry (1985) steel pipe 1.2 0.1 44.3 n.a. Smith and Slyh (1986) steel rod/steel pipe 0.7/2 n.a./0.19 3 - 25.5 n.a. Park (1987) concrete fill steel pipe 4.5 n.a. 93 - 104 1 / 1x2 Proctor and Khaffaf (1987) stainless steel pipe 1 ? 19.7 n.a. Franke (1988) PVC pipe 1.6 ? ? 1, 3, 8, 9, 16 Meyerhof et al. (1988) steel/wood/nylon pipe 0.5 ? 4 - 24 1 / 2x2 Shen et al. (1988) aluminum pipe 3.5 0.25 40 1 Shibata et al. (1989) aluminum/PVC pipe 0.8/0.9 0.06/0.09 31.5 2, 3, 4, 9, 16 Abduljauwad et al. (1990) steel pipe 1.1 0.06 30.5 n.a. Darr (1990) aluminum pipe 1 0.04 34 n.a. Adachi and Kimura (1992) aluminum tube 0.8 0.12 17.3 1, 1x2 Agaiby et al. (1992) drilled shaft 3, 6 n.a. 9 - 54 n.a. Mayne et al. (1992) drilled shaft 2 - 6.9 n.a. 10.5 - 41.3 n.a. Niiro et al. (1992) PVC pipe 1.5 0.16 11.3 1, 2, 3 Tanaka et al. (1994) steel pipe 4 0.13 78.7 1, 4, 6, 9 McManus and Chambers (1995) Poulos et al. (1996) aluminum pipe 1, 1.5, 2 0.05 - 0.08 14.8 - 26.5 n.a. Chen et al. (1996) aluminum pipe 1 0.05 26.5 2, 3, 4, 8 Bouckovalas (1996) aluminum pipe 0.75 0.12 15.7 n.a. Caliendo et al. (1996) aluminum pipe 1.315 0.331 60 n.a. Nagataki et al. (1996) reinforced concrete 4.9 n.a. 74.8 1x3 Gandhi and Selvam (1997) aluminum pipe 0.72 0.03 20 1, 2, 3, 4, 6, 9 Moss et al. (1998) aluminum pipe 1.315 0.133 60 1x5 Rao et al. (1998) aluminum/steel pipe 0.5,0.85,1 0.03 - 0.06 10 - 40 1, 2, 4, 6 n.a. above grade n.a. n.a. above grade above grade above grade above grade
inserted inserted inserted inserted pinned at base driven inserted inserted
dry calcareous sand dry calcareous sand remolded clay soft clay soft/very soft soil dry sand silty clay marine clay
static lateral static lateral static/cyclic axial static lateral static/cyclic lateral static lateral cyclic lateral static lateral
pile head fixity pile cap pile installation model soil test loading fixed above grade driven sand/silty clay static lateral fixed above grade driven dry fine sand static lateral fixed n.a. inserted remolded clay static lateral free n.a. pinned at base bentonite clay static/cyclic lateral free n.a. embedded saturated sand static lateral fixed n.a. inserted remolded clay static/cyclic lateral cast above grade embedded dry sand static/cyclic lateral free n.a. embedded saturated sand static lateral free/fixed at / above grade embedded dry sand static/cyclic lateral fixed ? ? medium sand static/cyclic lateral fixed n.a. inserted remolded clay static/cyclic axial free n.a. inserted remolded clay static lateral free n.a. inserted stiff, soft clay static lateral free n.a. inserted kaolinite clay static lateral fixed above grade inserted remolded clay cyclic axial fixed above grade inserted kaolinite/bentonite clay static lateral free n.a. embedded dry sand static lateral free n.a. inserted dry sand / remolded clay cyclic lateral free n.a. inserted soil-cement slope face static lateral free/fixed above grade inserted clay, sand static inclined fixed n.a. inserted clay/sand static inclined fixed above grade embedded/inserted dry sand static/cyclic lateral free n.a. inserted dense sand cyclic lateral fixed n.a. inserted clay / loose/dense sand static torsional/lateral free/fixed above grade embedded loose / medium sand static/cyclic lateral fixed n.a. inserted remolded clay cyclic axial free/fixed above grade embedded dry sand static lateral free/fixed above grade inserted loose sand / soft clay static lateral free n.a. embedded silty clay / sand static/cyclic lateral free above grade embedded dry sand static lateral free n.a. embedded saturated sand static/cyclic lateral free n.a. inserted fire clay static/cyclic inclined free none embedded dry sand static lateral free n.a. drilled/cast-in place dry sand static/cyclic lateral free n.a. drilled/cast-in place kaolinite/supersil static/cyclic lateral free/fixed above grade ? silty sand static lateral cast above grade driven dry sand, gravel cyclic lateral n.a free/fixed 2.5 - 7.5d free/fixed n.a. free n.a. free 48d fixed 4 - 12d fixed 3d free 3 - 10d free
pile spacing n.a. 4d n.a. n.a. n.a. n.a. 2 - 8d n.a. 3 - 4d 4d n.a. n.a. n.a. n.a. 1.8d 0.5 - 5d n.a. n.a. n.a. 3d n.a. 1.9 - 3.8d n.a. n.a. 6d n.a. 2d 3d n.a. 1.8 - 9.1d n.a. n.a. 2 - 5d n.a. n.a. 2.5, 3.5d 3d
Table 4-3 Model Pile Loading Tests
1 1 1006 1 ? 1 50 1
300+ 1 3
1 1 1 ? 1 100+ 100 1 4 115 280 1 1 1 267 1 1 ? 1 1 1 ? 6 1 ? 500+ 1 1 2500 1 150 50 1
max. # of cycles
the authors correctly deduced that this behavior would only apply to the near surface region of cohesive soil-pile systems. Tests were also made of fully buried model pile segments laterally pulled through a remolded clay soil, and rigid vertical pile segments laterally loaded in the remolded clay. These two test methods were intended to evaluate the deep soil-pile and near surface soil-pile response to lateral loading. Rate of loading, length to diameter ratio, and embedment depth were varied, and the nonlinear loaddeformation response was compared with results of field tests. In his project summary report, Matlock (1962) extended the laboratory test technique to cyclic lateral loading, and performed “pot tests” of rigid cylindrical pile segments vertically embedded in remolded clay, shown schematically in Figure 4.11 along with a representation of a typical loading cycle.
These tests, in conjunction with field studies, significantly
contributed to the current API recommendations for the construction of p-y curves in soft clay under static and cyclic lateral loads.
Figure 4.10 - Stress Fringe Patterns of Rigid Cylinder Laterally Translating in Elastic Medium (after Matlock and Ripperger, 1957)
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Figure 4.11 - a) Schematic of Pot Test; b) Typical Loading Cycle with Slack Zone while Traversing Gap (after Matlock, 1962) Gaul (1958) provided a detailed analysis of scale model similitude in his reporting of static and cyclic lateral loading tests of model piles in bentonite clay. Figure 4.12a depicts data from 1 Hz cyclic loading tests with the interesting result of the bending moment envelope progressively decreasing with the application of an overburden pressure of 50 psf, and subsequent removal. A comparison of static and cyclic loading bending moment envelopes is provided in Figure 4.12b, indicating only minor cyclic degradation of lateral soil resistance in these tests; this result is no doubt a function of the very high plasticity index of the foundation medium, in this case 550 %. Prakash (1962) in his Ph.D. dissertation performed static and cyclic tests on groups of model piles embedded in sands. Pile spacing was varied from 2d to 8d in his tests, and he concluded that group effects were negligible for spacings greater than 8d in
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the direction of loading, and greater than 3d normal to loading. He also observed that the effect of cyclic loading was to increase, at a decreasing rate, the deflections and moments under a constant load level. These findings have been quite influential, as they have been commonly cited for the design of pile groups.
Figure 4.12 - Model Pile Head Loading Test Bending Moment Diagram: a) Variation with Overburden Pressure; b) Dynamic and Static Loading (after Gaul, 1958) .
Davisson and Salley (1970) performed lateral load tests on single model piles and
very large groups in sand, including battered piles, to develop design criteria for foundations for locks and dams for the U.S. Army Corps of Engineers. Their objective was to develop a better understanding of group behavior, so that model tests could be correlated to single pile field load tests, which could then be extrapolated to group design. They found that cyclic loading of a single pile caused deflections roughly twice that of static loading, and that bending moment distribution increased moderately at depth, but the maximum moment was unaffected.
Tests on 6 pile groups (vertical/battered)
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illustrated the effects of pile head fixity and cap contact with the soil surface. The largescale group tests again demonstrated increased deflections under cyclic load (150 % of static loading deflections) and analysis of group effects with Hrennikoff’s (1950) method proved reasonably accurate. Allen and Reese (1980) conducted lateral load tests on model piles in soft clay (Test 1) and soft clay covered with a progressively stiffening upper layer (Tests 2 - 5). They compared their test data to results predicted by the COM623 computer program using default p-y curve criteria for stiff and soft clays. The match between predicted and observed results was good, and is illustrated in Figure 4.13. As observed by the authors, some inaccuracy may have resulted from the dependence of deflection on pile diameter, as suggested by Stevens and Audibert (1979), and borne out by lateral load tests on large diameter piles.
Figure 4.13 - Comparison of Experimental and Analytical Model Pile p-y Curves (after Allen and Reese, 1980)
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Matlock et al. (1982) performed an important study of model pile groups in remolded clay instrumented to measure pore pressures and frictional resistance at the pile wall during installation, subsequent consolidation, and cyclic axial loading. The pore pressure measurements were consistent with consolidation theory, but showed inconsistent and minor changes during pile loading, not correlating well with effective stress concepts of degradation of frictional resistance. The authors therefore postulated that the mechanism of cyclic degradation was concentrated in a thin shear zone at some finite distance from the pile wall, as shown in Figure 4.14. Figure 4.15 depicts the reduction in shear transfer of a single pile over 100 cycles of constant deflection; Figure 4.16 illustrates the reduction of shear transfer over progressively increasing displacements. Group efficiency under vertical loading greater than 1.0 was measured, thought to be the result of consolidation between the closely spaced piles; per pile group displacements exceeded those of equivalent single piles.
Figure 4.14 - Shear Zone Behavior in Axially Loaded Model Pile in Remolded Clay (after Matlock et al., 1982)
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Figure 4.15 - Shear Transfer Behavior During Cyclic Axial Loading of Model Pile in Remolded Clay (after Matlock et al., 1982)
Figure 4.16 - Shear Transfer Under Progressively Increasing Displacements During Cyclic Axial Loading of Model Pile in Remolded Clay (after Matlock et al., 1982)
Figure 4.17 - Group Efficiency As a Function of Pile Spacing As Determined by Model Pile Tests (after Cox et al., 1983)
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Cox et al. (1983) described a parametric study of pile spacing and orientation to loading on lateral group efficiency using pile segments inserted into very soft clay. The pile segments were chosen for testing efficiency, and with the belief that the lateral loading effects are well modeled by considering only the near surface portion of the soilpile system. This approach is similar to Matlock’s pot tests, although the rigid body pile deflection mode seems better suited to studying single pile response, as the interaction of a rigid pile group may be quite different than a flexible pile group. A summary of their computed group efficiencies is presented in Figure 4.17. Kishida et al. (1985) made x-ray pictures of cyclic lateral loading tests of model piles in sand and clay, illustrating gap infill and compaction behavior in sand, and a gap standing open in clay (see Figure 4.18). In a similar vein, Hughes and Goldsmith (1977) made a study of pile-soil displacement fields under lateral loading with a stereoscopic photogrammetric technique.
Figure 4.18 - Diagram of Laterally Loaded Model Soil-Pile Displacement Vectors Obtained by X-Ray Technique Illustrating Gap Infill in Sand and Open Gap in Clay (after Kishida et al., 1985)
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Park (1987) published a comprehensive study of the seismic performance of steelencased concrete piles, primarily focused on the structural behavior of these composite members under lateral loading1. Both free-head and fixed-head intermediate-scale piles were tested in loose and medium dense sands. Observed trends included higher pile forces developed in medium than in loose sands, sand densification in a gap around the pile head, expansion and migration of the depth of peak curvature during cyclic loading, lead piles load-shadowing trailing piles, and the formation of distributed zones of yielding in the piles. Interestingly the increased soil stiffness due to densification in the gap was partially offset by the lowered soil surface and hence increased unsupported length of the pile; this effect is also a function of pile installation technique. Despite the formation of local buckling at low ductility levels, strength, ductility, and energydissipating characteristics were judged to be equal or superior to equivalent reinforced concrete members. Under contract to the Electric Power Research Institute, researchers at Cornell University undertook an extensive series of static and cyclic lateral loading tests on large model drilled shafts in sand and clay, as reported by Agaiby et al. (1992) and Mayne et al. (1992), respectively. In the case of the tests in clay soil, large test chambers were filled with clay slurry, which were then consolidated over a period of weeks and even months to obtain the desired overconsolidated strength profiles. The model drilled shafts were constructed with similar care to replicate soil/concrete interface roughness. The static test results showed nonlinear load deformation response, with no apparent yielding,
1
Other researchers who have studied the structural integrity of full-scale precast piles under seismic loading include Banerjee et al. (1987), Priestly and Park (1990), Kokusho et al. (1984), and Sheppard (1983); Meyersohn (1994) researched the structural performance of piles subject to liquefaction induced loading.
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except in dense sands where post-peak softening occurred. Cyclic loading led to an increase in accumulated displacements, which increased at a decreasing rate, except in dense sand, which was considered a metastable condition. Subsequent post-cyclic static loading to failure showed no loss of lateral capacity, save a minor reduction in initial stiffness.
4.3.2 Model Pile Dynamic Tests A limited number of dynamic tests have been conducted on model scale piles and pile groups in field and laboratory conditions, and are summarized in Table 4-4. The experimental results have generally reinforced those obtained in field pile dynamic tests. Several researchers have prepared artificial clay soils as a testing medium, including Kana et al. (1986), who carefully considered scale model similitude in the development of their model soil and pile, and successfully compared the experimental test results with prototype test data, providing some validation for the use of 1-g dynamic model tests of piles in cohesive soils (using a scaling factor of 10.75). Novak has concentrated his experimental efforts on the dynamic testing of model pile groups, and most notably has conducted a test on a 102 pile group, which represents the largest full scale or model pile group whose dynamic response has been recorded (El Sharnouby and Novak, 1992). The layout of this closely-spaced group is shown in Figure 4.19. The group was placed in a hole excavated in the field, and a fly ash/sand mixture designed to have similar dynamic properties to the free-field was backfilled around the group. In this manner, boundary effects typically imposed by a laboratory test container were eliminated, but the experiment can be faulted for not properly replicating the soil
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Reference Moore and Crossley (1972) Agarwal (1973) Novak and Grigg (1976) Novak and Grigg (1976) Novak and Grigg (1976) Novak and Grigg (1976) Novak and Grigg (1976) Richart and Chon (1977) El Sharnouby and Novak (1984) El Sharnouby and Novak (1984) El Sharnouby and Novak (1984) Butterfield and Khan (1985) Butterfield and Khan (1985) Kana et al. (1986) Kim et al. (1987) Gao et al. (1988) Stanton et al. (1988) Hassini and Woods (1989) El-Marsafawi et al. (1992) El-Marsafawi et al. (1992) Burr et al. (1997)
model pile material steel bar brass pipe steel pipe steel pipe steel pipe steel pipe steel pipe steel pipe / steel tube steel pipe steel pipe steel pipe steel pipe steel pipe aluminum pipe drilled shaft plexiglass rod stainless steel pipe steel pipe steel pipe steel pipe steel pipe
pile diameter (in) 0.94x0.06 0.4 2.4 / 3.5 2.4 / 3.5 2.4 / 3.5 2.4 2.4 3.5 / 4.5 1.1 1.1 1.1 1.3 1.3 1 6 1.2 1.2 2.4 4 4 1, 1.5, 2 31 12 92.5 / 88.5 92.5 / 88.5 92.5 / 88.5 82 82 36 - 60 41.7 41.7 41.7 62.5 18.8, 31.3 59.3 60, 90, 120 16.5 45 78 114.2 114.2 ?
pile length (in)
pile freq. resonant pile pile head pile range freq. group spacing fixity pile cap installation model soil test loading (Hz.) (Hz.) n.a. n.a. free n.a. inserted clayey silt vertical FV 15 - 30 ? n.a. n.a. free n.a. inserted plastellina, clay horizontal FV 15 - 30 27 n.a. n.a. fixed n.a. driven silty sand vertical FV 7 - 60 40 - 48 n.a. n.a. fixed n.a. driven silty sand horizontal FV 7 - 60 7-8 n.a. n.a. fixed n.a. driven silty sand rocking FV 7 - 60 7-8 2x2 7.5d fixed at / above grade driven silty sand horizontal FV 7 - 60 11 - 13 2x2 7.5d fixed at / above grade driven silty sand rocking FV 7 - 60 38 - 46 n.a. n.a. free n.a. inserted drained, saturated sand ringdown n.a. 7.1 - 20 102 3d cast above grade backfilled artificial sand vertical FV 6 - 60 32 102 3d cast above grade backfilled artificial sand horizontal FV 6 - 60 18 - 27 102 3d cast above grade backfilled artificial sand torsional FV 6 - 60 28 - 30 n.a. ? ? ? driven soft remolded clay horizontal FV 6 - 20 10 - 13 2x2 ? ? ? driven soft remolded clay horizontal FV 10 - 70 40 - 48 n.a. n.a. fixed above grade driven bentonite/aerosil/veegum horizontal FV 10 - 158 17 - 19 n.a. n.a. ? n.a. cast-in-place sand horizontal FV 10 - 1500 60 - 120 1, 2, 3 2 - 5d free/fixed above grade embedded fine to medium sand horizontal FV 10 - 70 35 - 60 n.a. n.a. free n.a. embedded dry sand horizontal FV 10 - 110 ? 2, 4 2d - 10d fixed ? backfilled sand vertical FV 5 - 60 22 - 25 1, 6 3, 4d cast above grade driven silty sand horizontal FV 10 - 70 16 - 18 1, 6 3, 4d cast above grade driven silty sand vertical FV 10 - 70 45 - 70+ 2x2 2.3 - 15d fixed above grade driven soft, stiff clay horizontal FV 5 - 21 12 - 20
Table 4-4 Model Pile Dynamic Loading Tests
damping (%) ? 12.4 ? ? ? ? ? 4 - 53.1 ? ? ? ? ? 0.9 - 5.5 ? 14 - 22 ? 5.4 - 6.8 ? 7.8 - 9.2 ?
displacement and densification that occurs during pile installation (though this is compensated by the fact that elastic continuum theories do not consider this effect). Forced vibration, impact, and static lateral load tests were conducted on the pile group, and a seismic cross-hole survey was made to verify the shear wave velocities of the freefield and backfill soil.
The forced vibration and impact test results showed good
agreement, and even under higher force amplitudes the response was seen to remain linear elastic.
Figure 4.19 - Layout of 102 Model Pile Group Subjected To Dynamic Testing (after Novak and El Sharnouby, 1992)
Novak and El Sharnouby (1992) evaluated group effects from these tests with static interaction factors (Poulos), dynamic interaction factors (Kaynia and Kausel), complete dynamic analysis (Waas and Hartman), and an equivalent pier concept (Novak and El Sharnouby). Stiffness and damping of a single pile were computed by Novak’s method with PILAY2, ignoring the top 10 cm of soil resistance, incorporating a weak zone around the pile, and proscribing a parabolic variation of soil modulus with depth.
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The pile group impedance was then assembled with interaction factors for the first two methods, and computed directly for the latter two. For vertical response, the Waas and Hartman method, which transforms the pile group into an axisymmetric one for solution efficiency, provided the best match to the test results without modification.
Good
performance of the other three models required consideration of the total or apparent mass, which included the soil between the piles, no modification to stiffness, and adjustment of damping as follows: x 10 % for static interaction, x 50 % for equivalent pier, and x 200 % for dynamic interaction methods, respectively.
For horizontal
excitation, the Waas and Hartman and Kaynia and Kausel methods provided good results without modification. The equivalent pier model required consideration of apparent mass and reduced damping (x 40 %) to replicate the test data; the static interaction factors provided poor correlation to the test results. A summary of the observed horizontal response and model predicted behavior is shown in Figure 4.20.
Figure 4.20 - Experimental Model Pile Group Horizontal Response Curve Compared With Theoretical Models: P, Equivalent Pier; K, Kaynia and Kausel Interaction Factors; and W, Waas and Hartmann Direct Analysis (after Novak and El Sharnouby, 1992)
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The conclusion that can be drawn from this work is that dynamic response of large closely spaced pile groups is a very complex matter, and currently available theories provide a fair estimation of response, with some modifications required. Considering static interaction only may provide an approximate estimate of dynamic group stiffness for small groups at low frequencies, but may otherwise underestimate stiffness.
It
appears that the theories systematically overpredict damping, as they do not account for formation of a soil-pile gap or soil nonlinearity; inclusion of a weak zone surrounding the pile may alleviate this problem. For the particular soil conditions and pile spacing at this test site, the total mass of piles and intervening soil appeared to vibrate as a rigid body.
4.3.3 Model Pile Centrifuge Tests Centrifuge studies of scale model piles have provided a valuable means for understanding and validating aspects of SSPSI that are not readily accomplished by other experimental methods.
A centrifuge apparatus consists of a rotating arm with an
experiment package fixed to a swivel at one end; the centrifugal acceleration of the rotating arm induces an elevated gravitational field onto the model, which swivels to a position normal to the arm (see Figure 4.21). The principal advantage of centrifuge testing is that the gravitational stress field in the model can replicate the prototype. This consideration is crucial when testing materials such as cohesionless sands whose stressstrain behavior is a function of confining pressure. In clay soils, where overburden stresses are not as significant, the centrifuge does offer the important capability of consolidating the deposit during spin-up, thereby achieving a more realistic soil strength profile. Centrifuge tests of model piles have been conducted with both head loading
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schemes, and beginning in the 1980’s, base excitation by shaker devices. Another recent innovation is the installation of piles in-flight while the centrifuge is spinning at the test g-level, so as to properly reproduce the displacement and stress fields around the model pile. Craig (1985) reviewed a range of model pile installation procedures and concluded that for model pile axial loadings in sand “it is imperative that installation be carried out at appropriate acceleration levels...”. He noted that for lateral, cyclic, and dynamic loadings, the effect may be less critical, and considered the undrained behavior of model piles in clay to be relatively insensitive to the installation method. He also stated that the method and rate of in-flight installation can be important variables.
Although not
commonly observed, it would seem to follow that in-situ soil characterization should also be accomplished at the proper in-flight stress level. General limitations of centrifuge model studies include boundary effects from the test container, spatial and temporal variation in the induced gravity field, and only 1-D shakers are presently available. Nonetheless, centrifuge model pile tests have been employed successfully, particularly to study liquefaction phenomena, for which they are well-suited.
Figure 4.21 - Representation of Centrifuge Testing Scheme (after Scott, 1994)
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A summary of centrifuge model pile test programs reviewed is given in Table 4-5, with a comment as to what degree scale model similitude has been addressed in the reference. It can be seen in this table that several references make use of a laminar or hinged box in an attempt to reduce container boundary effects. Fiegel et al. (1994) provide a discussion of this design consideration with the conclusion that all types of model containers, whether rigid or flexible, have unique dynamic characteristics which must be considered in the evaluation of test results. A popular technique is to design a box that has a stiffness profile equivalent to the expected soil stiffness profile during shaking; the challenge in this approach is to choose an appropriate soil stiffness profile representative of perhaps a range of shaking intensities. Unfortunately no researchers, including these ones, compare measured model site response with theoretical free-field response; this comparison would provide an excellent index of the container’s effectiveness in suppressing boundary effects. Another feature apparent from Table 4-5 is that only 11 test programs with earthquake base excitation are reported; of these, only three have been in cohesive soils, two of which were conducted in hinged containers, and both only of moderate shaking intensity.
A third point of interest is that several
researchers used model piles of rectangular cross section (noted as a bar in Table 4-5) which do not present the correct profile to the soil, resulting in altered soil-pile interaction from the prototype conditions. The conclusion to be emphasized is that to date, only one centrifuge testing program (at U.C. Davis) of model piles in soft clay has been reported with high level base excitation, an effective flexible model container, and rigorous consideration of scale model. Comments on particular experimental programs follow.
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Reference Scott et al. (1977) Scott (1979) Scott (1981) Prevost and Abdel-Ghaffer (1982) Prevost et al. (1982) Scott et al. (1982) Zelikson et al. (1982) Barton (1984) Ko et al. (1984) Ko et al. (1984) Ting and Scott (1984) Luong (1984) Nunez and Randolph (1984) Oldham (1984) Finn and Gohl (1987) Steedman and Maheetharan (1989) Terashi et al. (1989) Chang et al. (1990) Bouafia and Garnier (1991) Cafe (1991) Gohl (1991) Hamilton et al. (1991) Lenke et al. (1991) Miura et al. (1991) Terashi et al. (1991) Kotthaus and Jessberger (1993) Levacher and Schoefs (1994) McVay et al. (1994) Stewart et al. (1994) Chacko (1995) Liu and Dobry (1995) Wilson et al. (1995) Abdoun et al. (1996) Abdoun et al. (1996) Fukuoka et al. (1996) Horikoshi and Randolph (1996) Pinto et al. (1997) Ohtsuki et al. (1998) Wang et al. (1998)
model pile material steel bar aluminum rod aluminum bar aluminum pipe aluminum pipe stainless steel pipe aluminum rod aluminum pipe aluminum pipe tapered wood rod stainless steel pipe steel pipe alum. pipe, polypropelene rod stainless steel pipe stainless steel pipe dural tube steel, aluminum, acrylic bar steel pipe aluminum pipe annealed steel rod/rubber stainless steel pipe aluminum rod aluminum pipe stainless steel pipe steel, aluminum, acrylic bar aluminum pipe aluminum pipe aluminum pipe brass rod aluminum pipe brass pipe stainless steel pipe brass pipe PE rod steel pipe brass pipe aluminum pipe, some battered aluminum pipe aluminum pipe
pile pile pile pile diameter wall length pile pile head structural pile (in) (in) (in) group spacing fixity pile cap mass installation model soil 0.17x0.24 n.a. 7.9 n.a. n.a. free n.a. yes inserted dry sand 0.16x0.16 n.a. 8 n.a. n.a. free n.a. yes inserted saturated sandy silt 0.24x0.14 n.a. 8 n.a. n.a. free n.a. yes inserted saturated fine sand 0.22 0.02 4.8 - 10.6 1, 2x2 4.5 - 18.3d free/fixed above grade no ? loose/dense/dry/sat. sands 0.22 0.02 9.9 n.a. n.a. free n.a. yes ? loose/dense/dry/sat. sands 0.5 0.01 8 n.a. n.a. free n.a. no inserted dry, saturated silty sand 0.4 n.a. 4.7 10 ? fixed above grade yes ? saturated sand 0.375 - 0.63 ? ? 1, 2, 3, 6 2 - 8d fixed n.a. no ? saturated fine sand 0.11 - 0.22 ? 5.2 - 10.3 3x3 3d fixed above grade no driven in flight kaolinite clay 0.14 - 0.28 n.a. 4.8 - 9.6 2x4 3d fixed above grade no driven in flight dry sand 0.53 0.01 10 1, 2, 4 2 - 7d free/fixed above grade no inserted saturated sand 0.53 0.1 13.8 2x4, 4x2 ? free/fixed above grade ? ? ? 0.42 - 0.54 0.01 9.3 - 15.6 n.a. n.a. free above grade yes installed in flight consolidated clay 0.75 0.05 13.5 n.a. n.a. free n.a. no driven in flight dry sand 0.375 0.01 8.25 1x2 2 - 6d free/fixed above grade yes inserted loose/dense dry sand 0.375 ? 8 n.a. n.a. free above grade yes embed/inserted dry sand 0.4 - 1.3x0.1 - 0.3 n.a. 3.9 - 16.1 n.a. n.a. free n.a. no fixed at base uniform dense sand 0.375 0.03 4 2x2 10.7d fixed above grade yes inserted medium dense dry sand 1.1 - 1.8 0.04 - 0.08 11.8 - 13.2 n.a. n.a. free n.a. no embed/inserted medium dense, dense sand 0.25 n.a. 8 2x4 8d fixed above grade yes inserted peat 0.375 0.01 8.25 1x2, 2x2 2 - 6d free/fixed above grade yes inserted loose/dense dry sand 0.52 - 1.1 n.a. 4.5 - 9 n.a. n.a. pinned/fixed n.a. no inserted kaolinite clay w/free water 0.25 0.04 5 n.a. n.a. free n.a. no ? dry uniform silica sand 0.38 0.01 8.4 2x2 2.5d fixed above grade yes inserted dry/saturated sand 0.4 - 1.3x0.1 - 0.3 n.a. 3.9 - 16.1 n.a. n.a. free n.a. no fixed at base sloping sand 1.2 0.08 23.6 1x3 3, 4d free above grade no embedded dry fine sand 1.1 ? 15.4 n.a. n.a. free n.a. no embedded dry sand 0.375 0.04 11.5 1 / 3x3 3, 5d free / fixed above grade no driven in flight loose, medium dense dry sand 0.125x0.125 n.a. 8.9 2x7 4.9, 6.5d fixed above grade no ? soft clay, dense sand 0.25 0.03 12 n.a. n.a. free above grade yes inserted dense sand, remolded Bay Mud 0.375 0.014 6.625 n.a. n.a. free / fixed n.a. no embedded medium dense saturated sand 0.875 0.05 22 1, 2x2 4d fixed embed / above yes driven loose, dense saturated sand 0.375 0.01 7.1 n.a. n.a. fixed n.a. no fixed at base layered saturated sand 0.375 n.a. 8.7 n.a. n.a. fixed n.a. no ? layered saturated sand 0.6 0.01 18.1 2x2 5.1d fixed above grade yes pinned at base saturated sand 0.125 0.028 6 5 - 69 5d, 8d fixed embed / above yes inserted kaolin clay 0.375 0.035 11 1 - 21 3, 5d free / fixed above grade yes driven in flight loose, medium dense dry sand 0.4 0.04 10 2x2 15d fixed embedded yes pinned at base oil saturated sand, gravel 0.25 0.03 8.5 n.a. n.a. free n.a. yes inserted dense sand, remolded Bay Mud
Table 4-5 Model Pile Centrifuge Tests
? ? ? ? ? ? ? rigid cylinder rigid cylinder rigid cylinder ? ? rigid cylinder ? ? ? ? ? ? ? ? ? ? laminar box rigid box ? ? ? ? hinged box ? laminar box laminar box laminar box laminar box rigid box ? laminar box hinged box
test container
max. centrifugal accel. model accel. (g) input excitation (g) similitude 100 free vibration head loading n.a. yes 100 cyclic lateral head loading n.a. yes 100 cyclic lateral head loading n.a. no ? FV head load -> 1200 Hz. n.a. no 100 free/forced vibration head loading n.a. yes+ 50 FV head load -> 500 Hz. n.a. yes 100 explosive excitation 0.8 no 30 - 120 cyclic lateral head loading n.a. yes 50, 70, 100 static axial loading n.a. yes+ 50, 70, 100 static axial loading n.a. yes+ 48 free/forced vibration head loading n.a. no 100 EQ head loading 0.5 yes+ 100 static/cyclic axial tension loading n.a. yes 52.5 static/cyclic lateral head loading n.a. no 60 EQ base excitation 0.15 yes+ ? base excitation ? no 20 - 75 cyclic lateral head loading n.a. no 50 base excitation/cyclic head loading 0.2 no 18 - 20 static lateral head loading n.a. no 60 Loma Prieta base excitation 0.48 yes 60 sine waves/EQ base excitation 0.14 yes+ 46 - 93 static lateral head loading n.a. no 60 FV vertical head loading ? no 50 El Centro base excitation 0.25 yes 25 - 75 static lateral head loading n.a. no 50 static lateral head loading n.a. no 18 cyclic lateral head loading n.a. yes 45 static lateral head loading n.a. no 110 in-flight embankment loading n.a. no 50 Santa Cruz, Landers base excitation 0.32 no 40 base excitation + lateral head loading 0.4 no 30 EQ base excitation 0.55 no 40 cyclic lateral head loading n.a. no 50 base excitation 0.2 no 45 El Centro base excitation 0.11 no 100 static lateral head loading n.a. yes 45 static lateral head loading n.a. no 25 Tokachi-oki base excitation 0.2 yes 50 Kobe base excitation 0.25 no
Scott et al. (1977) were the first to test model piles in the centrifuge, and conducted a pilot study of free vibration tests on steel bars instrumented with strain gages inserted in dry sand. Basic scaling relations and trends of damping and subgrade reaction were observed. In following work, Scott (1979) improved the loading system to deliver cyclic lateral loading to the pile head; degradation of soil resistance was clearly discerned. In Scott (1981), the centrifuge experiment was designed to model Reese et al.’s (1974) Mustang Island full scale pile tests, with moderate success (see Figure 4.22). Scott et al. (1982) carried out a parallel field/laboratory program of dynamic forced vibration pile tests.
The field test was discussed in section 4.2.3, and a typical
comparison of prototype and model results is shown in Figure 4.23. The discrepancy can possibly be attributed to pile installation effects, container boundary reflections, and variable pore pressure response, illustrating some of the difficulties in centrifuge modeling. Ting and Scott (1984) investigated small pile group lateral interaction factors which they judged to compare favorably to Poulos’ elastic interaction factors; they found that dynamic pile group interaction was less pronounced than cyclic interaction. They did note pore pressure dissipation was more rapid in the model test than the prototype, and different gapping and gap infill behavior than observed in their field tests. Prevost et al. (1982) reported on centrifuge experiments of model piles excited by forced and free vibration tests, including small pile groups. Static lateral loading of the model piles again designed to replicate the Mustang Island tests resulted in p-y curves roughly ½ the stiffness of the prototype.
Under dynamic loads, nonlinear soil-pile
response, frequency dependent stiffness, and frequency independent damping were detected. Theoretical stiffness predictions were not well met, and the authors suspected
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Figure 4.22 - Laterally Loaded Model Pile Centrifuge Test Data Compared with Prototype Results of Mustang Island (MI) Test (after Scott, 1981)
Figure 4.23 - Centrifuge Test Model Pile Forced Vibration Displacement and Bending Moment Response Compared with Prototype (P9) Test Results (after Scott et al., 1982)
191
that waves reflected from the rigid walls of the test container may have corrupted their results. As researchers developed ways to deliver earthquake shaking to centrifuge models, Zelikson et al. (1982) advanced a novel approach which consisted of generating a programmed series of explosions inside an echo box equipped with filters situated adjacent to the model container on the centrifuge.
The resultant “earthquake-like”
excitations could be scaled in magnitude and frequency content. Barton (1984) investigated Poulos’ static group lateral interaction factors in her centrifuge tests, and found nonlinear response that did not correlate well with Poulos’ elasticity-based theory. The author suggested that nonlinear soil-pile response initiates with the onset of yielding in tension behind the displacing pile, which occurs at much smaller strains than compressive yielding in front of the pile.
In addition, Barton
performed tests with three differently scaled models at three g-levels in a technique known as “modeling of models” to successfully validate the scale modeling technique. Oldham (1984) was the first to laterally load piles installed in flight, and lateral load results from piles installed at 1 g and at 52.5 g illustrate a measurable difference in stiffness (see Figure 4.24). Static and cyclic p-y curves were constructed, and stiffer response under cyclic loads was observed, postulated to be the result of sand densification in the soil-pile gap. Finn and Gohl (1987) implemented a base shaker device that imparted earthquake and sine wave motions to their centrifuge models; they also positioned bender elements in their models to measure in-situ in-flight soil moduli. Excitations were moderate so that elastic response would be achieved. Results from single pile tests showed that pile
192
head and free-field motions were magnified relative to the base input. The predominant period of the pile head response exceeded the free-field, indicating that the pile filtered out high frequency components of the ground motion and was dominated by the inertial response. Tests of small pile groups revealed no interaction effects for offline shaking, and increasing interaction and influence on the bending moment diagram as pile spacing was varied from 6d to 2d. In his Ph.D. dissertation, Gohl (1991) provided a detailed examination of the complete series of centrifuge model pile group tests, with the conclusion that elastic interaction factors underestimated group deflections at close spacings (d/b < 4) and overestimated interaction for larger spacings. He also compared cyclic p-y curves to those constructed according to API recommendations, with the latter implying substantially stiffer response, particularly at depth. Simulation of the single pile experimental results with the computer code SPASM 8 was very successful.
Figure 4.24 - Influence of In-Flight Pile Installation on Subsequent Load Deformation Response of Model Pile in Centrifuge Test (after Craig, 1985) 193
Terashi et al. (1989) performed static lateral head loading of model piles in sand in a “modeling of models” approach at six different scale levels, obtaining remarkably consistent results. Significantly, the researchers recognized the influence of pile diameter on the results of their calculated p-y curves, and they concurred with Stevens and Audibert (1979) that soil-pile resistance is proportional to the square root of pile diameter. Hamilton et al. (1991) were the first to report on centrifuge tests of laterally loaded piles in clay. Much of their analysis focused on the computation of ultimate soil resistance, incorporating mechanisms of soil-pile suction and adhesion in their model. Normalized experimental p-y curves were compared with curves constructed by Matlock’s soft clay criteria (1970). In response to observed pile performance and site response during the 1989 Loma Prieta earthquake, a joint research project by CUREe and Kajima Corporation (1991) performed two series of centrifuge tests of model pile groups in liquefiable sands and soft peat.
The first project endeavored to replicate excess pore pressure generation and
liquefaction of the sandy test soil, but was challenged by the model scaling laws which imply different rates of pore pressure dissipation in the model and prototype. This is typically overcome by using a finer sized soil or more viscous fluid in the model, but these can also influence the soil constitutive relationship and the pore pressure response. The experimental approach taken was to use a uniform fine sand. Special features of these tests were that they were conducted in a laminar box, a set of stacked rings that is free to translate horizontally, thereby reducing boundary effects, (see Figure 4.25), and that they used a base shaker to impart earthquake motions to the model. The piles were
194
inserted into the soil at 1 g, which raises the question as to whether correct stress fields and realistic pore pressure response were truly modeled. Although purely horizontal input motion was delivered to the model, a substantial component of vertical acceleration was measured in the tests. General trends of site amplification, nonlinear pile response, and pore pressure response were observed, and a 2-D effective stress model (TARA-3) was applied to the results. Increasing bending moments toward deeper positions on the pile suggested that liquefaction-induced kinematic loads dominated the pile response.
Figure 4.25 - Laminar Box for Centrifuge Testing (after Hushamand et al., 1988) The second portion of the research project is reported by Cafe (1991) in her Master’s thesis. In these tests, a model of the Struve Slough Bridge, which suffered major damage in the Loma Prieta earthquake, and which was supported on peaty soil, was tested. Tests of a remolded peat deposit without a structural model were first made to calibrate the dynamic properties of the peat with iterative SHAKE analyses. The bridge tests consisted of 8 model piles supporting a single span bridge deck, in braced and unbraced configurations, to represent conditions of lateral restraint near the
195
abutments and no restraint near the center of the bridge. In the braced tests, the measured deck motions were comparable to the input motions, and large pile moments were observed both at the pile head and beneath the ground surface, indicating large kinematic loading from the soil. In the unbraced configuration, deck accelerations were of lower magnitude and longer period, similar to the surface free-field, and pile moments were much larger than the braced tests. A simplified finite element model of the soil-pile response was applied with fair agreement to the observed response. McVay et al. (1994) performed centrifuge tests of laterally loaded 3x3 pile groups driven in-flight in loose and medium dense sand. Figures 4.26a - d provides direct experimental evidence of the effects of a) soil relative density, b) load distribution among lead, middle, and trailing piles, c) pile spacing, and d) in flight installation. They found their test results compared very favorably with those of Brown et al.’s (1988) tests on a full scale pile group in sand (see section 1.2.2) and that the p-multiplier method for group effects matched their results closely, with minor adjustment of the multiplier factors. They also investigated Reese’s (1984) pile group equivalent pier concept, which was found to substantially overpredict observed group deflections. Pinto et al. (1997) used the same apparatus to conduct tests with varied pile head fixity and batter. Pile group efficiencies were verified to be independent of soil density but a function of spacing. Batter pile performance was found to be related to vertical dead load. Hoit et al. (1997) described the FLPIER computer program for analysis and design of pile supported bridge piers, which incorporated the results of the concurrent centrifuge testing program for use as pile design and group interaction parameters.
196
(a)
(b)
(c)
(d)
Figure 4.26 - Centrifuge Modeling of Laterally Loaded Pile Groups in Sand: a) Effect of Relative Density on Group Capacity; b) Load Distribution By Rows; c) Effect of Pile Spacing on Total Lateral Resistance; d) Influence of Acceleration Level During Driving on Total Lateral Resistance (after McVay et al., 1994) The centrifuge testing facilities at U.C. Davis have been the site of a series of research projects dealing with SSPSI. Chacko (1993) described model tests of single piles embedded in remolded Bay Mud in a hinged container on the small centrifuge, and analyzed the results with the free-field and pile response computer codes SRANG and NONSPS from Kagawa (1980, 1983). The analyses showed only fair agreement with the
197
test results (related to the limitations of the codes), and emphasized the dependence of the soil-pile interaction analysis on the accuracy of the computation of the free-field motions. Wang et al. (1998) applied several numerical codes to Chacko’s centrifuge test results, including PAR, NONSPS, and a p-y formulation in the general finite element code DRAIN-2D. They demonstrated that the SHAKE free-field analysis was superior to the SRANG results, and that a Novak-Nogami representation of radiation damping in the DRAIN-2D model provided the most accurate simulation of the centrifuge data (see Figure 4.27). In fact the results were found to be fairly sensitive to the implementation of radiation damping; placing the linear viscous dashpots in series with the hysteretic p-y springs was found to be superior to a parallel arrangement. Wilson et al. (1995) performed model tests of pile supported structures in liquefiable sands on the large centrifuge facility at U.C. Davis. This machine is equipped with a 1-D base shaker, an “equivalent shear beam” laminar box to suppress boundary effects, and special container end conditions to provide complementary shear stresses and reduce unintended vertical accelerations. There is however no capability for driving piles in flight. An extensive series of tests was made of single piles and small groups in saturated sands with a range of shaking intensities and development of very high excess pore pressure ratios, and in some cases consequent liquefaction. Pile motions were dominated by inertial forces from the superstructure, pile cap embedment had a significant effect on response, and peak pile bending moments during liquefaction events occurred close to the soil surface. Further work is reported by Wilson (1998) including the successful derivation of p-y curves from the experimental data and the favorable comparison of the tests results to the Caltrans pseudo-static analysis method.
198
Figure 4.27 - Comparison of Centrifuge Test Experimental and DRAIN-2D Computed Acceleration Response Spectra at Pile Head and Superstructure (after Wang et al., 1998)
199
4.3.4 Model Pile Shaking Table Tests Shaking table tests of model piles have provided another important means for understanding and validating SSPSI effects. The principal feature of shaking table tests are that they are conducted in a 1-g environment, and therefore cannot achieve the elevated stress field suitable for tests of cohesionless soils, as in centrifuge tests. The 1-g test environment is most appropriate for tests involving cohesive soils, whose undrained stress-strain behavior is not dependent on confining pressure. This has, however, not prevented researchers from conducting the great majority of shaking table tests on problems of pile response to liquefaction. Like centrifuge tests, shaking table model tests are sensitive to boundary effects imposed by the test container, and hinged, laminar, and shear boxes have been employed to overcome these effects. Researchers have rarely published comparisons of recorded shake table and theoretical free-field site response, which would be indicative of the container’s effectiveness in suppressing boundary effects.
The greatest advantage of shaking table model tests is that a number of
experimental facilities have the capability for two- and three-dimensional shaking, a distinctly more realistic condition than the 1-D shaking capability presently offered by centrifuges. Shaking table model pile tests do not require special in-flight procedures for pile installation or verification of in-situ soil properties. Scale model similitude is more complex in shaking table testing than in centrifuge testing, as will be discussed in Chapter 5. A summary of shaking table model pile test programs reviewed is given in Table 4-6, with a comment as to how scale model similitude has been addressed in the reference.
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Reference Prakash and Aggarwal (1965) Tajime et al.(1965) Kubo (1969) Yamashita and Inatomi (1970) Hakuno et al. (1977) Tatsuoka et al. (1978) Sugimura (1980) Yao (1980) Kagawa and Kraft (1981) Mizuno and Iiba (1982) Ranjan et al. (1982) De Alba (1983) Heng-Li (1985) Korgi (1986) Gohl and Finn (1987) Mizuno et al. (1988) Stanton et al. (1988) Tamori and Kitagawa (1988) Yoshikawa and Arano (1988) Gohl (1991) Liu and Chen (1991) Nomura et al. (1991) Yan et al. (1991) Finn and Gohl (1992) Mori et al. (1992) Taga et al. (1992) Tazoh and Shimizu (1992) Tokida et al. (1992) Yamamoto et al. (1992) Yao and Kobayashi (1992) Sreerama (1993) Kagawa et al. (1994) Ohtomo and Hamada (1994) Sakajo et al. (1995) Dou and Byrne (1996) Hideto et al. (1996) Ohtomo (1996) Makris et al. (1997) Tao et al. (1998)
pile pile pile diameter wall length model pile material (in) (in) (in) aluminum pipe 0.6 0.1 13 steel pipe 1 - 1.2 0.04 - 0.06 7.9 steel pipe 3.9 0.1 118 steel bar 3.9x0.4 n.a. 45.3 aluminum rod 0.8 n.a. 27.6 aluminum rod 0.8 n.a. 27.6 steel bar 2x0.2 n.a. 28.2 aluminum pipe 0.4 0.04 21.3 steel bar 2.4x0.2-0.4 n.a. 31.5 steel bar 2x0.2 n.a. 28.2 ? 0.3 ? 13 brass pipe 1 ? 2.5 acrylic pipe 0.3 0.1 12.6 steel bar 2x0.2 n.a. 28.1 aluminum pipe 0.25 0.05 24 steel bar 2x0.2 n.a. 28.1 stainless steel pipe 1.2 0.19 45 steel bar 2x0.2 n.a. 28.1 aluminum pipe 4 ? 21 aluminum pipe 0.25 0.05 16 aluminum pipe 0.4 ? 11.8 ? 1.9 - 3 ? 78.7 aluminum pipe 0.25 - 0.5 ? 13.8 aluminum pipe 0.25 0.05 24 aluminum rod 2 n.a. 39.4 aluminum bar 0.2x0.4 n.a. 15.7 aluminum pipe 1.2 0.04 35.4 PVC pipe 0.9 ? 31.1 brass pipe 0.8 0.12 26.3 aluminum tube 1x2 0.08 68.9 aluminum pipe 0.44 0.03 17.5 steel rod 2x0.24 n.a. 36.1 polycarbonate, PE pipe 0.7 - 1 ? 24.4 - 26 plastic pipe 1 0.1 35.4 aluminum pipe 0.25 0.03 15 acrylic resin 1.2 0.08 23.6 aluminum, stainless pipe 1 ? 27.6 aluminum pipe 0.8 0.04 38.2 steel pipe 12 0.25 240 n.a. 2x2 3x? 2x2 2x2, 2x3, 3x3 2x2, 2x3, 3x3 1x2 1, 3x3 n.a. 1x2 2x2, 3x3, 4x4 2x2 10 2x? n.a. 1x2 n.a. 2x? 2x2 1, 1x2, 2x2 3x9, 5x9, 9x9 2x? n.a. 1x2, 2x2 3x3 3x3 3x3 1 - 16 8 2x2 1, 1x2, 2x2 1x2 n.a. 6x6 n.a. n.a. 1x2 n.a. n.a.
pile group
pile max. pile head structural accel. model spacing fixity pile cap mass pile installation model soil test container input excitation (g) similitude n.a. free none ? embedded sand rigid box 2 -10 Hz. ? no ? fixed embedded yes fixed at base sand/plaster/water rigid box 1.4 - 8 Hz. ? no ? fixed above grade yes fixed at base cinder sand/oil rigid box 1 - 4Hz. 0.1 yes 50d fixed above grade yes inserted dry sand ? sine waves 0.15 no 3d fixed above grade yes fixed at base saturated loose sand hinged box 10 - 20 Hz. 0.13 yes 3d fixed above grade yes fixed/free at base saturated loose sand hinged box 5 - 45 Hz. 0.1 no ? ? embed / above yes ? polyacrylamide/bentonite ? 3 - 15 Hz. 0.1 no ? free/fixed above grade yes inserted clayey silt hinged box 4 - 45 Hz. 0.1 no n.a. free ? yes ? saturated sand hinged box 10 Hz. 0.1 no ? fixed embedded yes pinned at base polyacrylamide/bentonite rigid cylinder sine waves, Japan EQ 0.1 yes 2 - 5d ? ? ? inserted saturated sand rigid box 4 Hz. 0.3 no 2.5d fixed above grade n.a. inserted saturated medium sand laminar cylinder cyclic ? no 2 - 2.7d fixed above grade yes ? silicon gum ? 2 - 24 Hz., Japan EQ ? yes ? fixed embedded yes pinned at base polyacryl./bentonite/fly ash rigid cylinder 1 - 30 Hz., Japan EQ 0.12 no n.a. free above grade yes inserted dense dry sand rigid box 5 - 50 Hz. 0.6 no ? fixed embed / above yes ? polyacrylamide/bentonite rigid cylinder 1 - 30 Hz., EQ 0.12 yes+ n.a. free ? ? embedded dry sand flexible cylinder 1 - 40 Hz. ? no ? hinged embedded yes pinned at base plasticine/oil, polyacr./ben. rigid cylinder 0 - 30 Hz., EQ 0.8 yes 4.4d ? embedded yes ? loose saturated sand shear box 10 - 25 Hz., w/ vertical 0.1 yes 2 - 8d fixed above grade yes inserted dry sand rigid box 5 - 70 Hz., Taft 0.69 yes+ 3d ? ? ? inserted saturated sand ? ? 0.6 no ? ? above grade yes embedded saturated clean silica sand shear box Taft, El Cento EQ 0.3 yes n.a. free none yes ? saturated uniform fine sand hydraulic gradient 10, 20 Hz. 0.51 yes 3 - 8d fixed above grade yes inserted dry sand rigid box 7.5, 10 Hz. 0.45 no ? fixed above grade yes fixed at base saturated sand shear box EQ 0.14 yes 22d pin partial embed yes ? dry sand rigid box 1 - 10 Hz. 0.2 yes 2.5d fixed above grade yes fixed at base dry sand shear box 1 - 30 Hz. 0.25 no ? free none no fixed at base sloping saturated sand rigid box 2 Hz. 0.25 no ? free/fixed above grade yes fixed at base N-methylol propene, sand shear box El Centro EQ ? no 15d ? above grade yes embedded saturated sand shear box 1 - 7 Hz. 0.3 no 3 - 8d free/fixed above grade yes inserted low plasticity remolded clay rigid box 1 - 12 Hz. ? no 16d fixed above grade yes pinned at base saturated sand shear box 0 - 25 Hz. 0.16 no n.a. free none no fixed at base sloping saturated sand rigid box 10 Hz. 0.68 no 2.5d fixed above grade no fixed at base saturated sand/gravel shear box 10 Hz. 0.1 no n.a. free above grade yes inserted saturated uniform fine sand hydraulic gradient 17.5, 30 Hz 0.49 no n.a. free n.a. yes embedded dry sand shear box 10 - 60 Hz., EQ 0.3 no 10d fixed embedded no ? saturated sand rigid box 10 Hz. 0.4 no n.a. fixed embedded yes fixed at base dry sand shear box frequency sweep ? no n.a. free n.a. no pinned at base loose moist sand laminar shear box sweep 1-20 Hz., KPI EQ 0.45 no
Table 4-6 Model Pile Shaking Table Tests
A feature immediately apparent from Table 4-6 is that the great majority of shaking table test programs have studied the seismic response of piles in cohesionless soils, with very few studies conducted in cohesive soils. Single piles and small groups have been tested, with only two tests reported of larger groups. A number of tests have used flat bars as model piles, which as noted earlier, present an incorrect pile crosssection to the soil. A recent trend toward using shear boxes for the model container can be distinguished. Input motions have primarily consisted of sine waves, with a limited number of earthquake record base excitations, and only a handful of cases could be considered to be at strong levels of shaking. Reporting of adherence to scale model similitude has been inconsistent and often incomplete. To date, no shaking table testing program of model piles in soft clay has been reported with a high level earthquake base excitation, an effective flexible model container, and rigorous consideration of scale model similitude. Comments on particular experimental programs follow: Kubo (1969) was the first to report on shaking table model pile tests conducted with attention to scale model similitude. The results of his large model tests emphasized the kinematic component of soil-pile interaction, and he detected bending moment profiles and deflections consistent with computed prototype behavior. Yao (1980) drove groups of aluminum pipes into silty clay and performed static lateral load tests in addition to shaking table tests. The static test results showed evidence of pile group behavior, but they did not directly correlate to the observed dynamic pile group response.
Strong resonant dynamic response was observed when the natural
frequencies of the superstructure and soil deposit coincided. Kagawa and Kraft (1981) proposed a nonlinear p-y type analysis method that
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incorporated pore pressure response, and compared their analytical technique against shaking table test results of model piles in sand.
Through the shaking events, the
measured fundamental resonance frequency of the soil-pile-structure system decreased from 34 to 4 Hz, passing through the resonant condition of the 10 Hz input motion. This behavior illustrates the dramatic softening behavior of the system during liquefaction. The numerical model compared favorably to the experimental results in the early and late stages of the loading sequence, but underestimated the response during the onset of liquefaction. Mizuno and Iiba (1982) were the first to subject their models to earthquake time history base excitations, and published a comprehensive discussion of scale model similitude.
They attempted to fabricate an elastic soil medium with a mixture of
polyacrylamide and bentonite, and used model piles of rectangular cross-section supporting single mode model structures. They simulated the response of structures with mat, fixed pile head, and free pile head foundations, and discovered important variability in response (Figure 4.28a). Greater forces were detected in the fixed head model piles, and higher earth pressures on the embedded mat foundation. Parametric studies of three building models confirmed the effects of building frequency on dynamic interaction, with pile response dominated by kinematic interaction effects at the relatively low levels of shaking in these tests. They also conducted tests on a model that corresponded to an eleven story prototype structure, and compared the experimental results to the actual recorded motions at the site.
Figure 4.28b depicts recorded and experimental
building/pile tip transfer functions that compare favorably, given the simplifications made in the model construction. Korgi (1986) extended these tests to investigate the
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effects of different soil deposits and pile cap embedment on the system response. A trench around the footing removed the lateral resistance afforded by the pile cap, and this condition was found to have the strongest system response and induced the greatest pile bending moments. The structure’s fixed base period was also found to lengthen due to SSPSI effects.
(a)
(b) Figure 4.28 - SSPSI Shaking Table Model: a) Influence of Three Foundation Conditions on Superstructure Response; b) Comparison of Experimental and Recorded Seismic Response (after Mizuno and Iiba, 1982) Stanton et al. (1988) fabricated a large cylindrical shear bag 48 in diameter and 48 in tall to conduct shaking table tests of model piles in dry sand. Shortcomings in the container design and loading system performance contributed to experimental difficulties, but general trends of static and dynamic response were obtained and found to be in agreement with established methods of analysis. The authors correctly observed that pile
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head-loading response is most sensitive to the near-surface soil properties, and pile seismic response is sensitive to the properties of the entire soil deposit. In addition to the centrifuge tests previously described, Gohl (1991), in his Ph.D. dissertation, performed shaking table tests of model piles. Ringdown, impact, frequency sweep, and free vibration tests were first made of single piles embedded in sand to ascertain whether the mode of loading, kinematic or inertial, affects the computation of the pile’s natural frequency and damping. The different methods computed a range of values that could be equally ascribed to the influence of amplitude, number of cycles of vibration, and the effect of previous strain history. Base excitation tests of small groups verified trends of group interaction for inline and offline shaking. Comparing shaking table test results to centrifuge test results, a deeper distribution of bending moments was observed in the former case, underscoring the effects of lower confining pressure in the shaking table tests. Cyclic p-y curves constructed by the API method were found to be considerably softer than the experimental results, which displayed nonlinear and strong hysteretic characteristics.
Again, the computer code SPASM 8 was successfully
employed to simulate the test results. Liu and Chen (1991) tested large groups of model piles in liquefiable sands, and investigated the effects of pile installation on densification of the foundation soils. Excess pore pressure ratios were measured to be lower in the piled zone than in the freefield, as would be expected, but quantitative conclusions could not be drawn from the test results due to erroneous stress fields in this 1-g model. The authors did acknowledge that although driven piles may densify the immediate surrounding soil, global liquefaction mechanisms can still render such foundations susceptible to lateral or bearing capacity
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failures. Of the numerous researchers studying pile response during liquefaction, one of the best efforts has been made by Nomura et al. (1991). A laminar box model container was used to allow shear deformations of the soil deposit, and different pile rigidities were tested.
An effective stress free-field response analysis was coupled to a horizontal
subgrade reaction pile model to simulate the experimental results, and excellent agreement between the observed and computed response was obtained (Figure 4.29). The two basic conclusions these researchers derived were: “Regardless of pile rigidity, the dynamic response of the pile-structure system before liquefaction is significantly influenced by the response of the soil.” and “Unless the pile is rigid enough, the dynamic response of the pile-structure system after liquefaction is also influenced by the response of the soil.” Other researchers have come to a variety of conclusions from soil-pile liquefaction shaking table tests, as soil relative density and layering, pile spacing and installation procedure, and input motions can all contribute to unique test results.
Figure 4.29 - Comparison of Shaking Table Model Pile Liquefaction Response to Analytically Computed Fourier Amplitude Spectra (after Nomura et al., 1991)
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Sasaki et al. (1991) and later Tokida et al. (1992) and Ohtomo and Hamada (1994) have studied the effects of lateral spreading on model pile groups in shaking table tests. They have considered variations in the slope of the ground surface, the slope length, the thickness of the liquefiable layer, and pile group configurations on the development of drag forces acting on the resisting piles. A clever variation of standard shaking table tests is presented by Yan et al. (1991), who applied a hydraulic gradient to a cohesionless model soil deposit in order to increase the stress level in the model with depth in a similar fashion as to centrifuge tests. Special scaling laws were derived, which Dou and Byrne (1996) validated in a “modeling of models” approach, while conducting free and forced vibration tests on model piles in the hydraulic gradient apparatus. Yamamoto et al. (1992) utilized shaking table model tests to investigate the performance of a pile foundation viscous damping device. Tests in both soft ground and liquefied sand verified the performance of the viscous dampers in attenuating ground motions (Figure 4.30), but such equipment must be designed to be multidirectional to be effective.
Figure 4.30 - Fourier Spectra Illustrating Effect of Viscous Damping Device in Shaking Table Model Test of Pile Foundation (after Yamamoto et al., 1992)
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Sreerama (1993) tested small pile groups embedded in soft clay at different spacings subjected to small amplitude base excitations in order to investigate pile group dynamic interaction. Pile stiffness and damping were computed as a function of soil shear strain, to account for nonlinearity of response. He proposed a dynamic group interaction factor as a function of pile spacing and number of piles in the group, but independent of frequency, and compared his results to methods proposed by other researchers (Figure 4.31). Pile group stiffness was found to increase with pile spacing, and decrease with increasing strain (though the experimental strain range was small). Total pile group damping was found to decrease with increasing pile spacing, but radiation damping was computed with elastic interaction factors ignoring wave interference effects. Makris et al. (1997) compared the results of shaking table tests on single piles in sands with an advanced dynamic Winkler foundation model that incorporated frequency dependent stiffness and damping terms. The authors also applied an alternate method for calculating bending moments and axial strains that was not computed from the second derivatives of the pile deflected shape, but rather was based on inertial forces acting on the pile-superstructure system (the Clough method), and was found to give superior results. Tao et al. (1998) conducted large-scale shaking table tests at the new NIED facility in Tsukuba, Japan. This table is 15 m x 15 m, with a payload capacity of 500 tons at 0.5 g. A large-scale laminar shear box and full-size pile were tested, and the results compared to the Kagawa suite of analyses (SHAKE21, SRANG, NONSPS).
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Figure 4.31 - Shaking Table Model Pile Group Interaction Factor Versus Pile Spacing, Experimental Data, and as Computed by a Variety of Methods (after Sreerama, 1993)
From full-scale tests to the other extreme, Konagai et al. (1998) performed virtual soil-pile interaction shaking table tests by mounting a beam to a shaking table and using analog circuits to simulate the soil-structure interaction effects.
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4.4 Summary of Experimental Findings Together, field and laboratory pile load test programs have made a vital contribution to our understanding of SSPSI. Field pile tests have delivered inertial pile head loading, and have shed light on single pile, pile group, and dynamic response. Matlock’s original 1962 work emphasizing the nonlinearity of soil pile response, along with cyclic degradation and gapping, are the basis for this entire field of study. Analysis of Gill’s results (1968) does suggest that universal p-y curves may be inappropriate for some cases, including Bay Mud. Tests of full-scale pile groups have clearly illustrated shadowing effects on load sharing, cyclic degradation, batter pile performance and pile cap contributions to resistance. Dynamic testing of single piles and pile groups has shown that response is site, frequency, load level, pile cap, and pile group spacing dependent. The variability in dynamic test results by various experimental methods has been demonstrated by several researchers. Scale model tests have successfully been calibrated against prototype test results, importantly demonstrating the viability of the scale modeling technique. Matlock’s laboratory soil-pile experimental work from 1957 to 1962 greatly complemented his field studies, and stands as a complete investigation of its own. At the same time, scale models have been demonstrated to be sensitive to container boundary effects, scale modeling techniques, and adherence to similitude laws. The results of many scale model experiments are compromised by not paying proper heed to these issues. Nonetheless, advanced scale models can deliver both kinematic and inertial loads to soil-pile-superstructure systems.
Novak’s (1992) series of dynamic
experiments with model pile groups demonstrated the limitations in our present ability to accurately predict complex pile group behavior. Gohl (1991) conducted both centrifuge
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and shaking table tests of small model pile groups, successfully reproducing single pile and group response, but with important differences in the two methods. Wilson (1998) has performed the highest quality centrifuge experiments dealing with SSPSI to date, with high level shaking and strong inertial response. Sreerama (1993) produced shaking table results of small pile groups in clay, and showed the variability in currently available dynamic pile group analysis methods.
With this background, the next chapter will
describe the development of scale modeling criteria and test components for this experimental program.
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CHAPTER 5
ONE-G SCALE MODELING
5.1 Introduction The use of scale models in geotechnical engineering offers the advantage of simulating complex systems under controlled conditions, and the opportunity to gain insight into the fundamental mechanisms operating in these systems. In many circumstances (e.g., a static lateral pile load test), the scale model may afford a more economical option than the corresponding full-scale test. For other investigations (e.g., seismic soil-pile interaction), scale model tests allow the possibility of simulating phenomena that cannot be achieved “at-will” in the prototype. The practice of conducting parameter studies with scale models can be used to augment areas where case histories and/or prototype tests provide only sparse data. In addition to qualitative interpretation, scale model test results are often used as calibration benchmarks for analytical methods, or to make quantitative predictions of the prototype response. For such applications it is necessary to have a set of scaling relations that relate the observed model and predicted prototype behavior. This chapter will first describe theories of scale model similitude, and elucidate the development of scale modeling criteria for the shaking table test program. The application of these criteria to and design of the model soil and model piles used in the test program will then be described.
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5.1.1 Theories of Scale Model Similitude The relationship between a scale model and the corresponding prototype behavior is described by a theory of scale model similitude. Kline (1965) defines three methods of increasing complexity and power for scale modeling applications. They are dimensional analysis, similitude theory, and the method of governing equations. Dimensional analysis consists of converting a dimensionally homogenous equation, containing physical quantities and describing a physical phenomenon, into an equivalent equation consisting of dimensionless products of powers of the physical quantities. Dimensional analysis may be used exclusively to understand the form of the problem solution without application to scale modeling. Similitude theory identifies the forces operating in the system and uses dimensional analysis to construct and equate dimensionless terms for the model and prototype.
The scaling relations between model and prototype are also known as
prediction equations. The method of governing equations involves the transformation of the differential equation describing the process to nondimensional form, and the formation of similarity variables that relate model to prototype. Similarity variables must also be determined for both initial and boundary conditions operating on the system. Scale models can be defined as having geometric, kinematic, or dynamic similarity to the prototype (Langhaar, 1951). Geometric similarity defines a model and prototype with homologous physical dimensions.
Kinematic similarity refers to a model and
prototype with homologous particles at homologous points at homologous times. Dynamic similarity describes a condition where homologous parts of the model and prototype experience homologous net forces. Scale models meet the requirements of similitude to the prototype to differing degrees, and researchers apply nomenclature such
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as “true”, “adequate”, or “distorted” to the model (Moncarz and Krawinkler, 1981). A true model fulfills all similitude requirements. An adequate model correctly scales the primary features of the problem, with secondary influences allowed to deviate; the prediction equation is not significantly affected. Distorted models refer to those cases in which deviation from similitude requirements distorts the prediction equation, or where compensating distortions in other dimensionless products are introduced to preserve the prediction equation. Dimensional analysis in its simplest form proposes to reduce an engineering parameter to its fundamental Mass-Length-Time “measures of nature” while developing scale factors for each of the three quantities. For example, modulus of elasticity is a measure of stress with units of force/area and dimensions ML-1T-2, so scale factors for mass µ, length λ, and time τ are combined to form a scaling relation µλ−1τ−2 that relates model to prototype stress response. Following the same line of reasoning, strains map 1:1 between the model and prototype, as strain is a dimensionless quantity. Model and prototype material densities are commonly used as a basis for determining the relation between the µ and λ scale factors. If ρmodel/ρprototype = 1, then µ can be computed as equal to λ-1/3. The time scaling factor τ can then be derived by equating the inertial force ratio (m subscripts refer to model quantities, and p subscripts refer to the prototype) M m Am γ m 3 Am M A = γ λ A p p p p with the weight ratio
214
(5.1)
γ m 3 λ γ p
(5.2)
with the result that the model accelerations must equal the prototype accelerations. Therefore Am =1= A p
Lm 2 2 T m = λ T p T Lp m 2 T p
(5.3)
2
from which
T m =λ T p
(5.4)
and
τ= λ
(5.5)
With the mass µ, length λ, and time τ scale factors all determined in terms of λ, a complete set of dimensionally correct scaling relations can be derived for all variables being studied. This is the methodology followed by Clough and Pirtz (1956) and Seed and Clough (1963), who used scale models to study the earthquake resistance of dams. A drawback to this method is that each variable is treated independently without particular regard to its function in the system. A more sophisticated type of dimensional analysis involves application of the Buckingham Pi Theorem, which states that any dimensionally homogeneous equation involving certain physical quantities can be reduced to an equivalent equation involving a complete set of dimensionless products. Thus the solution equation for some physical quantity of interest, i.e., F(X1, X2,…, Xn) = 0
(5.6)
G(π1, π2,…, πm) = 0
(5.7)
can be expressed in the form
215
where the Pi terms are independent dimensionless products of the physical quantities X1, X2,…, Xn. The number of dimensionless products (m) is equal to the number of physical variables (n) minus the number of fundamental measures that are involved. The individual Pi terms are formed by grouping the physical variables into dimensionless terms; all variables must be included and the m terms must be independent. There is theoretically no unique set of Pi terms for a given problem, but for scale modeling problems it is essential that the correct variables be identified and the Pi terms be formed appropriately. Scaling relations may then be determined by equating model and corresponding prototype Pi terms, i.e. πi,m must equal πi,p. As previously noted, similitude theory attempts to describe the problem more rationally by basing the formation of the Pi terms on the forces prevailing in the system. Moncarz and Krawinkler (1981) consider the formation of Pi terms for the determination of the time history of stress components σij(r,t) in a scale model resultant from an imposed acceleration time history a(t). They point out two requirements to meet “true” scale modeling criteria: the Froude and Cauchy conditions. Given stress as a function of σ = F (r, t, ρ, E, a, g, l, σo, ro)
(5.8)
where r = position vector, t = time, ρ = density, E = modulus of elasticity, a = acceleration, g = gravitational acceleration, l = length, σo = stress, and ro = initial position vector, the following Pi terms can be formed: σ r t E a glρ σ o ro = , , , , , , E l l ρ g E E l
216
(5.9)
In 1-g scale modeling, the dimensionless product a/g (Froude’s number, commonly expressed as v2/lg) must equal unity, which implies that the ratio of model to prototype specific stiffness (E/ρ) equals the geometric scaling factor λ. This is known as the Cauchy condition and can also be stated in terms of shear wave velocity:
(Vs )p = (Vs )m
λ
(5.10)
Moncarz and Krawinkler also show that the Cauchy condition is a necessary requirement for simultaneous replication of restoring forces, inertial forces, and gravitational forces in a dynamic model system. The difficulty in designing “true” scale models lies in selecting model materials that have a combination of both small modulus and large mass density to meet the Cauchy condition. Two alternatives are to conduct what the authors call “artificial mass simulation” and “gravity effects ignored” scale model tests.
5.1.2 Scale Model Similitude As Applied to Soil Mechanics Rocha (1957) was the first to systematically describe scale modeling for problems in soil mechanics. He differentiated between total stress and effective stress conditions, deriving separate similitude relations for each case. To account for the different stress regime present in a 1-g scale model from the prototype, Rocha proposed that the soil constitutive behavior be scaled, and therefore assumed that both the stress and strain held a linear relationship between the model and prototype. This concept is illustrated in Figure 5.1, where α is the stress scaling factor and β is the strain scaling factor (Note that scaling strain is contrary to the dimensional analysis approach). He limited his derivations
217
to elastic deformations, and opined that the analysis becomes “insuperably complicated” when nonlinear response is considered.
Figure 5.1 - Scale Model Constitutive Behavior Described by Stress and Strain Scaling Factors (after Rocha, 1957)
Figure 5.2 - Critical State Soil Mechanics Concept of Geometrically Similar Stress Paths for Prototype A1Z1 and Model A2Z2 (after Roscoe, 1968) Roscoe (1968) investigated the difficulty of scale models replicating prototype constitutive behavior for soils whose response is dependent on self-weight, i.e., confining pressure. He extended Rocha's assumptions and recast them in the form of critical state soil mechanics, asserting that the strain behaviours of two elements of soil will only be identical when the elements are subjected to two geometrically similar stress paths if their initial states on an e-ln σ' plot are equidistant from the critical state line. This
218
theory is illustrated in Figure 5.2, and was substantiated by limited laboratory testing. He also observed that centrifuge testing presented a potentially viable alternative to such an approach.
Figure 5.3 - Tangent Modulus Formulation for Scale Modeling of Soil Constitutive Behavior (after Iai, 1989) Kana et al. (1986) describe the application of the Buckingham Pi theorem to the problem of scale modeling the dynamic interaction of a pile in clay. They formed the following nondimensional equation 2 4 2 2 x y Mc , J3 c , M 2 , EI 4 , EI 4 , F D , M D ω , ω T o , ω D (5.11) = , D D DM D M ρ D E r D E l D EI EI g
where x = lateral deflection, D = pile diameter, Mc = pile cap mass, M = pile mass per unit length, Jc = pile cap moment of inertia, ρ = soil density, E = pile Young’s modulus, I = pile section moment of inertia, Er = soil storage modulus, El = soil loss modulus, F = applied lateral load, ω = frequency of oscillation, To = linear freuency sweep duration, and g = acceleration due to gravity, which implies the requirement for an elevated gravity field in the last term. But the researchers surmised that gravity effects were negligible for lateral pile response in overconsolidated clay, and therefore conducted their tests under this
219
scaling regime but in a 1-g environment. Their findings demonstrated the noneffect of gravity for the particular conditions being tested, and suggested that frequency response was primarily dependent on soil and pile properties. Gohl (1991) also used dimensional analysis to derive the following functional relationship for scale model similitude as applied to shaking table tests of model piles: l ρ y EI ω 2 uo mo = K , p , , , 4 3 b g ρ ρ u G u u o o o s s s
(5.12)
where y = dynamic lateral deflection of the pile, b = pile diameter, l = pile length, uo = amplitude of input base motion, ρp = pile mass density, ρs = soil mass density, EI = pile flexural rigidity, Gs = depth and strain level dependant shear stiffness of the soil, ω = frequency of input base motion, g = gravitational constant, and mo = superstructure mass. Gohl points out that it is very difficult to simultaneously satisfy the second scaling law, which implies the same model and prototype material densities, and the third scaling law, which derives the ratio of prototype to model pile flexural rigidity as equal to λ5. He comments that a way of accepting imperfect model similitude is by viewing the tests as prototype events themselves, against which analytical models can be verified. He also suggests that the test results may be expressed in terms of dimensionless variables to allow comparison with full scale results. Iai (1989) built on Rocha's work by considering a tangent modulus approach to scale model constitutive behavior for saturated soils (see Figure 5.3). He derived a comprehensive set of scaling relations for a soil-structure-fluid system under dynamic loading and defined the entire problem in terms of geometric, density, and strain scaling
220
factors. His method proscribes the geometric (λ) and density (λp) scaling factors, and then derives the strain scaling factor (λε) from shear wave velocity tests in both the model and prototype soil: λε =
λ
[(V s) p (V s )m]
2
(5.13)
The non-intuitive result is that certain model quantities with the same dimensions may have different scaling factors, such as length and deformation. Again, the validity of his technique was demonstrated by laboratory testing. Iai qualifies his method by stating that it only applies for small strains where the soil particles do not lose contact, but does make some application to liquefaction problems involving medium to dense sands.
Iai’s
complete set of scaling factors is listed in Appendix A. Scott (1989) applied the method of governing equations to dynamic equilibrium for constructing model soil scaling relations for centrifuge testing. Gibson (1996) refined this derivation and generalized it for a granular saturated soil subject to 1-g or centrifuge testing: * * * 2 1 − x * x 2 ρ * ρ m ∂ u2im + ∂ u jm ∂ ∂uim = 1 − x * X * X im σ * ∂ t m ∂x jm ∂t m σ t ∂ tm
(5.14)
where x represents length, σ is stress, t is time, ρ is density, X is the body force, and starred (*) quantities refer to the prototype to model ratio. Gibson also considered the problem of scaling soil constitutive behavior for 1-g testing, and proposed modifying the model material so that under 1-g stress conditions it would still exhibit strain behavior similar to the prototype. This approach utilizes the steady state line and is depicted in Figure 5.4; it differs from Rocha’s and Iai’s methods which both elected to modify the
221
constitutive relation rather than the soil properties. Gibson also showed that the dynamic time scale and the diffusion time scale (related to pore pressure response and liquefaction) were incompatible for 1-g testing, unless provisions were made to use a finer grained soil or a more viscous pore fluid.
Figure 5.4 - Definition of Model Soil Properties Based on Steady-State Line (after Gibson, 1996) An important fact should become apparent in the work of the soil mechanics researchers described in this section.
They have added the important feature of
constitutive similarity to the set of scale modeling requirements for soil response problems. This reflects the fact that it is not adequate to simply model a discrete elastic parameter of the system, but rather to consider its full range of nonlinear behavior. Constitutive similarity will be discussed with reference to the model soil and model pile designs in sections 5.2 and 5.3, respectively.
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5.1.3 Scale Modeling Methodology and Implied Prototypes Consider the SSPSI problem at hand, previously depicted in Figure 1.1, with its interdependent processes.
This figure constitutes a crucial component of the scale
modeling method in that it delineates the variables and modes of the system, and the scale model program must be designed to adequately capture the behavior(s) of principal interest. It is clear that no governing equation can be written that describes this entire system, nor can dimensional analysis or similitude theory be directly applied to this complex system to achieve “true” model similarity. The viable scale modeling approach for this application therefore consists of identifying and successfully modeling the primary forces and processes in the system, while suppressing secondary effects, thereby yielding an “adequate” model. This scale modeling design procedure is implemented as an iterative process that can be described by the flowchart shown in Figure 5.5. Figure 5.5 describes a scale modeling approach in which the primary modes of system response are first identified and prototype values for the variables contributing to these modes are established. Scaling relations are derived and used to compute scale model parameters for the variables of interest. Scale model components are fabricated and tested to verify their actual behavior. Scaling relations are then used to determine whether the measured model behavior implies a reasonable prototype response. This method of implied prototypes provides a suitable modeling approach for the wide range of potential prototype soil, pile, and superstructure conditions. Caution must be exercised when interpreting scale model test results in terms of the prototype, however.
The most
accurate use of numerical analysis applied to the modeling process is analysis of the scale model, not to predict the behavior of the (implied) prototype. Full extension of model
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Identify primary modes of system response and variables contributing to these modes
Use dimensional analysis to develop scaling relations for primary modes of system response
Assign target range of prototype parameters to primary system variables
Use scaling relations to compute trial scale model parameters for primary system variables
Select and fabricate model materials to meet trial model parameters
Establish actual model parameters and model response by component testing
Use scaling relations to compute prototype parameters implied by actual model parameters
Are implied prototype parameters reasonable and within target range ?
No
Figure 5.5 - Flowchart Describing Scale Modeling Methodology of Implied Prototypes
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scale results to quantitative prototype behavior implies a high confidence in all aspects of the modeling process (see Section 6.4.5).
One technique employed to evaluate the
accuracy of the scale modeling technique is known as “modeling of models”. In this approach, independent tests of the same prototype are conducted at different scaling factors; if the results uniformly meet similitude requirements, then the modeling technique can be judged sound.
5.1.4 Scale Modeling Factors for Shaking Table Testing Examining Figure 1.1, the relevant modes of SSPSI system response can be identified. They are the free-field soil site response, soil-pile lateral kinematic interaction, soil-pile lateral inertial interaction, soil-pile axial response, and pile and pile cap radiation damping. Table 5-1 lists the variables associated with each interaction mode. Table 5-1 Identification of SSPSI Primary System Modes and Associated Variables SSPSI Interaction Mode
Variables
1. Free-field Site Response
(Vs(z), ρ(z), Modulus Degradation & Damping(z))soil
2.
Soil-Pile Lateral Kinematic 1 + (EI, l, d, fixity)pile, (σ-ε, Su(z))soil
Interaction 3.
Soil-Pile
Lateral
Inertial 2 + (M, K)superstructure
Interaction 4. Soil-Pile Axial Response
1 + (E, l, d)pile, (σ-ε, Su(z))soil, (M, K) superstructure
5. Radiation Damping
1 + (l, d, M, E)pile
The objective of the scale modeling procedure for this test program is to achieve what has been previously defined as “dynamic similarity”, where model and prototype experience homologous forces. Dimensional analysis is the framework for scale model
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similitude in this test program. Three principal test conditions establish many of the scaling parameters. The first is that testing is conducted in a 1-g environment, which defines model and prototype accelerations to be equal. Secondly, a model soil with similar density to the prototype soil is desired, which fixes another component of the scaling relations.
Thirdly, the test medium is primarily composed of saturated clay, whose
undrained stress-strain response is independent of confining pressure, thereby simplifying the constitutive scaling requirements. As previously shown in section 5.1.1, by defining scaling conditions for density and acceleration, the mass, length, and time scale factors can all be expressed in terms of the geometric scaling factor λ, and a complete set of dimensionally correct scaling relations (ratio of prototype: model) can be derived for all variables being studied. The scaling relations for the variables contributing to the primary modes of system response are shown in Table 5-2. Table 5-2 Scaling Relations for Primary System Variables Expressed in Terms of the Geometric Scaling Factor λ Mass Density
1
Acceleration
1
Length
λ
Force
λ3
Shear Wave Velocity
λ 1/2
Stress
λ
Stiffness
λ2
Time
λ 1/2
Strain
1
Modulus
λ
Frequency
λ -1/2
EI
λ5
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With the shear wave velocity scaling factor = λ1/2, the Cauchy condition is met, and Iai’s strain scaling factor can be calculated equal to one, with the result that his set of scaling relations falls in absolute agreement with the values derived for this study. The application of the scaling relations and development of model soil, pile, and superstructure system components will be discussed in the following sections. But before doing so, it is important to recognize the following problem conditions that can propagate into the scale modeling process. They must be accounted for in the design of the model components and/or testing procedures: •
Initial Conditions - referring to both the soil and pile initial stress states,
•
Boundary conditions - incorporating not only model boundary conditions but interface conditions between soil and pile, and soil and cap,
•
Constitutive behavior - remains a soil scale modeling criterion ,
•
Ductility - for pile and superstructure,
•
Material damping - applicable to soil, pile, cap, and superstructure,
•
Strain rate effects - applies to both soil and pile,
•
Long term effects - such as consolidation or creep for the soil, and
•
Group effects - reflecting the configuration of piles in groups.
5.2 Model Soil Design Model soil properties are reflected in all five primary modes of SSPSI described in Table 5-1, but can be segmented into the general categories of free-field response and soilpile interaction. Free-field site response is primarily a function of the small strain soil properties, while soil-pile interaction is ultimately a large strain phenomenon.
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The
parameters describing these soil properties are shear wave velocity, density, modulus degradation and damping, stress-strain response, and undrained shear strength. These parameters are both discrete and nonlinear, and are a function of the loading rate, the number of cycles and strain reversals. The method of implied prototypes is therefore especially well suited to this complex scale modeling problem.
5.2.1 Identification of Soil Modeling Criteria With the model soil density equal to the prototype soil density, one scaling condition is determined.
The nonlinear stress-strain and modulus degradation and
damping curves are not directly modeled from a prototype case, but rather the method of implied prototypes is used to consider whether the scale model properties for these parameters are reasonable. This leaves undrained shear strength and shear modulus (or shear wave velocity) as the principal soil modeling criteria. If the elastic response of both the free-field soil and the soil-pile system is desired, the soil shear modulus should be properly modeled. If the inelastic response of the soil-pile system is desired, then the undrained shear strength should be emphasized. If the full nonlinear system response is desired, then both criteria must be satisfied simultaneously.
Unfortunately these
parameters have different scaling factors, λ for undrained shear strength and λ1/2 for shear wave velocity, which greatly complicates the scale modeling effort. An additional soil modeling criteria not reflected in Table 5-1 is plasticity index. Both static and dynamic soil behavior are known to be strongly influenced by plasticity index (PI), and it is therefore desirable to use a model soil with a similar PI to the prototype (PI is dimensionless and therefore scales 1:1 from model to prototype).
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5.2.2 Definition of Prototype Soil Parameters The target prototype soil selected for this study is San Francisco Bay Mud, a marine clay whose index properties have ranges of values, and is therefore well-suited to the method of implied prototypes. It is also a well-characterized soil that was the subject of a study by Bonaparte and Mitchell (1979), who conducted tests on samples of Bay Mud retrieved from Hamilton Air Force Base in Novato, California. Their findings are shown in Table 5-3, which reflects prototype parameters adopted for this research. Table 5-3 Selected Properties of San Francisco Bay Mud Property
Value
Saturated Unit Weight (pcf)
94
Natural Water Content (%)
90
Liquid Limit (%)
88
Plastic Limit (%)
48
Plasticity Index (%)
40
Undrained Strength Ratio SU/P’
0.32
Coefficient of Consolidation Cv (ft2/yr)
8-10
Dickenson (1994) investigated the seismic response of Bay Mud during the 1989 Loma Prieta earthquake, and proposed the following empirical relationship between undrained shear strength and shear wave velocity: Vs = 18 (Su)0.475
(5.15)
where Vs is in feet per second and Su is in pounds per square foot. This relationship, shown in Figure 5.6, was used to establish the target shear wave velocities for the prototype soil. For prototype soil undrained shear strengths from 600 psf to 1200 psf,
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appropriate shear wave velocities from 375 ft/sec to 525 ft/sec are computed.
Figure 5.6 - Variation of Shear Wave Velocity with the Undrained Shear Strength (Static) of Shallower Cohesive Soils (after Dickenson, 1994)
5.2.3 Model Soil History The option of using a reconstituted soil as the model soil was considered, a technique commonly used in centrifuge testing. In this approach, a natural soil is mined and then mixed with water to form a slurry that can easily be placed in the test container. The soil is then consolidated to achieve the desired strength/stiffness profile, a process greatly facilitated during spin-up in the centrifuge. The consolidation process offers the advantage of fixing anisotropy and a stress history into the soil. But this method was deemed impractical due to the large size of the test container and the very long time that would be required for consolidation in a 1-g environment.
More importantly, a
reconstituted soil would not be able to satisfy the competing scale modeling criteria of undrained shear strength and dynamic shear modulus. Therefore a synthetic model soil was chosen as the soil medium for the testing
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program. A synthetic soil was recognized to sacrifice actual in-situ soil properties such as heterogeneity, anisotropy, fabric, and stress history, but without serious detriment to the performance of a well-designed model soil.
Tavenas et al. (1973) describe the
development of an artificial model soil using kaolinite, Portland Cement, and bentonite to replicate a brittle Lake Champlain clay. Blaney and Mallow (1987) tested numerous stiffening agents used in conjunction with bentonite to fabricate a synthetic overconsolidated clay for dynamic soil-pile interaction tests. Their final model soil design consisted of fumed silica and bentonite, and was extruded in blocks that were bonded together in the test container. Tables 4-3 to 4-6 described model pile testing programs using a variety of model soil materials including kaolinite, bentonite, supersil, plastellina, aerosil, veegum, silicon gum, plasticine, polyacrylimide, sands, and reconstituted clays and clayey silts. But the most extensive research with model clay soil has taken place at U.C. Berkeley. This work originated with Seed and Clough (1963), who developed a mix of kaolinite and bentonite for shaking table modeling of the seismic response of earth embankments. The mix was proportioned as 3 kaolinite:1 bentonite, at approximately 200 % water content, as that fraction of bentonite was found to arrest the consolidation process over the testing time frame; this mix was also noted to exhibit pronounced thixotropy.
In addition, the scaled stress-strain curve of the model soil favorably
compared to that of typical dam core materials.
Seed and Clough defined inelastic
deformations and therefore undrained shear strength as their primary modeling criterion, which was found to be a function of water content. But they also recognized that it was the soil shear strength under dynamic loading which was of interest, and that model and
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prototype soils experience different degrees of dynamic strength gain from the reference static strength. They proposed that the prototype soil static shear strength be multiplied by an additional scaling factor of 0.65 to account for the unequal dynamic strength increases between model and prototype. Sultan and Seed (1967) continued using this model soil for shaking table tests of sloping core earth dams, also at water contents in the range of 200 %. Kovacs (1968) investigated the dynamic response of clay embankments and conducted cyclic simple shear tests to evaluate dynamic moduli and damping ratios for the model clay soil. His model soil was batched at water contents ranging from 88 - 125 %. Arango-Greiffenstein (1971) studied the seismic stability of slopes in saturated clay by shake table testing of embankments constructed from the model soil, again at water contents approaching 200 %. Bray (1990) used the same model soil mixed at 130 - 136 % water content to examine fault rupture propagation through scale model clay deposits. This stiffer mix was required to properly reproduce a fault rupture failure mode, as higher water contents resulted in too viscous behavior. Lazarte (1996) also studied fault rupture propagation with tests on model soil mixes at water contents ranging from 97 - 120 %, and characterized the timedependent strength and stress-strain properties of the model soil. He recognized that the relatively high tensile capacity of the model soil may have suppressed the formation of cracks and unrealistically redistributed the strain field in zones under tension. Figure 5.7 is a summary plot of the model soil undrained shear strength as a function of water content as determined by these researchers.
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Water Content (%)
300 250 200 150 100 50 0 1
10
100
Undrained Shear Strength (psf)
Seed and Clough (1963) - Direct Shear Sultan and Seed (1967) - Direct Shear Kovacs (1968) -Vane Shear Arango (1971) - Model Tests Bray (1990) -UUTX Lazarte (1996) -UUTX
Figure 5.7 - Model Soil Undrained Shear Strength Versus Water Content As Determined by Various Researchers (after Lazarte, 1996)
5.2.4 Development of Model Soil The development of a model clay soil for this research project commenced in 1995 with initial mix designs following the traditional 3 kaolinite: 1 bentonite Berkeley “recipe”. The kaolinite used was a Huber 35 hydrated aluminum silicate, and the bentonite an American Colloid Volclay KWK montmorillonite (these products are similar in composition but not identical to other bentonites and kaolinites used by previous researchers). Small trial batches were prepared in 5 gallon plastic buckets by initially blending together the dry materials and then mixing in the water by hand. The buckets were sealed with an airtight lid and stored in a constant-temperature high humidity wet room. Test specimens were prepared by retrieving material from the storage buckets and remolding the clay into 1.4 and 2 in diameter cylindrical molds for unconsolidated-
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undrained triaxial (UUTX) and bender element shear wave velocity tests, respectively. The time from mixing to testing is referred to as “mix age” and the time from specimen preparation to testing is termed “cure age”. UUTX compression tests and bender element shear wave velocity tests were performed on specimens with a range of water contents from 50 - 130 % to assess the model soil performance. Details of using bender elements for the determination of soil shear wave velocity are provided by Viggiani and Atkinson (1995) and Riemer et al. (1998). Initial tests indicated that for a given undrained shear strength, the corresponding shear wave velocity was too low to meet the criteria of the implied prototype. It was therefore desired to find an admixture that would increase the small strain dynamic stiffness without appreciably affecting the undrained shear strength. The effect of several admixtures, including fine sand, silt, and fly ash, in varying proportions and over a range of water contents, was tested; only fly ash was found to have the desired effect. Fly ash is a silt-sized calcium-rich byproduct from the combustion of coal at electric power plants, and was considered as an economical admixture for the model soil. Results from a series of UUTX compression tests on specimens with 20 % fly ash (all fly ash contents are stated as a percentage of dry weight) are shown in Figure 5.8, illustrating the dependence of undrained shear strength on water content. Figure 5.9 plots the undrained shear strength versus the water content of the clay fraction of the model soil for test specimens with fly ash contents ranging from 0 - 60 %; the clear trend in the data indicated that the fly ash had little influence on the shear strength of the model soil.
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500
Deviatoric Stress (psf)
450 400 350 300 250 200 150
Wc = 61%, Su = 207 psf Wc = 71%, Su = 132 psf Wc = 79%, Su = 92 psf Wc = 94%, Su = 57 psf
100 50 0 0.00
0.05
0.10
0.15
0.20
0.25
Axial Strain Figure 5.8 - Unconsolidated-Undrained Triaxial Compression Test Results For Model Soil Mixture with 20% Fly Ash at Four Water Contents 250
0% Fly Ash 20% Fly Ash 28.5% Fly Ash 40% Fly Ash 60% Fly Ash
Su (psf)
200
150
100
50
0 60
70
80
90
100
110
120
130
Water Content Clay Fraction (%) Figure 5.9 - Model Soil Undrained Shear Strength Versus Water Content of Clay Fraction
235
140
Gruber (1996) carried out a series of 66 UUTX tests on model soil specimens and samples of Bay Mud retrieved from Hamilton Air Force Base in Novato, California to ascertain whether the nonlinear stress-strain response of the model soil implied a reasonable prototype behavior.
The model soil specimens were prepared at water
contents ranging from 60 - 110 % and all contained 10 % class C fly ash. Testing was performed under confined (1 kilogram per square centimeter) and unconfined conditions, and at “normal” (0.045 in/min) and “fast” (4.5 in/min) strain rates. Figures 5.10 and 5.11 illustrate representative UUTX test results for the model soil and Bay Mud. These model soil specimens had a cure age of 4 and 5 days and water contents ranging from 98 - 100 %, while the Bay Mud was sampled from a depth of 4.8 m and had water contents ranging from 89 - 94 %. It is evident that both materials exhibited higher peak strengths under “fast” loading, and decreased sensitivity under confining pressure. Bay Mud displayed higher failure strains under “fast” loading, while the model soil failure strains remained relatively constant for both loading rates. In fact, the model soil behaved as a strain hardening material when tested under confining pressure at both “normal” and “fast” loading rates. Under “normal” unconfined loading, the model soil had a similar failure strain to Bay Mud, but was less sensitive. This raises the question as to whether peak strength or residual strength is most appropriate to model. The observation that lateral and axial pile capacities are formulated in terms of peak strength supports that modeling approach. In summary, the model soil did not precisely replicate the prototype stressstrain behavior, but it did exhibit a reasonable response and was therefore found to constitute an adequate scale model of a higher plasticity soft to medium stiff clay such as San Francisco Bay Mud.
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400
350
Deviatoric Stress (psf)
300
250
200
150 unconfined, strain rate = 0.045 in/min 100
unconfined, strain rate = 4.5 in/min confined (1 ksc), strain rate = 0.045 in/min
50
confined (1 ksc), strain rate = 4.5 in/min 0 0
0.05
0.1
0.15
0.2
0.25
Axial Strain (%)
Figure 5.10 - Model Soil Unconsolidated-Undrained Triaxial Compression Test Results Showing Effects of Strain Rate and Confining Pressure (after Gruber, 1996) 900 unconfined, strain rate = 0.045 in/min 800
unconfined, strain rate = 4.5 in/min confined (1 ksc), strain rate = 0.045 in/min
700
Deviatoric Stress (psf)
confined (1 ksc), strain rate = 4.5 in/min 600 500 400 300 200 100 0 0
0.05
0.1
0.15
0.2
0.25
Axial Strain (%)
Figure 5.11 - Bay Mud Unconsolidated-Undrained Triaxial Compression Test Results Showing Effects of Strain Rate and Confining Pressure (after Gruber, 1996) 3.0
Su dynamic /Su static (peak)
2.5
2.0
1.5
1.0
0.5
0.0 60
70
80
90
100
110
120
130
140
Water Content Clay Fraction (%)
Figure 5.12 - Ratio of Undrained Shear Strength at Dynamic (4.5 in./min.) and Static (0.045 in./min.) Strain Rates for Model Soil in Unconsolidated-Undrained Triaxial Compression Tests (after Gruber, 1996)
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The purpose of studying higher strain rates was to explore Seed and Clough’s (1963) observation that model soil and Bay Mud have different shear strength increases under dynamic loading, and to quantify what correction must be made to equilibrate the dynamic shear strengths. The Bay Mud dynamic strength increase was on the order of 70 % for both confined and unconfined conditions, while the model soil dynamic strength increase was 25 % and 10 % for confined and unconfined conditions, respectively. Figure 5.12 summarizes the model soil dynamic strength increase for all specimens tested; this data suggests that an average dynamic strength increase on the order of 25 % may be adopted. Following Seed and Clough’s methodology, the dynamic strength correction factor to be applied to the scaled prototype undrained shear strength is therefore 0.75. Wartman (1996) conducted a detailed study of the effects of fly ash on the geotechnical properties of the model clay soil. Both class F and class C fly ash materials were tested; the class F fly ash was generated at the Jim Bridger power plant in Point of Rocks, Wyoming, and the class C material was obtained from the Laramie River power plant in Wheatland, Wyoming. The chemical composition of the two fly ash materials is summarized in Table 5-4. He concluded that class F fly ash acted as an inert filler material with only a marginal effect on the model soil’s undrained shear strength and shear wave velocity, but that class C fly ash had appreciable effects: “The class C fly ash used in this study acted as a chemically reactive material when mixed with the kaolinite-bentonite clay. The chemical reactivity is attributed to the high calcium oxide content of the fly ash. When mixed with the clay, the class C fly ash caused rapid cation exchange to occur on the clay minerals leading to a substantial reduction in plasticity. The cation exchange caused the double layer around the clay mineral to shrink resulting in an increase in stiffness and by association, shear wave velocity. The class C fly ash also caused cementacious pozzolanic reaction products to form in the specimens. Increases in undrained strength were
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not always realized from these cementacious bonds, however, because many of the fly ash specimens were remolded as part of the preparation procedures for the unconfined compression tests.... Cure age had little to no effect on the undrained strength of the specimens over the period of interest in this study (days to weeks). Mix age had no effect on the undrained strength of the fly ash-clay mixtures.”
Table 5-4 Chemical Composition of Class F and Class C Fly Ashes Chemical Composition
Class F Fly Ash
Class C Fly Ash
Calcium Oxide (%)
5.97
30.13
Silicon Oxide (%)
61.71
31.53
Aluminum Oxide (%)
19.67
16.87
Iron Oxide (%)
4.47
5.82
Wartman performed bender element tests to determine the shear wave velocity of the model soil mixtures, following recommendations for discerning pulse travel times by Riemer, et al. (1998). Soil shear wave velocity versus cure time for an assortment of model soil mixtures is plotted as Figure 5.13. The strong influences of fly ash content and cure time on shear wave velocity are apparent, with the most dramatic increases in stiffness occurring in the first few days after mixing. A constant rate of strain (0.00012 in/min) consolidation test was performed on a specimen of model soil with 10 % class C fly ash at an initial water content of 100 %. The e-log p curve is shown in Figure 5.14, and the coefficient of consolidation Cv was calculated as 10 in2/year. This slow rate of consolidation implied relatively stable soil properties throughout the shaking table testing time window.
239
200
Shear Wave Velocity (ft./sec.)
180 160 140 120
20% class F - 100% m.c. 20% class C - 100% m.c.
100
10 % class C - 110% mc 80
10% class C(#2) - 100% m.c. 10% class F - 100% m.c.
60
10% class C(#2) - 100% m.c.
40
20% class F - 80% m.c. 10% class C(dyn) - 100% m.c. 5% class F - 100% m.c. 0% fly ash - 100% m.c.
20 0 0
5
10
15
20
25
Cure Age (days)
Figure 5.13 - Shear Wave Velocity Versus Cure Age for Model Soil Specimens with Varying Fly Ash Contents (after Wartman, 1996) 3.20
3.00
Void Ratio
2.80
2.60
2.40
2.20
2.00 100
1000
10000
100000
Stress (psf)
Figure 5.14 - Void Ratio Versus log Pressure for Constant Rate of Strain Consolidation Test of Model Soil Specimen
240
Cyclic triaxial testing of the model soil was performed to determine modulus reduction and damping curves, but testing inaccuracies initially yielded incomplete data to construct these curves. An advanced triaxial testing device was later used to establish modulus reduction and damping curves from samples of the insitu model soil, which were then compared with reference curves for Bay Mud and medium plasticity clays. This work is described in Chapter 7, and the model soil specific curves were used for site response and SSPSI analyses. Finally a model soil composed of 67.5 % kaolinite, 22.5 % bentonite, and 10 % class C fly ash, at 100 % water content was selected as the design mix. This water content was expected to provide the key elements of mixability and pumpability for shake table model testing. The model soil had a unit weight of 94 pcf, a liquid limit of 115, a plastic limit of 40, and a plasticity index of 75. The undrained shear strength of the mix at a cure age of 5 days was determined to be 85 psf, and the shear wave velocity at the same cure age was 130 ft/sec. This benchmark cure age was used as it was expected that the time from soil placement to time of testing and the time between tests would be approximately five days. The prototype values implied by these model properties with a geometric scaling factor of 8 are a static undrained shear strength of 520 psf (with 0.75 dynamic strength correction factor) and a shear wave velocity of 365 fps. These values are in agreement with Dickenson’s relation and the model soil was therefore found to constitute an adequate scale model of a higher plasticity soft to medium stiff clay such as San Francisco Bay Mud.
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5.3 Model Pile Design As for the model soil, the model pile was subject to competing scale modeling criteria. By addressing the principal governing factors of pile response, a successful model pile design was attained. The four primary modes of pile response recognized in Table 5-1 are soil-pile lateral kinematic interaction, soil-pile lateral inertial interaction, soil-pile axial response, and pile radiation damping.
5.3.1 Identification of Pile Modeling Criteria Numerous pile properties contributing to the principal modes of pile response were identified, including slenderness ratio L/d, flexural rigidity EI, yield behavior/mechanism, ductility, moment-curvature relationship, buckling properties Pcr and d/t, natural period of vibration, and relative soil/pile stiffness. Geometric similarity was adopted as a strict modeling constraint, so that overall pile slenderness and relative contact surface area would be preserved in the model. This also ensured that pile group relative spacing and consequent group interaction would be replicated at the model scale. The pile moment-curvature relation was selected as a primary modeling criterion as it encompasses both flexural rigidity and yield behavior to describe the full range of nonlinear pile response to lateral loading. In this regard it is important to consider the current state-of-practice seismic design for bridge pile foundations.
The prevailing
philosophy is to generally design piles to respond in their elastic range without yielding, concentrating ductile behavior in the bridge columns. The rationale is that damage to above ground structures is much easier to detect and repair than damage to subsurface elements.
The implication for this modeling program is that by scaling pile EI and
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ensuring a yield point equal to or greater than that of the scaled prototype, the working range of pile lateral dynamic response is correctly modeled. With soil resistance properly scaled, both soil-pile lateral kinematic and inertial interaction should then be accurately reproduced in the model. Both nonlinear and cyclically degrading lateral pile response are therefore captured by the soil behavior. Soil-pile axial response for end-bearing piles is primarily a function of soil properties in the bearing strata. Soil-pile interface friction/cohesion along the shaft and pile elastic deformation constitute secondary factors for end-bearing pile axial response, especially in soft soils. While the axial loading is dynamic in nature, the static axial capacity of the pile is a crucial factor as it determines the inertial load the pile carries. Pile radiation damping can be considered to have two components. First, the inherent vibration characteristics of the pile determine its ability to generate energy to radiate into the soil. Second, the propagation of energy away from the pile depends on the relative soil-pile stiffness. With soil and pile elastic properties consistently scaled, the relative soil-pile stiffness automatically scales from the prototype to the model. But the inherent pile vibration characteristics are a more difficult modeling criterion to meet. The frequency of vibration of an end-bearing pile can be idealized by the equation describing the frequency of vibration of a cantilever rod (Clough and Penzien, 1996), which is seen to be a function of the rod’s mass: ω = 3.516
EI 4 mL
(5.16)
With pile geometry and EI scaled as previously described, the mass per unit length of the model pile must be scaled by a factor of 1/λ2 from the prototype. With conventional
243
materials and other modeling constraints, this criterion could not be satisfied.
But
recognizing that radiation damping is most pronounced at smaller levels of shaking, it could be expected to have a diminished influence at the strong levels of shaking planned in this test program. Secondly, piles are only a component of the soil-pile-superstructure system, and altering to some degree the vibration characteristics of a lesser component of that system would not be expected to as significantly affect the vibration characteristics of the entire system.
5.3.2 Definition of Prototype Pile Parameters From standard Caltrans design, a 16 in diameter x 0.5 in wall concrete-filled steel pipe pile was selected as the target prototype. Scaling constraints dictated a maximum prototype pile length of 44 ft, which provided a L/d ratio of 33, acceptable for a slender pile. The fixity conditions of the pile, known to be significant in lateral response, were established as fixed against rotation at the head, and fixed against (relative) translation at the tip. This corresponds to a pile driven into a firm strata at the base, and cast into the pile cap with a connecting reinforcing cage. The flexural rigidity EI of a composite concrete/steel pile is nonlinear due to concrete cracking; therefore the concrete contribution to the composite EI was degraded by 50 % to yield a composite EI of 181,920 k-ft2. The first mode period of vibration of a cantilever rod with the prototype pile properties was computed as 0.74 seconds.
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5.3.3 Development of Model Pile An iterative spreadsheet solution was employed to satisfy the principal pile design criteria of flexural rigidity EI and first mode vibration period of an equivalent cantilever rod (see Appendix B). A geometric scaling factor of 8 was found to optimize both soil and pile scaling requirements. With a target model EI of 5.55 k-ft2 and the model pile outer diameter fixed at 2 in, the moment of inertia was computed for cases of solid and thin wall tubes, and the corresponding lower and upper bound elastic moduli were calculated to be 1000 and 10000 ksi, respectively. At these two bounding values, the pile material density was calculated that would impart the scaled vibration modes. Unfortunately, these density values ranged from 1880 to 3650 pcf for the solid and thin wall sections, respectively. Obviously such materials are not feasible, and this requirement was relaxed as previously explained in section 5.3.1. Many materials were investigated to ascertain their suitability as a model pile material; Table 5-5 summarizes the moduli and yield stresses of these prospective materials. From this table it can be seen that aluminum 6061 T-6 alloy is the only candidate that falls in the range of acceptable modulus, and must be configured as a thin wall section to meet the EI criterion. A wall thickness of 0.0265 in was calculated as producing the correctly scaled model pile flexural rigidity. The minimum wall thickness of commercially available aluminum tubing is 0.028 in, which results in an EI of 5.86 k-ft2, a 5 % deviation from the target value. Although a thin wall tube provides a potential local buckling mechanism not present in the solid prototype cross-section, this geometry proved favorable for the external mounting of foil strain gages and internal routing of the gage lead wires. Importantly, aluminum is a relatively economical material, is readily available
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in thin wall tube sections, and is suitable for mounting foil strain gages. With respect to axial performance, calculations of driving stresses, static loads, and stresses under dynamic loading were found not to exceed the aluminum tube buckling load Pcr. To ensure elastic response of the thin-walled aluminum tube, the theoretical moment-curvature relation of the trial model pile was compared to that of the prototype. The moment-curvature relation describes the pile nonlinear response to applied loading and is analogous to a soil stress-strain curve. Lower and upper bound prototype cases were established using yield stresses in the steel pipe pile of 50 and 70 ksi, with contributions of 0 and 100 % of concrete EI representing intact and fully cracked sections. The pile analysis code COM624P was used to define the lower and upper Table 5-5 Mechanical Properties of Candidate Model Pile Materials Material
Elastic Modulus (ksi)
Yield Stress (ksi)
29000 17000 10000 420 420 410 410 390 - 480 300 - 350 250 170 - 250 213 160 150 140 135 60 - 180 70 58 50 35 14 - 38
60 30 40 17 14.5 12 10 – 14 12 – 17 13.5 4 – 14 7 9.7 2.9 6 15.5 10 7 3 2–5 2.7 - 3.1 4.2 2.3
Steel copper aluminum 6061 T-6 nylon PVC polyamide polyacetal acrylic PMMA polycarbonate ABS polypropylene PVDF ryton CPE vinylester fiberglass epoxy fiberglass high density polyethylene flurocarbons teflon TFE teflon FEP polybutylene low density polyethylene
bound moment-curvature relations shown in prototype scale in Figure 5.15. This method 246
was calibrated against the results of a four-point loading test conducted by Caltrans on a 24 in diameter concrete-filled steel pipe pile (Brittsan, 1995). To compute the momentcurvature of the model pile, the method of Langhaar (1951) was followed, where the equation of statics describing bending of a ductile beam of circular cross-section is expressed as 3 1
M = 2 c ∫ β σ ζ dζ 0
(5.17)
in which c is the radius, ζ is the ordinate from the neutral axis divided by the radius, β is the width of the cross-section at the ordinate divided by the radius, and σ is the stress at the ordinate of the cross-section. This derivation assumes an elastic-perfectly plastic stress-strain relation for the beam. The moment-curvature relation for the trial aluminum model pile is superimposed on Figure 5-15 at prototype scale, and can be seen to exceed the yield behavior in the target prototype range. As previously explained, this is an acceptable result as the pile is intended to respond in its elastic range. An “ideal” model pile material that would precisely fit the scaled moment-curvature relation was calculated to have a wall thickness of 0.2 in, an elastic modulus of 3000 ksi, and a yield stress of 2 ksi. Extensive research indicated that such a material could not be obtained nor easily manufactured, and the thin-walled aluminum tube was proof tested to confirm its performance.
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20000 18000 16000
Moment (k-in)
14000 12000 10000 8000 6000 Aluminum Tube 2" dia. X 0.028" wall scaled up
4000
Steel Yield = 80 ksi, Concrete = 7 ksi
2000
Steel Yield = 50 ksi, Concrete = 0
0 0
0.0005
0.001
0.0015
0.002
Curvature (/in)
Figure 5.15 - Theoretical Lower and Upper Bound Moment-Curvature Relations for Prototype Pile as Determined by COM624P Loading Diagram P/2
P/2
strain gages 0.875 P
Bending Moment Diagram
Figure 5.16 - Diagram of Four-Point Loading Test of Model Pile 5000 4500
Moment (lb-in)
4000 3500 FAILURE
3000 2500 2000 1500 1000
Experimental Data Theoretical
500 0 0
0.005
0.01
0.015
0.02
Curvature (/in)
Figure 5.17 - Theoretical and Experimental Moment-Curvature Relations for 2” Diameter x 0.028” Wall Aluminum Tube Model Pile
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5.3.4 Four Point Loading Test A 6 ft long section of the 2 in diameter aluminum tube with a wall thickness of 0.028 in was load tested to verify its moment-curvature relation. A four point loading test was performed, with the tube simply supported near its ends, and equal loads were applied at two points as diagrammed in Figure 5.16. This loading pattern results in a zone of constant moment being applied across the central section of the member. Foil strain gages mounted to the compression and tension faces of the tube were read at each loading increment, and moment and curvature calculated from the strain data. The experimental moment-curvature relation for the model pile is shown in Figure 5.17, superimposed on the theoretical plot, both at model scale. The agreement in the range of elastic response is excellent, and the test pile failed instantaneously with a buckling mechanism very near the theoretical yield point. The failure load was 163 lbs, imposing a bending moment of 3420 lb-in. These results proved the aluminum tube to be an adequate model pile for the scale model testing program. With scale model similitude relations defined and a model soil and model pile designed, the following chapter will describe the development of the shaking table test program for the study of SSPSI.
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CHAPTER 6
SHAKING TABLE TEST PROGRAM
6.1 Introduction – Test Objectives The purpose of performing shaking table scale model tests as part of this research was twofold. First, the tests were designed to provide qualitative insight into a variety of SSPSI problems, as will be examined in Chapter 8 of this dissertation. Secondly, the tests were conducted with the intent of generating a data set with which to calibrate an advanced numerical analysis tool for SSPSI being developed at U.C. Berkeley, which is the subject of current work by Lok (1999). The shaking table tests were conducted in two phases, in November/December 1997, and July/August 1998. The intervening time period was used to analyze the Phase I test data, consult with the research sponsor (Caltrans), make improvements in the testing procedures, and focus Phase II testing on matters of particular interest to the sponsor. The issues and objectives addressed in the Phase I test series included the following: •
Evaluate free-field site response to verify model container performance,
•
Examine inertial and kinematic interaction for single piles,
•
Contrast pile group rocking and translational response, and frequency effects,
•
Consider the influence of pile cap embedment on lateral and rocking stiffness,
•
Study performance of pile raft foundations, and
•
Simulate wave loading with impounded water to induce scour in soil-pile gaps. The subjects of Phase II testing included:
•
Revisit free-field site response performance,
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•
Revisit the pile cap embedment issue,
•
Investigate pile group effects,
•
Consider applicability of 2-D analysis to 3-D response (biaxial input motions), and
•
Compare single pile and pile group stiffness derived from static and dynamic head loading tests with the seismic response of similar structures. This chapter will describe the shaking table test facility, the development of the
model testing container, test instrumentation and data acquisition, and provide a description of the overall test plan and the procedures followed for setting up the shaking table scale model tests.
6.2 Earthquake Simulator Facility The shaking table tests were performed on the newly upgraded earthquake simulator at the Pacific Earthquake Engineering Research Center (PEER) at the University of California Richmond Field Station. This shaking table was originally brought on line in 1970 in a uniaxial configuration, but has recently been retrofitted to provide for six controlled degrees of freedom, thus allowing for two- and three-dimensional input motions. This unique capability permits deformation modes not presently attainable in centrifuge model testing. The testing platform measures 20 ft x 20 ft in plan, is 1 ft thick, and weighs approximately 100,000 lbs. The platform is constructed from a combination of reinforced and prestressed concrete, stiffened by transverse ribs to inhibit bowing or warping, and is supported by 8 vertical and 8 horizontal actuators located in a pit beneath the table (see Figure 6.1). The 1 ft gap between the shaking table and the pit wall is sealed by a continuous vinyl-covered nylon fabric.
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In operation, the pit is sealed off and
pressurized, so that the total mass of the table and model is supported by the differential air pressure, thereby “floating” the table and relieving load on the actuators (1.5 psi counteracts the weight of the “bare” table). The actuator forces are counteracted by a massive foundation, which consists of a reinforced open box structure with 5 ft thick walls. 32' 20'
Plan
10'
5' Section
Figure 6.1 - Shaking Table Layout The shaking table is driven by hydraulic actuators equipped with servo-valves. The (8) 70 kip horizontal actuators are 10.5 ft long, and the (4) 25 kip and (4) 75 kip vertical actuators are 8.67 ft long. The positions of the actuator pistons are controlled by means of an electronic closed-loop displacement feedback system, supplemented by velocity and force feedback signals to improve performance characteristics. The MTS multiple channel feedback analog control system allows the table to run under
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acceleration, velocity, and displacement control.
The shaking table has a maximum
payload of 130 kips, and the table performance is a function of both the payload and different limiting factors over the frequency band. At frequencies lower than 1 Hz, the table motion is limited by the maximum actuator stroke of 5 in.
At intermediate
frequencies from 1 – 4 Hz, the servo-valves can accommodate table velocities in excess of 25 in/sec.
At higher frequencies the force capacities of the actuators limit table
accelerations to 2.5 g (all specifications for longitudinal axis). Vertical capacities are ± 2 in displacement, 15 in/sec velocity, and 4.0 g acceleration. Shaking table-structure interaction causes the frequency content of the table response to be altered from that of the command signal, near the resonant frequency of the test structure. This is particularly undesirable since the purpose of many earthquake simulation tests is to excite the structure at its resonant frequency. Rinawi and Clough (1991) made a study of the U.C. Berkeley shaking table before the recent upgrade and found that significant table-structure interaction was limited to cases of testing tall and heavy models, where large overturning moments could cause undesirable table pitch, twist, and roll motions. The effect of table-structure interaction was seen to result in a lower system frequency and increased damping. In an earlier study, Rea et al. (1977) found that foundation compliance affects the frequency response of the shaking table only at low frequencies, the magnitude of which depends on the transmissibility function of the foundation with respect to the table. Characterization of the new table configuration is an ongoing process and preliminary results seem to substantiate earlier findings, which is favorable to the short and relatively lightweight models used in this research. 6.3 Model Testing Container
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Physical modeling of soil deposits requires a container to support the model soil, and the container/model contact imposes boundary conditions that do not exist in the prototype condition. A successful container design allows the model the freedom to deform under seismic loading in the same manner as the prototype free-field soil deposit, and minimizes the influence of boundary conditions. For this research project it was desired to take advantage of the shaking table’s unique capabilities and for the model container to provide full 3-D motion. Other container design goals included rendering correct response over the range of test conditions, including shear failure of the soil. Fiegel (1995) performed centrifuge testing of four model containers filled with dry sand subjected to 1-D seismic shaking to investigate the performance of the different designs. The containers tested included 3 flexible types, an equivalent shear beam, a hinged plate, a laminar box, and a fixed end design. The different response of the four containers is summarized in Figure 6.2, which shows that the fixed end design has adequate performance when the stiffness contrast between the soil (in this case dense sand) and the wall is not great.
Fiegel used the hinged plate container for further
centrifuge studies of the seismic response of soft clay deposits. For this research project studying soft soil response, the simple shear deformation mode achieved by flexible containers was recognized as a necessary feature. The model container was therefore designed with a cylindrical geometry to provide 3-D capability, and was designed to be laterally flexible in simple shear to allow multi-directional shear deformation. But the container was also required to be radially stiff, to prevent lateral bulging and vertical pumping of the soil mass. The model container was designed to have constant wall stiffness over its height, suitable for cohesive soils whose stress-strain
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response is independent of confining pressure.
Figure 6.2 - Comparison of Free-Field Soil Response in Four Model Containers (after Fiegel, 1995)
6.3.1 Numerical Modeling of Container Effects Lok (see Riemer and Meymand, 1996) performed numerical modeling of various container designs with the computer code QUAD4M to explore the flexible cylinder design. The benchmark case was a 40 ft deep deposit of San Francisco Bay Mud, and three hypothetical model container configurations containing model soil were also excited with the same base input seismic motion. The container configurations were modeled in two dimensions, and consisted of a rigid-wall box, a box with inclined rigid walls, and a flexible-wall box; these are shown in Figure 6.3. The box with inclined rigid walls was thought to have the potential of trapping and attenuating reflected wave energy in the tapered end zones. The flexible-wall box was assigned a modulus slightly higher than that of the soil to reflect its confining properties. The results of the QUAD4M analysis are shown in the 5% damped response spectra of the acceleration time history recorded at the
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center of the soil surface (Figure 6.4), with all results plotted at model scale. This analysis clearly demonstrated the advantage of a flexible-wall container over rigid-wall designs in replicating the prototype response. Results for soil response at other points nearer the wall, deeper in the soil, etc., showed the same trend. 2
level ground 5 ft.
Bay Mud Prototype
1
Winged Model Box 4 5 ft.
rigid walls 5 ft.
3
20 ft. 3.75
40 ft.
1
Rigid Wall Box
Flexible Wall Barrel
Figure 6.3 - Evolution of Model Container Design for this Research Project 4
Damping = 5%
Wing Wall Box Rigid Wall Box
3 2.5 2 1.5 1 0.5 0 0.01
Spectral Acceleration (g)
3.5
Prototype Flexible Wall Barrel: Gwall = 50 ksf, Gsoil = 30 ksf
0.1
1
10
Period (Sec.)
Figure 6.4 - Comparison of Free-Field Soil Response of Rigid and Flexible Wall Model Containers with Prototype Condition 6.3.2 Small-Scale Container Shaking Table Tests To test the feasibility of the flexible cylinder design, a small-scale mock-up was
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conceived and built from simple “hardware store” parts. Although only intended as a demonstration tool, the mock-up was tested on the small shaking table in Davis Hall to evaluate and refine the container design. In fact, between May and September 1996, five generations of this mock-up container were tested, with each version an improvement on the former. It consisted of a 3/32 in thick rubber membrane formed into a 16 in diameter cylinder 18 in tall, with an integral bottom, and surrounded by Kevlar bands. This cylinder was attached at the top to a 26 in outer diameter plywood ring, which was in turn supported by steel rods with universal joints at top and bottom. Six rods bolted to a bottom ring in the first version, and four rods bolted directly to the shaking table in later designs. The base connection details were improved in each version, and finally consisted of a steel plate over the rubber base bolted directly to the shaking table. The small-scale test container is shown during shake table testing in Figure 6.5.
Figure 6.5 - Small Scale Model Container Testing on Davis Hall Shaking Table
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Spectral Acceleration (g)
2 Test 2.03 - 3 Hz. Base Input Surface Response 1
Surface SHAKE91
0 0.01
0.10
1.00
10.00
Period (sec)
Figure 6.6 - Site Response in Small Scale Model Container Illustrating Correlation Between Observed and Computed Response Dozens of tests were performed on the five model containers, with a variety of sinusoidal and earthquake input motions. The models consisted of soft soil, stiff over soft soil, and soft over stiff soil site profiles. Single model piles were included in three of the test containers, and accelerometers were deployed to measure soil, container, and pile head accelerations. The tests and model components were not designed or conducted in accordance with scale model similitude. The computer codes SHAKE91 and QUAD4M were used to simulate the experimental results. A consistent result initially obtained was that the model containers exhibited amplification of response through the soil column at both the site period and input excitation period, whereas the numerical analyses predicted amplification only at the site period. Much attention was devoted to improving the base fixity of the model container design, which did result in decreased amplification of the input period, but did not eliminate it entirely. It was realized that additional efforts must be made to decrease system compliance at the base and in the connections, as well as to isolate the soil from the top ring by not filling the container to the top, and to provide a
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more flexible wall. A comparison of the observed response and the response simulated with SHAKE91 for a later test is shown in Figure 6.6. While the small-scale model container tests did not afford perfect validation of the design concept, invaluable insight into full-scale container design details was gained, along with important experience with instrumentation and data acquisition and processing techniques.
6.3.3 Full Scale Container Design and Construction To translate the design concept into a working detailed design for the model container, it was necessary to estimate the forces in the system in order to size the components. Work done by Veletsos (1984) on the seismic response and design of liquid storage tanks was used as the basis for estimating the wall pressures and hoop stresses in the model container. This analysis is contained in Appendix C, and as it assumes both convective and hydrostatic components of dynamic response, it is conservative for this application. To determine the structural loads on the top ring and rod/universal joint assemblies, it was assumed that the shear strips on the interior of the container would carry loads into the structure equal to the peak shear strength of the soil multiplied by the surface area of the shear strips. Kevlar bands were selected that would carry the hoop stresses in the walls of the container, but it was also necessary to determine the allowable spacing between the bands. Timoshenko and Woinowsky-Krieger (1959) give a solution for the deflection of a banded cylindrical shell subject to constant internal pressure. This solution requires a value for the modulus of the shell, which in our case was unknown (and is not a manufacturers specification due to rubber’s highly nonlinear stress-strain response). Two
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series of tests were performed to establish the modulus of the ¼ in neoprene rubber intended to be used as the membrane material. The first was a wide strip tension test in which 6 in wide specimens of the neoprene were loaded in tension to establish the material specific stress-strain response. The second test was a very unique experiment consisting of a 3 ½ in diameter closed end neoprene cylinder 8 in tall, fabricated with rigid external bands spaced from 1 - 4 in. The cylinder was pressurized through the top cap and deflections at the midpoints between bands were measured (see Figure 6.7). From these two tests a modulus for the specific membrane material was established, and a 2 in spacing between the Kevlar bands was determined adequate to prevent excessive bulging of the model container during dynamic loading.
Figure 6.7 - Laboratory Pressure Test of Rubber Cylinder for Design of Band Spacing
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The full-scale container confines a soil column 7 ½ ft in diameter up to 7 ft in height, and is shown in Figure 6.8. The external cross-bracing is for temporary support while building the models and is removed during testing. The top ring and base plate are constructed from 5/8 in thick steel plate. The top ring is supported by four extra heavy wall 2 7/8 in diameter steel pipes with heavy-duty universal joints connecting the pipes to the top ring and the shaking table, thereby providing the model with full translational and rotational freedom, but preventing bending of the soil column. A ¼ in thick cylindrical 40 durometer neoprene rubber membrane is bolted to the top ring and base plate with compression rings. Woven Kevlar bands 2.0 in wide and 0.072 in thick are arrayed circumferentially around the exterior of the membrane. This high strength and high
Figure 6.8 - Full Scale Container Mounted on Shaking Table, with Support Struts, and Soil Mixer/Pump in Background
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tensile modulus Kevlar material is manufactured by Bally Ribbon Mills and has a minimum breaking strength of 12,000 lbs. The combination of the rubber membrane and the Kevlar bands provides the desired container properties of lateral flexibility and radial stiffness. Full-length textured geomembrane strips (40 mil GSE HyperFrictionFlex) are hung in an alternating pattern from the top ring and base plate around the inner circumference of the rubber membrane. These 6 in wide strips provide a path for complementary shear stresses developed in the soil to be carried in the container. The base plate of the container was roughened by epoxying a high friction coating containing angular crushed gravel pieces onto its surface.
6.4 Test Instrumentation Three types of data were desired to be obtained from the shaking table tests, and therefore three classes of instrumentation were required. Accelerations of the soil mass, pile heads, pile caps, superstructures, and model container required a general purpose accelerometer sensor. Displacements of the pile heads, pile caps, and superstructures could best be obtained by wire potentiometers fixed to reference frames mounted off the shaking table. Bending and axial strains in the model piles were to be recorded by resistance-type strain gages. The option of measuring pore pressure data in the soil was not pursued as the scale model was designed for undrained conditions.
6.4.1 Accelerometers As part of the test program, it was necessary to obtain accelerometers that could be placed in the soil mass of saturated clay. In addition to being waterproof, the selection
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criteria for the accelerometers were high sensitivity, DC response, small size, and economy. Solid-state piezoresisitive accelerometers (model 3022-005g) manufactured by IC Sensors, were found to provide excellent performance at a low cost, although a separate watertight case had to be fabricated for each unit. These accelerometers consist of a micromachined silicon mass suspended by multiple beams from a silicon frame. Piezoresistors in the beams change their resistance as the motion of the suspended mass stresses the beams.
The sensing elements are arranged in a Wheatstone bridge
configuration and supplied with an excitation voltage, thereby canceling off-axis, temperature, and other spurious inputs. These accelerometers are critically damped with a resonant frequency in the range of 1 KHz, and a flat response past 300 Hz, as can be seen in the typical calibration record shown in Figure 6.9.
Figure 6.9 - Calibration Record of Typical IC Sensors 3022-005g Accelerometer The accelerometers were mounted in specially fabricated anodized aluminum watertight cases and attached to 3 x 4 in thin plexiglass cards, in order to increase the surface area for resistance to twisting in place in the soil.
Pile head and structure
accelerometers were fixed in their cases directly to the structures. As the aluminum cases were hollow inside, the net mass of the accelerometers relative to the soil displaced, and the structures was negligible. For 2-D and 3-D accelerometer stations in the soil, the
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plexiglass cards were glued together with orthogonal faces. An open case with the accelerometer sensor visible and a 3-D station are shown in Figure 6.10.
Figure 6.10 - IC Sensors Accelerometer Mounted in Protective Case and 3-D Array
6.4.2 Strain Gages The model piles were instrumented with temperature-compensated bonded electrical resistance foil strain gages to detect bending and axial strains.
Each
instrumented pile was equipped with seven pairs of strain gages fixed to opposing faces of the aluminum tube at the positions shown in Figure 6.11. This gage configuration was employed to provide adequate resolution of the expected pile strain profiles, which is normally concentrated in the upper 1/3 of the pile. The gages were oriented on the tension and compression faces of the model pile with respect to the direction of shaking to detect bending strains, and 90 degrees from this axis to detect axial strains.
Several
model piles were fabricated with gages on all four faces so that bending and axial strains could be simultaneously recorded in a single pile.
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Superstructure
S1T
Column S1FR S1B
S1RR Pile Cap
depth below ground surface 8" 12" 18"
Piles 30"
48"
60" 66"
Bearing Layer Base Plate
Figure 6.11 - Section Showing Model Pile Strain Gage Locations Relative to Ground Surface and Position of Supestructure Accelerometers The exterior of the model piles was prepared by cleaning and sanding the gage locations. Micro-Measurements Group model CEA-13-125UW-120 strain gages were fixed to the exterior of the model piles with M-Bond 200, and lead wires were soldered and passed through small holes in the pile wall and routed through the interior of the piles. The gage and wire assemblies were covered by a multi-step surface treatment consisting of M-Coat A polyurethane, M-Coat B nitrile rubber, and M-Coat J protective coatings.
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Wheatstone bridge gage completion circuits for both axial and bending strain configurations were mounted on the top ring of the test container, which were in turn wired into the data acquisition system. The half bridge configuration shown in Figure 6.12a is such that bending of the pile causes equal and opposite resistance changes in the two active gages, and the net voltage output doubles the voltage change across each arm of the bridge. Compressive or tensile strains result in a net voltage output of zero. The half bridge configuration shown in Figure 6.12b is such that axial straining of the pile causes equal resistance changes in the two active gages, and the net voltage output doubles the voltage change across each arm of the bridge. Bending strains result in a net voltage output of zero.
(a) (b) Figure 6.12 - Diagram of Wheatstone Bridge for Detecting: a) Pile Bending Strains; b) Pile Axial Strains (after Gohl, 1991)
6.4.3 Wire Potentiometers The wire potentiometers used to measure displacements were model PT101-30A manufactured by Celesco Transducer Products. The wire pots consist of a primary and secondary coil assembly and magnetic core which, when displaced along the axis and within the core of the coil assembly, produces a voltage output proportional to the displacement. The moving core is fixed to a tensioned spool of fine wire with a travel length of ± 15 in. The wire pots were mounted on stiff reference frames positioned off the
266
shaking table, and the end of the tensioned spool was linked to an extension wire which was connected to the superstructure model at the point of interest. As it was desired to isolate translational displacement from bending displacements, pairs of wire pots were deployed with a fixed vertical separation and attached to a stiff mast which was mounted to the model superstructure.
6.4.4 Signal Conditioning and Data Acquisition System The data acquisition system was managed by the integrated software package Autonet, which is run on a network of desktop computers and interfaces with the MTS shaking table control system. The amount of instrumentation used for the model tests was constrained by the availability of signal conditioners, with a maximum of about 144 channels of data acquired for any given test. The shaking table has built in acceleration and displacement sensors, which occupy the first 16 data channels.
Constant input
excitation voltages were supplied to the accelerometers, strain gages, and wire potentiometers, and their outputs were amplified using Pacific model 8255 signal conditioners/amplifiers. The signal conditioner low pass filters were set at 100 Hz for all data channels. The analog to digital conversion was performed by a Preston model GMAD-2A multiplexer with 15 bit resolution and a throughput of 300 KHz.
The
sampling rate for the model tests was normally 200 Hz, but rates up to 2.5 KHz were used for the hammer blow tests. Time delay between channels and waveform aliasing were therefore not of concern. The interpolation of the analog waveform from the digitized data is known to be accurate up to the Nyquist frequency, which is equal to one-half the sampling rate. Resolution of the model test data to 100 Hz reflects information in the
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prototype up to 35 Hz, which was judged adequate for the purposes of this research. The shaking table data acquisition and control console is shown in Figure 6.13.
Figure 6.13 - Shaking Table Control Console Each accelerometer and wire potentiometer was individually calibrated before installation. The accelerometers were calibrated in the field of gravity with a two point calibration method. The wire pots were calibrated with gage blocks also with a two point calibration method. The pile strain gages were calibrated by shunt resistors. An online calibration check was performed just before each shaking table test through the data acquisition system, thereby identifying any malfunctioning or miswired sensors. With the calibration routine embedded in the data acquisition system, the acquired data was automatically transformed into engineering units of g (acceleration), µstrain (bending and axial strain), and inches (displacement). Overall the performance of the accelerometers and wire pots was excellent, and the strain gages had a failure rate of < 5%, primarily due to chemical attack of the fly ash in the model soil. The test data was processed with the software program Matlab, and automated and interactive routines were written that provided for immediate visualization and analysis of test results.
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6.4.5 Data Precision and Accuracy Sabnis et al. (1983) provide a detailed discussion of “Accuracy and Reliability of Structural Models”. They point out various factors over the entire course of the scale modeling process that may affect the model confidence level. In the model design phase, similitude and size effects may affect the model, though chapter 5 of this dissertation has outlined the careful development of the scale modeling process employed for this test program. In the manufacture of materials phase, imperfections or overstrength may alter the scale model performance during testing. For these reasons, component proof testing and in-situ testing have been employed in this test program to verify the actual model material properties.
In the model construction phase, installation procedures and
boundary conditions may result in different stress conditions between model and prototype. The design of the model container has endeavored to minimize the influence of boundary conditions, and the model pile installation procedure was designed to mimic that of the prototype. The loading phase is another source of variability between model and prototype, although the philosophy has been taken that minor variations between the command signal and actual input are acceptable, so long as the actual input to the system is known and recorded. Instrumentation errors may occur in the deployment of the sensors, the sensing, or data recording. The effect of the sensor on the model is an issue to be considered. Uncertainty arising from the interpretation of the model data is primarily due to human error, which may also occur in human-written computer algorithms used in processing the data. Finally, extension of the model test data to the prototype must again utilize scale model similitude; as previously noted, the best application of scale models is to gain insight into prototype behavior, not to derive precise prototype performance.
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Scale model test data is more appropriately used to calibrate analytical models at the model scale. The sources of error arising from instrumentation consist of inherent sensor accuracy and sensor deployment; the instrumentation used in this research provided high precision. The IC Sensors accelerometers are rated with a flat response from zero to in excess of 300 Hz, well beyond the frequency range of interest for these tests, and with a maximum nonlinearity < 0.2%. The positioning of the accelerometers in the soil was accomplished by manual surveying methods, which if not perfectly orthogonal to the axis of shaking, could result in a reduced output signal. And individual accelerometer arrays could possibly have experienced small permanent movements during the course of testing. But even a 10 degree off-axis shift would result in a signal reduction < 1.5%. The strain gage transverse sensitivity is specified as 1.2 ± 0.2 %, and inaccurate gage mounting or pile driving not perfectly perpendicular to the axis of shaking could potentially result in very small signal distortions. The wire potentiometers are rated with a linearity within 0.1%.
6.5 Model Construction The model container was filled with model soil once for each test phase. Each test phase included five series of tests on the model setups described below in section 6.6.4. Each model was disassembled the day after testing, and the piles were removed and the holes backfilled with model soil. Model piles for the subsequent setup were driven the following day, and approximately five days elapsed until the following tests to allow for the beneficial effects of model soil thixotropy. The model setups were positioned such
270
that each installation utilized a different part of the container and the soil mass in the vicinity of the piles being tested was relatively undisturbed by previous models.
6.5.1 Model Soil Mixing and Placement Phase I of the test program commenced with erecting the model container on the shaking table and placing a 6 in layer of stiff model soil as a bearing stratum. This stiff model soil had originally been mixed at 130 % water content but it had been spread out and allowed to air dry for two weeks; consequently it was very heterogeneous but overall it was fairly dry and chunky (this material was never formally characterized). Over the course of the next 8 days, 13 batches of model soil were mixed and pumped into the container. The plot of water content for 2 samples from each of the 13 batches shown in Figure 6.14a illustrates the batch consistency, except for the first batch which included excess water in the pump; the plot of water content for the second test phase is shown in Figure 6.14b. In Phase II, a 6 in layer of sand was compacted with a plate vibrator and saturated to form the bearing stratum, and 12 batches of model soil were placed in 5 days
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170
160
160
Water content (%)
Water content (%)
to fill the container. The sand gradation curve is shown in Figure 6.15.
150 140 130 120 110
150 140 130 120 110 100
100 1
2
3
4
5
6 7 8 Batch
9 10 11 12 13
1
2
3
4
5
6 7 8 Batch
9 10 11 12
(a) (b) Figure 6.14 - As-Placed Model Soil Water Content During a) Phase I; b) Phase II
271
% finer by weight
100 90 80 70 60 50 40 30 20 10 0 0.01
0.1
1
10
particle size (mm)
Figure 6.15 - Sand Gradation Curve for Bearing Stratum in Phase II A continuous progressive cavity mixer/pump was specially constructed for the project by ChemGrout, and is depicted in Figure 6.16. This pump design was inspired by equipment originally constructed by Arango-Greiffenstein (1971), but was adapted for the special requirements of this project. The mixer/pump consists of a 30 ft3 hopper with a funnel shaped bottom that directly feeds into a progressive cavity pump. The pump returns the material to the top of the hopper, or upon completion of mixing, a valve is opened sending the material through a 3 in diameter discharge hose. The mixing action is achieved by the material simply passing through the pump. An optimum mixing procedure was achieved by trial and error, and consisted of adding all the water to the hopper, then adding proportional amounts of kaolinite and bentonite while circulating the mix, and at the final stage before pumping, adding the fly ash, which had a dramatic stiffening effect. Several hours of mixing was found to be required to break down bentonite clumps and to achieve a reasonable mix consistency. In Phase II, this process was expedited by inserting an electric paddle mixer into the soil mix. The model soil mix was at the limit of pumpability, and lower water contents or higher fly ash contents could not be sustained.
272
The consistency of the model soil discharged into the test container was such that all the material had to be hand packed to minimize voids. In both testing phases, the container was filled to a height of 6 ½ ft, leaving a 1½ ft gap between the top of the model soil and the container top ring. In this fashion, the soil mass was isolated from inertial forces imposed by the top ring of the container during shaking. The top of the model container was sealed with plastic sheeting between tests and small amounts of water were sprayed on the model soil to counteract surface dessication.
Dry material hopper Pressure lid
30 CF Tank
Hydraulic controls Electrical Controls Progressive cavity pump
I
O
I
O
B D
BF4
Electric motor & hydraulic pump
Figure 6.16 - Schematic of Chemgrout Mixer/Pump
6.5.2 Installation of Single Piles and Pile Groups After strain gaging and attachment of gage lead wires, aluminum conical tips were fitted to the model piles to provide a closed end condition. Pile locations were surveyed and the model piles were driven into the soil in single or group configurations through an
273
18 in tall template to ensure location and verticality (Figure 6.17). The template was constructed with special cutouts to accommodate the irregular profile of piles with external strain gages. For pile groups, holes were pre-excavated in the model soil to accept the pile cap after pile installation. A 200 lb lead weight was suspended from the overhead crane and provided the mass to push the piles to refusal. A nylon pile head driving adapter was crafted and utilized to protect the strain gage lead wires protruding from the pile head during driving.
Figure 6.17 - Model Pile Installation Through Template
274
Figure 6.18 - Design Detail of 3x3 Pile Group As the model piles were instrumented with external strain gages, the gages and their multi-layer protective coatings constituted protrusions on the surface of the piles up to 2 in long and ¼ in thick. For this reason the piles could not be driven through a cap, but a cap had to be fit over the piles. A permanent pile cap/pile group construction would not provide flexibility for instrumenting different piles in the groups, and casting concrete or cement grout around a group would be too time consuming. For this reason modular pile caps were designed that allowed temporary but robust pile to cap connections. Another design objective was to utilize standard steel and pipe sections, and avoid custom fabrication of each pile cap and pile connection. The pile caps were constructed from 6 in deep steel tube sections 5/16 in thick, either 12 in wide for a 2x pile group or 18 in wide
275
for a 3x pile group. Figure 6.18 illustrates a 3x3 pile group cap design. This tube section was cut to an 18 in length, and 9 holes 2 1/8 in diameter were cut in both top and bottom faces of the tube in a 3d (6 in) center-to-center spacing. This pile spacing was adopted as typical of Caltrans pile group design. On the top face of the tube, 4 threaded studs were welded around each pile opening, and a single coupling was welded to the center of the cap to attach a column. The 9 pile openings were then lined with 2 in diameter copper tubing, and the entire tube section was then filled with cement grout.
Figure 6.19 - Installation of 3x3 Pile Group
276
After the model piles were installed, a pile cap was lowered by the crane and fit over the group (see Figure 6.19). The tolerance between the outer diameter of the model piles and the inner diameter of the copper sleeves was very close, and aligning all the piles was an intricate process. Connectivity of the piles to the cap was provided by a 6 in long pipe nipple threaded to a flat face flange with 4 bolt holes. The pipe nipple outer diameter was built up by several layers of strapping adhesive tape, so that the pipe nipple could be wedged inside the model piles and provide a strong connection. The flange hole pattern fit precisely over the threaded studs welded on the pile cap, and the flange was bolted down finishing the connection. Columns of various lengths and stiffness were provided by steel pipe sections and couplings. Each pile head mass consisted of two steel channel sections C15x33.9, 26 in long, tensioned together and sandwiching the requisite lead weights to achieve the desired head mass. The bottom channel had a coupling welded to it so that it could easily attach to the pipe column.
6.5.3 Instrumentation During Phase I soil placement, 23 accelerometers were deployed in 4 vertical arrays in the soil as diagrammed in Figure 6.20.
Figure 6.21 depicts the 23 soil
accelerometers in 2 vertical arrays used in Phase II. Accelerometers were also attached to the pile caps and head masses to detect translation and rocking motions.
Wire
potentiometers were fastened to the pile head masses and rigid reference frames off the shaking table.
Tables 6-1 – 6-8 summarize the instrumentation (not including soil
accelerometers) deployed during Phase I and Phase II testing.
277
23 el 0 22 15
el -6"
18
20 21 19
16
17
el -24"
12
14
11
13
el -48"
8
10
7 9
4
6
2
1
el -75" 3
5 stack 1
stack 2 stack 4
stack 3
Principal Axis of Shaking
Figure 6.20 - Phase I Accelerometer Array 23 22 20
el 0
21
19
el -8"
18 16
el -18"
17 15 el -30"
14
13
12 11
el -48"
10 el -60"
9 7 4 8
el -66" el -72" el -75"
3
6 2 5 1 stack 1 stack 2
Principal Axis of Shaking
Figure 6.21 - Phase II Accelerometer Array 278
Table 6-1 Model Series 1.1 Instrumentation Structure
Sensors
S1
1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 1 pile head accelerometer (in plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages and 7 pairs axial strain gages, 1 pile head accelerometer (in plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages, 1 pile head accelerometer (in plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages, 1 pile head accelerometer (in plane)
S2
S3
S4
Table 6-2 Model Series 1.2 Instrumentation Structure
Sensors
S1
1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 4 piles w/ 7pairs bending strain gages, 1 pile w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane, out of plane, and 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 4 superstructure wire pots (2 in plane and 2 out of plane) 1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 4 piles w/ 7pairs bending strain gages, 1 pile w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane, out of plane, and 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 2 superstructure wire pots (in plane)
S2
Table 6-3 Model Series 1.3 Instrumentation Structure
Sensors
S1
1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 4 piles w/ 7pairs bending strain gages, 1 pile w/ 7 pairs axial strain gages, 3 pile cap accelerometers (in plane and 2 rocking), 1 superstructure accelerometer (in plane), 2 superstructure wire pots (in plane) 1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 4 piles w/ 7pairs bending strain gages, 3 pile cap accelerometers (in plane and 2 rocking), 1 superstructure accelerometer (in plane), 2 superstructure wire pots (in plane) 1 pile w/ 7pairs bending strain gages, 3 pile cap accelerometers (in plane and 2 rocking), 1 superstructure accelerometer (in plane), 2 superstructure wire pots (in plane)
S2
S3
279
Table 6-4 Model Series 1.4 Instrumentation Structure
Sensors
S1
2 piles w/ 7pairs bending strain gages, 2 piles w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane and out of plane, 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 4 superstructure wire pots (2 in plane, 2 out of plane) 2 piles w/ 7pairs bending strain gages, 2 piles w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane and out of plane, 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 2 superstructure wire pots (in plane)
S2
Table 6-5 Model Series 2.2 Instrumentation Structure
Sensors
S1
1 pile w/ 7pairs axial strain gages, 1 pile head DCDT (vertical) 1 pile w/ 7 pairs bending strain gages, 2 pile head accelerometers (in plane and out of plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs axial strain gages, 1 pile head DCDT (vertical), 1 pile w/ 7 pairs bending strain gages, 2 pile head accelerometers (in plane and out of plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages, 2 pile head accelerometers (in plane and out of plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages, 2 pile head accelerometers (in plane and out of plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages, 2 pile head accelerometers (in plane and out of plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages, 2 pile head accelerometers (in plane and out of plane), 2 pile head wire pots (in plane) 1 pile w/ 7 pairs bending strain gages, 2 pile head accelerometers (in plane and out of plane),
S2
S3 S4
S5
S6
S7
S8
S9
280
Table 6-6 Model Series 2.3 Instrumentation Structure
Sensors
S1
1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 3 piles w/ 7pairs bending strain gages, 1 pile w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane, out of plane, and 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 2 superstructure wire pots (in plane) 1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 3 piles w/ 7pairs bending strain gages, 1 pile w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane, out of plane, and 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 2 superstructure wire pots (in plane)
S2
Table 6-7 Model Series 2.4 Instrumentation Structure
Sensors
S1
1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 6 piles w/ 7pairs bending strain gages, 2 piles w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane, out of plane, and 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 4 superstructure wire pots (2 in plane and 2 out of plane) 1 pile w/ 14 pairs bending strain gages (7 in plane/7 out of plane) 2 pile head accelerometers (in plane and out of plane), 4 pile head wire pots (in plane and 2 out of plane)
S2
Table 6-8 Model Series 2.5 Instrumentation Structure
Sensors
S1
1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 3 piles w/ 7pairs bending strain gages, 1 pile w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane, out of plane, and 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 2 superstructure wire pots (in plane) 1 pile w/ 7pairs bending strain gages and 7 pairs axial strain gages, 3 piles w/ 7pairs bending strain gages, 1 pile w/ 7 pairs axial strain gages, 4 pile cap accelerometers (in plane, out of plane, and 2 rocking), 2 superstructure accelerometers (in plane and out of plane), 2 superstructure wire pots (in plane)
S2
6.6 Test Parameters 281
To achieve the objectives outlined in section 6.1, the shaking table model tests were designed as self-contained studies of particular SSPSI topics. This approach was taken as it was realized that the shaking table could not achieve perfect test to test repeatability with regard to input motions. During each phase of the test program, the test container was filled with model soil and the same soil deposit was used for all tests during that particular phase of testing.
In each of the two phases of the test program, 5
independent model setups were made and a series of tests was performed on each model.
6.6.1 Selection of Input Motions Three levels of excitation were desired for the soil-pile scale model tests. A low level sine sweep signal was intended as a diagnostic of the system resonant frequencies and stiffness properties; an acceleration level of < 0.05 g was targeted to ensure that response remained in the elastic range. A mid range signal with an MHA of about 0.2 g was desired to impart an intermediate level excitation. Finally, a strong shaking record with an MHA > 0.5 g was sought to induce nonlinear site and superstructure response, typical of design level events in regions of high seismicity. As the model site profile represented soft clay overlying a thin stiff soil layer overlying bedrock, motion recorded on bedrock was defined as the test input signal criterion. Preliminary test runs of the bare shaking table and the table with a 30 kip mass (roughly corresponding to the model mass) indicated that the table could be “tuned” to best reproduce particular input motions. For this reason, single mid level and high level motions were selected rather than a suite of input motions. In addition, the soil-pile models were expected to degrade with each test event, and therefore a parametric study of
282
multiple excitations typical of structural model tests was not deemed appropriate. These tests also indicated that the ability of the shaking table to reproduce the command signal was reasonable, but not perfect.
Other researchers have implemented techniques of
command signal compensation to achieve better table performance (Hwang et al., 1987). But modification of the command signal could potentially result in other unforeseen table response distortions; for this reason, careful tuning of the feedback control system was accepted as the best approach to optimize the command signal reproduction.
Most
importantly, the test instrumentation would record the table response and the actual input to the system; as long as this was known and reasonable, this comprised sufficient input data for further simulation and analysis. A number of candidate records were examined for their suitability as input motions, with MHA, displacement time history, and 5% damped response spectra as the primary selection criteria. These included sets of synthetic records developed by Dr. Bruce Bolt and Dr. Norm Abrahamson for the analysis of Hayward and San Andreas fault scenarios for the San Francisco-Oakland Bay Bridge. Ultimately the two records selected were actual recordings from recent earthquakes. They consisted of the Yerba Buena Island record 90 degree component from the Loma Prieta earthquake (YBI90), and the Port Island downhole array -79 m record north 00 east component from the Kobe earthquake (KPI79N00). The acceleration, velocity, and displacement time histories, and acceleration response spectra for these two records are shown in Figures 6.22 and 6.23. The YBI90 record has a predominant frequency of 1.5 Hz, a time step of 0.02 sec, and an MHA of 0.07 g, which for this testing program was scaled to 0.2 and 0.3 g. The KPI79N00 record has a predominant frequency of 2.9 Hz, a time step of 0.01 sec, and an
283
MHA of 0.69 g, which was scaled from 0.1 to 1.4 g for this testing program.
In
accordance with the scaling relations derived in section 5.2.1, the time steps of these two records were divided by (λ)0.5, or 2.828, resulting in time scales compressed relative to the original records. These single component input motions were used for uni-directional shaking in Phase I tests; the horizontal orthogonal component to these motions was added for biaxial shaking in selected Phase II tests as noted. The low level sine sweep motion consisted of a 60 sec duration record sweeping at 4 octaves/min from 0 to 20 Hz with ramped transitions at the beginning and end of the signal; this signal is shown in Figure
0.08
0.3
0
5% Damped Spectral Acceleration
Displacement (in)
Velocity (in/sec)
Acceleration (g)
6.24.
-0.08 8 0 -8 2 0
0.2
0.1
-2
0 0
20
40
0.01
0.1
1
10
Period (sec)
Time (sec)
Figure 6.22 - Acceleration, Velocity, and Displacement Time Histories, and Acceleration Response Spectra for the Yerba Buena Island Record 90 Degree Component from the Loma Prieta Earthquake (YBI90)
284
1.5
0
5% Damped Spectral Acceleration
Acceleration (g) Velocity (in/sec) Displacement (in)
0.8
-0.8 30 0 -30 10 0
1
0.5
-10
0 0
10
20
0.01
30
0.1
1
10
Period (sec)
Time (sec)
Figure 6.23 - Acceleration, Velocity, and Displacement Time Histories, and Acceleration Response Spectra for the Port Island Downhole Array -79 meter Record North 00 East Component from the Kobe Earthquake (KPI79N00).
Acceleration (g)
0.05
0.00
-0.05 0
5
10
15
20
25
30
35
40
45
50
55
60
65
Time (sec)
Figure 6.24 - Sinsweep Consisting of 65 Second Duration Record Sweeping at 4 Octaves Per Minute from 0 to 20 Hz with Ramped Transitions at the Beginning and End of Signal 6.6.2 Pile Head Loading Tests Five types of pile head loading tests were performed on single pile and pile group models to correlate pile head stiffness values derived from those tests with the observed seismic performance of similar models. Static lateral load tests were performed on single piles in Phase I and Phase II, and on a 3x3 pile group in Phase II (see Figures 6.25 and 6.26). A lateral load was applied by means of a cable and pulley system incrementally
285
loaded with steel plates; pile head or pile cap deflections and pile bending moments were recorded. A pile head impact test was conducted on a single pile in Phase II, and consisted of a hammer laterally striking the pile head and recording the free vibration and pile bending moment response. In a crude fashion, this is analogous to lateral statnamic pile tests. Forced vibration tests were carried out on a single pile in Phase II. For these tests an electrodynamic horizontal shaker manufactured by Acoustic Power Systems (model 129) was mounted to the pile head or pile cap and a 27.5 lb mass was excited with a frequency sweep ranging from 0 to 20 Hz. The pile head and bending moment response was recorded, with the peak amplitude of response indicating the resonant frequency of the soil-pile system. Finally, static and cyclic axial loading tests were performed on single piles in Phase II (Figure 6.27). For these tests, a pneumatic actuator was attached to the pile head in a vertical orientation. The static incremental loading test was carried to an ultimate load of 350 lbs, and the cyclic tests consisted of 10 cycles of alternating tensile/compressive loading at 3 increasing load levels. Pile head load and deflection and pile axial strains were recorded.
Figure 6.25 - Single Pile Lateral Load Test 2.20g at Maximum Deflection
286
Figure 6.26 - Pile Group Lateral Load Test 2.31 at Maximum Deflection
Figure 6.27 - Cyclic Axial Load Test 2.20b Setup 6.6.3 T-Bar Tests T-bars were pre-positioned in the test container and the model soil placed around the T-bars for later determination of the continuous soil strength profile versus depth. The T-bar method was originally introduced by Stewart and Randolph (1991), who applied it
287
to both field investigations and centrifuge testing procedures. The T-bar used for this project consisted of a ¾ in diameter steel cross bar, 3 ¾ in long, attached at a right angle to a ¼ in diameter vertical steel shaft 9 ft long, thus forming a “T”. The cross bar was positioned at the base of the model and the top of the shaft protruded out of the model soil and was threaded into a 250 lb load cell. The whole assembly was then pulled out of the soil by an overhead crane, thus acquiring continuous load resistance data of the bar segment translating through the soil. The T-bar was pulled at constant rate (Chapter 8 includes a discussion of T-bar rate effects) and over a known distance, so positional measures were not required. T-bar test results make use of the plasticity solution for the limiting pressure acting on a cylinder moving laterally through cohesive soil, as described by Randolph and Houlsby (1984). This analysis assumes full closure of the soil behind the cylinder such that gapping or suction do not occur, and ignores bar end effects and the influence of the relatively small cross-section presented by the shaft. The solution expresses the limiting force acting on an infinitely long cylinder as: SU =
P Nb d
(6.1)
where SU is the undrained shear strength of the soil, P is the force per unit length acting on the cylinder, d is the diameter of the cylinder, and Nb is the bar factor, which varies from 9 to 12, and is a function of the bar roughness/adhesion. Randolph and Houlsby (1984) recommend a value for Nb of 10.5 for general applications. Four T-bars were inserted in each model container so that continuous soil strength profiles could be obtained at various stages during the test program.
288
6.6.4 Shear Wave Velocity Tests The model soil shear modulus profile is a crucial component of site response and soil-pile interaction analyses. Shear wave velocity is related to shear modulus by: G V S=
ρ
VS =
G ρ
(6.2)
Laboratory testing of the model soil indicated distinct relationships between shear wave velocity and water content, and undrained shear strength, though laboratory samples and actual model conditions could be expected to have some variability. For this reason, insitu determination of the soil shear wave velocity profile was carried out. The in-situ test procedure consisted of striking the base of the container with a sledgehammer with the intent of generating shear waves in the soil. The differential arrival times of these shear waves would be detected by the accelerometer arrays in the soil, and knowing the distance between accelerometers, in-situ shear wave velocities could then be computed. As will be discussed in Chapters 7 and 8, the Phase I results were not conclusive, and the Phase II test procedures attempted to improve the fidelity of this test procedure. Phase II shear wave velocity testing used vertically denser accelerometer arrays, higher data sampling rates (>1000 Hz), and a cushioned hammer blow, which provided a lower frequency input. The test series 2.1 shear wave velocity tests were performed in a container devoid of piles, thereby eliminating alternate travel paths for the wave energy. Most importantly, the Phase II shear wave velocity tests were made by horizontally striking a plate coupled to the soil surface, which resulted in signals with more clearly identifiable P- and S-waves (see Figure 6.28).
289
Figure 6.28 - Surface Hammer Test to Determine Shear Wave Velocity Profile 6.6.5 Schedule of Test Conditions A typical test series for an individual model consisted of a T-bar test, a hammer blow test, a sinesweep test, the YBI90 motion, another sinesweep test, the KPI79N00 motion, another sinesweep test, and a final hammer blow test (both KPI79N00 in Phase II). The complete test series for a given model was conducted in a single day, with progressively increasing levels of excitation. In all, 6 YBI90, 6 KPI79N00, 2 wave loading, 13 sinesweep, 19 hammer blow, 5 T-bar, 12 pile driving, and 1 static lateral load test were conducted during Phase I; the schedule of Phase I tests is provided in Tables 6-9 – 6-13. Phase II tests included 14 KPI79N00, 17 sinesweep, 12 hammer blow, 4 T-bar, 2 static lateral load, 4 dynamic head loading, and 2 axial head loading tests; these are summarized in Tables 6-14 – 6-18. Model 1.1 consisted of four single piles with head masses ranging from 6.5 lbs to 160 lbs; this layout is shown in Figure 6.29. Model 1.2 contained two 3x3 pile groups, both with the same superstructure head masses, one with an 18 in tall column, and the
290
other with a 54 in tall column (Figure 6.30). Model 1.3 included two 3x3 pile groups with identical columns and head masses, but one had a trench excavated around its perimeter to remove the pile cap lateral soil resistance (Figure 6.31). A third pile raft foundation was also included in this model, which consisted of a pile cap for a 3x3 pile group, but with only one pile in the center of the cap. Model 1.4 had two 2x2 pile groups both with identical columns and head masses and pile caps above the ground surface, but one had water impounded around the pile cap and piles (Figure 6.32). Model 1.5 was a site response test with no piles or structures (Figure 6.33).
Table 6-9 Model Test Series 1.1 Test ID 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18
Test Description Static lateral load test on pile S4 T-Bar test Hammer blow test Sinesweep test YBI90 input motion scaled to 0.2 g Sinesweep test Hammer blow test YBI90 input motion scaled to 0.35 g
Table 6-10 Model Test Series 1.2 Test ID 1.21 1.22 1.23 1.24 1.25 1.26 1.27
Test Description T-Bar test Hammer blow test Sinesweep test YBI90 input motion scaled to 0.2 g Hammer blow test KPI79N00 input motion scaled to 0.7 g Sinesweep test
291
Table 6-11 Model Test Series 1.3 Test ID 1.30 1.31a 1.31b 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39a 1.39b
Test Description T-Bar test Hammer blow test below table Hammer blow test above table turn on vertical pressure Sinesweep test YBI90 input motion scaled to 0.2 g Hammer blow test above table Sinesweep test KPI79N00 input motion scaled to 0.7 g Sinesweep test Hammer blow test above table Hammer blow test below table
Table 6-12 Model Test Series 1.4 Test ID 1.40a 1.40b 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49a 1.49b
Test Description hammer blow test below table hammer blow test above table Sinesweep test YBI90 input motion scaled to 0.2 g Sinesweep test KPI79N00 input motion scaled to 0.7 g Sinesweep test 1 Hz. Wave loading scaled to 0.35 g 1 Hz. Wave loading scaled to 0.35 g Sinesweep test Hammer blow test above table Hammer blow test below table
Table 6-13 Model Test Series 1.5 Test ID
Test Description
1.50 1.51a 1.51b 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.510a 1.510b
T-Bar test hammer blow test below table hammer blow test above table Sinesweep test YBI90 input motion scaled to 0.2 g hammer blow test KPI79N00 input motion scaled to 0.7 g hammer blow test KPI79N00 input motion scaled to 1.05 g KPI79N00 input motion scaled to 1.4 g Sinesweep test hammer blow test above table hammer blow test below table
292
TBar Test S1 2D 1D Accel Stack 1 x 2 Layers
S2 2D
1D Accel Stack 2 x 2 Layers
2D Accel Stack 3 x 4 Layers
S3 1D 2D Accel Stack 4 x 5 Layers +Vertical
S4 1D
Shaking Axes
Figure 6.29 - Model 1.1 Layout with Four Single Piles
1D Accel Stack 1 x 2 Layers
1D Accel Stack 2 x 2 Layers
P1Lat
2D Accel Stack 3 x 4 Layers
P12Lat P7Lat
P3Lat P11Axial
P2Axial
P4Lat
P5Lat
P9Lat P8Axial
2D Accel Stack 4 x 5 Layers +Vertical
3x3 Pile Group S1 H/B = 3
P6Lat P10Axial
3x3 Pile Group S2 H/B = 1 TBar Test
Shaking Axes
Figure 6.30 - Model 1.2 Layout with Two 3x3 Pile Groups 293
P11Lat
Single Pile Raft S3 H/B = 1
1D Accel Stack 2 x 2 Layers
1D Accel Stack 1 x 2 Layers
2D Accel Stack 3 x 4 Layers
P12Axial
P1Lat
P3Lat
P7Lat P2Axial
P4Lat
P5Lat
P9Lat P8Axial
3x3 Pile Group S1 H/B = 1 No Cap Embedment
2D Accel Stack 4 x 5 Layers +Vertical
P6Lat P10Axial
3x3 Pile Group S2 H/B = 1 TBar Test
Shaking Axes
Figure 6.31 - Model 1.3 Layout with Two 3x3 Pile Groups and One Pile Raft Foundation
2x2 Pile Group S2 w/Water
2x2 PIle Group S1 P2Axial
P1Lat
P3Lat P4Axial
P7Axial
P8Lat
P5Lat P6Axial
1D Accel Stack 1 x 2 Layers
1D Accel Stack 2 x 2 Layers
2D Accel Stack 3 x 4 Layers
2D Accel Stack 4 x 5 Layers +Vertical
Shaking Axes
Figure 6.32 - Model 1.4 Layout with Two 2x2 Pile Groups 294
TBar Test
1D Accel Stack 1 x 2 Layers
1D Accel Stack 2 x 2 Layers
2D Accel Stack 3 x 4 Layers
2D Accel Stack 4 x 5 Layers +Vertical
Shaking Axes
Figure 6.33 - Model 1.5 Layout with No Piles In Phase II, model 2.1 re-enacted the free-field site response test with no piles or structures, and contrasted uniaxial and biaxial shaking (Figure 6.34). Model 2.2 included 9 single piles; five with head masses ranging from 6.5 to 160 lbs, which were subjected to base shaking, and four additional piles subjected to head loading tests before shaking. These tests included a static lateral load test, a dynamic head lateral impact test, a forced vibration head loading test, a static axial loading test, and a cyclic axial loading test (Figure 6.35). Model 2.3 consisted of two identical 3x3 pile groups, one of which was subjected to a static lateral loading test before shaking (Figure 6.36). Model 2.4 contained a 5x3 pile group and a single pile that were subjected to biaxial shaking (Figure 6.37). Finally, model 2.5 contained two identical 2x2 pile groups, one with and one without pile cap embedment, subject to biaxial shaking (Figure 6.38).
295
Table 6-14 Model Test Series 2.1 Test ID 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19
Test Description Hammer blow test Hammer blow test Sinesweep test KPI79N00 input motion scaled to 0.1 g KPI79N00 input motion scaled to 0.3 g Sinesweep test KPI79 input motions scaled to 0.1 g biaxial KPI79 input motions scaled to 0.3 g biaxial Sinesweep test Hammer blow test
Table 6-15 Model Test Series 2.2 Test ID 2.20a 2.20b 2.20c 2.20d 2.20e 2.20f 2.20g 2.21 2.22a 2.23a 2.23x 2.22b 2.23b 2.24 2.25 2.26 2.27 2.28
Test Description Static axial load test on pile S1 Cyclic axial load test on pile S3 Forced vibration test on pile S5 Forced vibration test on pile S5 Dynamic head impact test on pile S6 Forced vibration test on pile S5 Static lateral load test on pile S9 T-Bar test Hammer blow test Sinesweep test Sinesweep test Hammer blow test Sinesweep test KPI79N00 input motion scaled to 0.25 g Sinesweep test KPI79N00 input motion scaled to 0.7 g Sinesweep test Hammer blow test
Table 6-16 Model Test Series 2.3 Test ID 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39
Test Description Static lateral load test on pile group S1 T-Bar test Hammer blow test Sinesweep test KPI79N00 input motion scaled to 0.25 g Sinesweep test KPI79N00 input motion scaled to 0.7 g Sinesweep test Hammer blow test
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Table 6-17 Model Test Series 2.4 Test ID
Test Description
2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48
T-Bar test Hammer blow test Sinesweep test KPI79 input motions scaled to 0.25 g biaxial Sinesweep test KPI79 input motions scaled to 0.7 g biaxial Sinesweep test Hammer blow test
Table 6-18 Model Test Series 2.5 Test ID 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59
Test Description T-Bar test Hammer blow test Sinesweep test KPI79 input motions scaled to 0.25 g biaxial Sinesweep test KPI79 input motions scaled to 0.7 g biaxial Sinesweep test Hammer blow test KPI79 input motions scaled to 1.0 g biaxial KPI79 input motions scaled to 1.0 g biaxial
2D Accel Stack x 9 Layers + Vert Surface Accel
2D Accel Stack x 5 Layers + Vert Surface Accel
Shaking Axes
Figure 6.34 - Model 2.1 Layout with No Piles
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TEST SERIES 2.2 LAYOUT S1 static axial
S2
S7 S3 cyclic axial 2D Accel Stack x 9 Layers + Vert Surface Accel
S9 static lateral
S4 2D Accel Stack x 5 Layers + Vert Surface Accel
S8
S5 forced vibration
S6 impact
TBar Test
Shaking Axes
Figure 6.35 - Model 2.2 Layout with Nine Single Piles
TBar Test
P1Long P2Long
P7Long
P11Long
3x3 Pile Group S1 H /B = 3
P8Axial P12Axial
2D Accel Stack x 8 Layers + Vert Surface Accel
2D Accel Stack x 4 Layers + Vert Surface Accel
3x3 Pile Group S2 H /B = 3
P4Long P10Axial P6Axial
P5Long
P9Long P3Long
Shaking Axes
Figure 6.36 - Model 2.3 Layout with Two 3x3 Pile Groups 298
S2 2-D
P1Long P2Lat
P7Long
P12Long P10Long P9Long
P11Long
P8Lat
P4Axial
P3Lat
P6Axial
P5Lat
2D Accel Stack x 8 Layers + Vert Surface Accel
5x3 Pile Group S1 H/B =3 2D Accel Stack x 4 Layers + Vert Surface Accel
TBar Test
Shaking Axes
Figure 6.37 - Model 2.4 Layout with One 5x3 Pile Group and Single Pile
TBar Test
P1Axial
P7Axial
P2Long
P8Long
2x2 Pile Group S1 H/B = 2 No Cap Embedment 2D Accel Stack x 8 Layers + Vert Surface Accel
2x2 Pile Group S2 H /B = 2 2D Accel Stack x 4 Layers + Vert Surface Accel
P4Long
P3Long
P6Axial
P5Axial
Shaking Axes
Figure 6.38 - Model 2.5 Layout with Two 2x2 Pile Groups 299
CHAPTER 7
SHAKING TABLE TEST RESULTS
7.1 Introduction This chapter qualitatively presents the results of the shaking table test program, reserving quantitative analysis for the next chapter. As previously described, the shaking table tests were designed so that each test setup provided contrasting conditions of at least two, and in some cases up to five, structural models. In this manner direct inferences about the effect of superstructure inertial forces, pile cap embedment, etc., could be made. It is clearly impossible to present the complete experimental results in this dissertation, and therefore representative details are reported. The results are presented in the form of acceleration (and bending strain) time histories, and fast Fourier transforms (FFTs) and 5% damped response spectra of these time histories. Data processing and filtering of the acceleration records has consisted solely of zeroing the mean value and baseline correcting each record. These operations were found to have a negligible effect on the data, indicating permanent deformations were insignificant. In addition, bending moment envelopes computed from the model pile strain gages are plotted. The bending moment envelope is defined by the absolute peak strain at each gage during the excitation; it is not equivalent to the actual bending moment diagram at the time step when the peak strain is recorded. To remove low frequency drift from the strain gage records, a digital highpass Butterworth filter was applied with a passband of 0.5 Hz, a stopband of 0.1 Hz, a passband attenuation of 3 dB, and a stopband attenuation
300
of 20 dB. In rare instances a passband of 1 Hz and a stopband of 0.5 Hz were employed. Fifth order polynomials were fit to the bending moment data points, except in cases of gage failure when fewer data points dictated the use of lower order polynomials.
7.2 Shaking Table Performance An essential component of high quality experimental results is superior performance of the shaking table. The table performance can be evaluated with respect to the following criteria: How well did the shaking table replicate the command signal ? Was the table response repeatable ? Was the table motion well-controlled or were other degrees of freedom engaged ? These questions are to be considered in the context that though the table response may not have precisely matched the command signal, recording the actual table performance provides sufficient input data for numerical simulations of the tests.
7.2.1 Replication of Command Signals The shaking table is an analog controlled servo-hydraulic system that is sensitive to such factors as atmospheric conditions, “warm-up” procedures, test-specific table balance settings, etc. It proved to be moderately consistent in its ability to reproduce signals from one test to the next. Figure 7.1 plots the YBI90 command signal response spectra with the shaking table response spectra from all six YBI90 tests superimposed. The table response is computed as the average of the H41 and H23 accelerometers (see Figure 7.2 for the table instrumentation plan) and the spectra have been normalized to the unscaled command amplitude, 0.067 g (input amplitudes 0.14 – 0.28 g). The table response match
301
to the command signal is good, particularly at the predominant period of the record. The under-response of the table at periods greater than 0.3 seconds is somewhat surprising, though the variations in high frequency response are not. 0.3
Table Command
Acceleration (g)
Table Response
0.2
0.1
0.0 0.01
0.1
1
10
Period (sec)
Figure 7.1- Shaking Table Response Spectra for YBI90 Input Motions, Damping = 5 %
V4
H3-4
H4-1
V3
H2-3
Lateral
Longitudinal
V1
H1-2
V2
Figure 7.2 - Shaking Table Accelerometer Layout (dimensions in ft); H are horizontal accelerometers and V are vertical accelerometers 302
3.0
Table Command
Acceleration (g)
Table Response
2.0
1.0
0.0 0.01
0.1
1
10
Period (sec)
Figure 7.3 - Shaking Table Response Spectra for KPI79N00 Motions, Damping = 5% Figure 7.3 presents the KPI79N00 command signal response spectra with 20 KPI79N00 table response spectra overlain, all normalized to the unscaled command amplitude, 0.69g (input amplitudes 0.06 – 1.06 g). The table response is computed as the average of the H41 and H23 accelerometers for Phase I tests and the average of the H12 and H34 accelerometers for Phase II tests. The spectral match is consistent for periods greater than 0.5 sec. In the range of maximum energy and the predominant period, from 0.05 to 0.5 sec, the table response shows moderate variability, both under- and overreproducing the command signal. At high frequencies the table was generally unable to reproduce the full amplitude of the single high frequency acceleration spike in the Kobe record, as evidenced by the 0.01 sec period spectral accelerations ranging from 0.4 to 0.6 g for the majority of the records. And for two test events very severe twist accelerations
303
resulted in large average horizontal accelerations being calculated; these records constitute the two upper bound table response spectra.
7.2.2 Acceleration Response of Table Degrees of Freedom It is instructive to examine the response of the individual table degrees of freedom to understand some of the table response variability previously noted. Table twist is defined as H12 – H34 about the longitudinal axis and H41 – H23 about the lateral axis; table pitch is computed as (V1+V2) – (V3+V4) and table roll is (V2+V3) – (V1+V4). As these response quantities are defined at the accelerometer positions at the edges of the shaking table, the actual twist, pitch, and roll experienced by the models is approximately 36 % of the table response (3 ft model radial position/8.25 ft table accelerometer radial position). Table accelerometer time histories (modified twist, pitch and roll) for a representative 1-D shaking test are shown in Figure 7.4. Figure 7.5 depicts the corresponding FFTs for these time histories, indicating the frequency characteristics of these motions. In a perfectly responding system the H12 and H34 accelerometers should both reproduce the command signal, and all other degrees of freedom should be stable. This was certainly not the case, and important differences can be seen in these two longitudinal motions. The H12 motion has greater energy above 8 Hz than the H34 motion, though both records have greater high frequency energy than the command signal.
This is
manifested in the generation of out of plane (H23 and H41) and twist accelerations, both of which have peak amplitudes at approximately 10 Hz. The amplitude of the twist motion is not negligible, and the twist accelerations translate into
304
0.6
0.6
H34
H12
0.0
0.0
-0.6
-0.6
0.6
0.6 H23
H41
0.0
0.0
-0.6
-0.6
0.6
0.6 V2
V1
0.0
Acceleration (g)
Acceleration (g)
0.0
-0.6 0.6 V3
-0.6 0.6 V4
0.0
0.0
-0.6
-0.6
0.6
0.6 Longitudinal Twist
Lateral Twist
0.0
0.0
-0.6
-0.6
0.6
0.6 Pitch
Roll
0.0
0.0
-0.6
-0.6 0
3
6
9
12
0
3
6
9
Time (sec)
Time (sec)
Figure 7.4 - Test 2.37 Shaking Table Accelerometer Time Histories
305
12
0.02
0.02
H34
H12
0.00
0.00
0.02
0.02 H23
H41
0.00
0.00
0.02
0.02 V2
Acceleration (g)
Acceleration (g)
V1
0.00 0.02 V3
0.00
0.00 0.02 V4
0.00
0.02
0.02 Longitudinal Twist
Lateral Twist
0.00
0.00
0.02
0.02 Pitch
Roll
0.00
0.00 0
10
20
30
40
0
10
20
30
Frequency (Hz)
Frequency (Hz)
Figure 7.5 - Test 2.37 Shaking Table Accelerometer FFTs
306
40
out of plane components of motion in the vicinity of the models. The four vertical table accelerometers recorded relatively small motions, but they were out of phase, and very moderate pitch and roll motions resulted, with peak amplitudes at approximately 23 Hz (beyond the model range of interest). In summary, the shaking table performed adequately in reproducing the command motions. Minor variability between command and response can be accepted when the response is recorded and fully characterized. The model geometric scaling factor of 8 demanded that the shaking table reproduce high frequency motions by controlling very small displacements, an apparent limitation of the table.
This variability in table
performance may therefore be partially attributable to magnitude dependence.
The
unwanted out of plane, twist, pitch, and roll motions consistently appeared throughout the shaking table test series, and are a source of greater concern. The implications of these spurious motions to the one-dimensional site response idealization will be explored in greater detail in sections 7.3 and 8.4 of this dissertation.
7.3 Soil Column Response The recorded soil column response will be compared with analytical site response models in section 8.4, but this section will first consider trends of experimental site response. Site response amplification in a dense accelerometer array for a Phase II test will be examined, the coherence of site response will be considered for four vertical arrays in a Phase I test, and the issue of vertical accelerations will be studied for a Phase II test.
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7.3.1 Site Amplification It is now a well-established fact of geotechnical earthquake engineering that soil deposits can amplify the seismic rock motion through the soil column toward the surface. Soft clay deposits are known to particularly amplify shaking, though very strong shaking may attenuate surface motions due to soil nonlinearity and stiffness degradation (Idriss, 1990). It is also postulated that such motions may even induce shear failure in the soil deposit. The same amplification characteristics and nonlinear behavior are desired in the model soil column. Figure 7.6 depicts accelerometer time histories and FFTs for array #1 in shaking table test 2.24. The trend of amplification from base (0.22 g) to surface (0.44 g) is obvious, and the transformation of energy content is significant.
The FFT energy
concentration at 8.2 Hz in deeper instruments directly correlates to the 8.2 Hz acceleration spike in the KPI79N00 input motion. But above a depth of 30 in, energy at 3.4 Hz begins to dominate. This frequency reflects the fundamental site period, and this topic will be further addressed in section 8.4.
7.3.2 Coherence of Motions The model soil container is intended to approximate one-dimensional site response, which requires that ground motions be identical at all points on any horizontal plane. To evaluate whether the model soil column is behaving in this manner, the coherence of accelerometer response spectra from Phase I tests is considered. Figure 7.7 superimposes response spectra from four accelerometer arrays at five elevations from test 1.18. The excellent agreement for the spectra recorded in the plane of shaking confirms
308
0.5
0.02 Elev 0
0.0 -0.5 0.5
0.00 0.02 Elev -8
0.0 -0.5 0.5
0.00 0.02 Elev -18
0.0 -0.5 0.5
0.00 0.02
Elev -30
-0.5 0.5
Acceleration (g)
Acceleration (g)
0.0
Elev -48
0.0 -0.5 0.5
Elev -60
0.00 0.02
0.00 0.02
0.0 -0.5 0.5
0.00 0.02
Elev -66
0.0 -0.5 0.5
0.00 0.02
Elev -72
0.0 -0.5 0.5
0.00 0.02 Elev -75
0.0 -0.5
0.00 0
3
6
9
12
0
5
10
15
Frequency (Hz)
Time (sec)
Figure 7.6 - Test 2.24 Soil Accelerometer Array #1 Time Histories and FFTs
309
20
2.0
0.4 In Plane Elev 0
Out of Plane Elev 0
0.0
0.0
2.0
0.4 In Plane Elev -6
Out of Plane Elev -6
0.0
0.0
2.0
0.4 Out of Plane Elev -24
Acceleration (g)
Acceleration (g)
In Plane Elev -24
0.0
0.0
2.0
0.4 In Plane Elev -48
Out of Plane Elev -48
0.0
0.0
2.0
0.4 In Plane Elev -74
Out of Plane Elev -74
0.0
0.0 0.01
0.1
1
10
0.01
0.1
1
Period (sec)
Period (sec)
Figure 7.7 - Test 1.18 Soil Accelerometer 5%Damped Response Spectra
310
10
the coherence of motions across the site. The out of plane spectral peaks at 10 Hz indicate that table twist is contributing to these motions, which as expected vary in amplitude by radial position of the instrument. These analyses were performed for all Phase I tests and the results consistently confirmed these trends of site response coherence.
7.3.3 Vertical Accelerations Vertical accelerations were observed at the soil surface in the model tests, ranging in amplitude from 20 to 50 % of the horizontal motion, and were higher frequency in character. The sources of vertical acceleration in the model tests are threefold. The first source is vertical accelerations of the shaking table itself, including table pitch and roll. Such motions may generate compression waves in the soil that appear as vertical accelerations at the soil surface. A second source of surface vertical accelerations is surface waves generated at the soil surface and at the soil/model container interface. Modeling such phenomena is beyond the scope of this work. A third source of surface vertical accelerations relates to the deformation mode of the soil column. The model soil container was specifically designed to allow the model soil deposit to respond in the same manner as a free-field soil deposit, characterized by a simple shear deformation mode. The inclusion of shear strips to carry complementary shear stresses was intended to sustain this mode, and minimize soil column bending. The container deformation mode could be expected to introduce a vertical component to the soil column, imposing a “pseudo-simple shear” deformation mode, as shown in Figure 7.8 One method of evaluating the soil deformation mode is to examine the vertical
311
accelerations at the top of the soil column. Assuming a rigid and horizontal base, it is evident that vertical accelerations should be in phase for the pseudo-simple shear mode and perfectly out of phase for the column bending mode (see Figure 7.8).
a) pseudo-simple shear deformation mode
b) column bending deformation mode
Figure 7.8 - Comparison of Vertical Accelerations for Soil Column Deformation Modes Unfortunately, a rigid base condition does not exist as evidenced by the table pitch and roll motions; this greatly complicates understanding the observed vertical accelerations. Nonetheless, Figure 7.9 plots surface and base horizontal and vertical response spectra for two accelerometer arrays in test 2.46, and the transfer function estimate and transfer function phase for the two surface vertical accelerometers. The phase diagram clearly demonstrates that these motions are strongly out of phase, implying that some soil column bending is occurring. The small amplitude and higher frequency of vertical base accelerations suggest that this source is a minor contributor to surface vertical accelerations.
The effect of the soil deformation mode on soil column site
response will be evaluated in Section 8.4.
312
10.0
180
Degrees
Amplitude
Surface V1:V2 Transfer Function
1.0
Surface V1:V2 Phase
0
-180
0.1
0
Frequency (Hz)
20
0
4.0
Frequency (Hz)
4.0 Soil Surface Vertical 2
Soil Surface Vertical 1
0.0 4.0
0.0 4.0
Soil Surface Horizontal 2
Acceleration (g)
Soil Surface Horizontal 1
Acceleration (g)
20
0.0 4.0 Table (V1 + V4) / 2
0.0 4.0
0.0 4.0 Table (V2 + V3) / 2
0.0 4.0 Soil Base Horizontal 2
Soil Base Horizontal 1
0.0
0.0 0.01
0.1
1
10
0.01
0.1
1
10
Period (sec)
Period (sec)
Figure 7.9 - Test 2.46 Accelerometer 5% Damped Response Spectra and Transfer Function
313
7.4 Sine Sweep Tests A sine sweep signal was used as a diagnostic tool to investigate the changes in pile head and pile group frequency response over the course of testing. The sine sweep tests bracketed each earthquake shaking test, so that trends of degrading pile head stiffness could be tracked. These input motions were manually controlled for small amplitude shaking (< 0.05 g), intending to limit soil-pile vibrations to the elastic range so that pile head resonant frequencies would correlate to pile head stiffnesses.
But the small
amplitude base input motions generated fairly large pile head accelerations due to site amplification and structural resonance effects. For example, sine sweep test 2.27 had a MHA of 0.05 g, which was amplified to 0.15 g at the soil surface, and the five pile head accelerations varied from 0.11 to 0.34 g. These moderate acceleration levels could be expected to induce soil-pile nonlinearity in the immediate vicinity of the pile, compromising the direct calculation of pile head stiffness values. Nonetheless, the change in pile head resonant frequencies from test to test should still be indicative of degrading pile head stiffness due to the earthquake shaking events. Figure 7.10 charts a histogram of pile head resonant frequencies from three sine sweep tests which bracketed earthquake shaking tests 2.24 and 2.26 scaled to 0.22 and 1.0 g, respectively.
The pile head resonant frequency is defined as the frequency
corresponding to the peak amplitude of the FFT of the pile head acceleration time history. All five pile head resonant frequencies declined over the course of testing, indicating increasing foundation flexibility and degrading stiffness due to soil-pile nonlinearity developed during the earthquake shaking tests.
The changes in pile head resonant
frequency were most pronounced for the S2, S4, and S8 structures, which with heavier
314
head masses experienced stronger inertial interaction and resultant near surface soil-pile gapping and softened zones around the pile heads (see Figure 7.11). The S7 and S6 structures were lightly loaded and thereby dominated by kinematic soil-pile interaction, with less nonlinear soil-pile response and changes in pile head resonant frequencies.
12 10.3510.35
10.1910.19
10.02
Frequency (Hz)
9.26
6.26
5.8
4.31
3.8
3.59
3.38
S2 S4 S8 S7 S6
3.82
2.26 1.51 0 Sin223b
Sin225
Sin227
Figure 7.10 - Test Series 2.2 Sine Sweeps, Pile Resonant Frequency Response
Figure 7.11 - Test 2.26 Gap Formed Around Pile S2
315
7.5 Kinematic vs. Inertial Pile Response As previously established, SSPSI consists of components relating to superstructure inertial forces and kinematic forces exerted by the soil on the pile. As detailed in Chapter 3, it is common practice to decouple these factors and separately analyze inertial and kinematic interaction for their relative contributions to SSPSI. A corollary question is whether the relative proportions of inertial and kinematic interaction are magnitude dependent. It is therefore useful to discern these components from the model tests and examine the decoupling assumptions. Single pile test series 1.1 and 2.2 offer the best opportunity for isolating these mechanisms of SSPSI.
Figure 7.12 - Test Series 1.1 Setup 7.5.1 Test 1.15 Figure 7.12 shows the model setup for test series 1.1, with the primary shaking axis indicated by the arrow; the pile head masses were 160 lbs (S1), 100 lbs (S2), 25 lbs
316
(S3), and 6.5 lbs (S4). The pile head acceleration time histories and FFTs for test 1.15 are plotted in Figure 7.13. This test subjected the model to the YBI90 motion with a MHA of 0.16 g, resulting in a free-field MHA of 0.26 g and pile head peak accelerations ranging from 0.35 (S4) to 0.77 g (S1). Note the strong similarity of the S3 and S4 FFTs to the free-field soil response FFT. Figure 7.14 displays the bending moment envelopes for these four piles. Clearly S1 and S2 were dominated by inertial forces from the superstructure masses, which induced large bending moments near the pile heads. The location of maximum bending moment for the S3 and S4 piles, however, occurred at a depth of 30 in, indicating that kinematic forces from the soil produced the largest stresses in these piles. To further validate kinematic interaction effects, Figure 7.15 plots transfer function estimates, transfer function phase, and coherence functions for the S1 and S4 pile head accelerations to the free-field soil response. The S1:free-field transfer function, phase, and coherence show poor correlation, whereas the S4:free-field transfer and coherence functions are near unity and strongly in phase. It is therefore very interesting to note that for this single pile case (S4), wave scattering effects are negligible and the foundation input motion is nearly equivalent to the free-field ground motion. A second important observation is that this particular soft clay profile would be expected to intensify kinematic interaction through strong site response amplification, yet pile demands arising from inertial interaction exceeded the kinematic demands, except for the very lightly loaded piles. As will next be shown with the higher magnitude Test 2.24, these effects appear to be independent of shaking intensity.
317
1.0
0.04 S1
0.0
-1.0
0.00
1.0
0.04 S2
0.0
-1.0
0.00 0.04 S3
Acceleration (g)
Acceleration (g)
1.0
0.0
-1.0
0.00
1.0
0.04 S4
0.0
-1.0
0.00
1.0
0.04 Free Field Soil
0.0
-1.0
0.00 0
5
10
15
0
5
10
15
Frequency (Hz)
Time (sec)
Figure 7.13 - Test 1.15 Pile Head Accelerometer Time Histories and FFTs
318
20
0
1
Depth (ft)
2
3
4
S1 - Pile 1 S2 - Pile 3 5
S3 - Pile 5 S4 - Pile 6
6 0.0
0.5
1.0
1.5
Bending Moment (K-in)
Figure 7.14 - Test 1.15 Pile Bending Moment Envelopes S1:FF Transfer Function
Amplitude
10 1
1
0.1
0.1
0.01
0.01
S1:FF Phase
S4:FF Phase
180
Degrees
180
Degrees
S4:FF Transfer Function
10
0
-180
0
-180 S1:FF Coherence Function
1.0
0.5
0.5
0.0
0.0 0
5
10
15
S4:FF Coherence Function
1.0
20
Frequency (Hz)
0
5
10
15
Frequency (Hz)
Figure 7.15 - Test 1.15 Pile Head:Free-field Transfer Functions 319
20
7.5.2 Test 2.24 The setup for test series 2.2 is shown in Figure 7.16; for these tests the pile head masses were 160 lbs (S2), 120 lbs (S4), 80 lbs (S8), 40 lbs (S7), and 6.5 lbs (S6). This pile head mass distribution was intended to better differentiate the transition from kinematic to inertial interaction as a function of pile axial load. Figure 7.17 plots pile head and free-field acceleration time histories and FFTs for test 2.24, which subjected the model to the KPI79N00 record with a MHA of 0.22 g. The free-field soil MHA was 0.51 g, and the pile head accelerations ranged from 0.63 (S6) to 1.32 g, with the unexpected result that the maximum response was achieved by the lightly loaded S7 pile. Examining the S7 FFT, it is apparent that resonance with the predominant period of the input motion (8.2 Hz) strongly amplified the structural response, closely resembling damage patterns to a narrow frequency band of structures in the 1985 Mexico City earthquake.
Figure 7.16 - Test Series 2.2 Setup
320
1.5
0.1 S2
0.0
-1.5
0.0
1.5
0.1 S4
0.0
-1.5
0.0
1.5
0.1 S8
Acceleration (g)
Acceleration (g)
0.0
-1.5 1.5 S7
0.0 0.1
0.0
-1.5
0.0
1.5
0.1 S6
0.0
-1.5
0.0
1.5
0.1 Free Field Soil
0.0
-1.5
0.0 0
3
6
9
12
0
5
10
15
Frequency (Hz)
Time (sec)
Figure 7.17 - Test 2.24 Pile Head Accelerometer Time Histories and FFTs
321
20
The pile bending moment response of test 2.24 is depicted in Figure 7.18, and similar trends to test 1.15 are noted. Inertial interaction is seen to induce large bending moments in the upper sections of all piles except S6. Kinematic forces dominate pile S6 but are noticeable at depth for all piles. Finally, Figure 7.19 presents a transfer function analysis of pile head S2 and S6 and free-field accelerations. Again, the lightly loaded S6 pile exhibits much better correlation, coherence, and phase agreement to the free-field ground motion than the heavily loaded S2 pile, thereby confirming kinematic interaction effects. Unfortunately the transition from inertial to kinematic interaction as a function of axial load could not be clearly established from these tests, as the strongly resonant response of the S7 pile obscured the behavior in the range of interest. It can be inferred from the tests, however, that for these endbearing piles in soft clay, inertial interaction dominates the response except for piles with very low axial loads. Other single pile tests with base input accelerations up to 1.0 g support this conclusion. 0
1
Depth (ft)
2
3
S2 - Pile 2 4
S4 - Pile 4 S8 - Pile 8 5
S7 - Pile 7 S6 - Pile 6
6 0.0
0.5
1.0
1.5
Bending Moment (K-in)
Figure 7.18 - Test 2.24 Pile Bending Moment Envelopes
322
2.0
S2:FF Transfer Function
10
1
1
0.1
0.1
S2:FF Phase
S6:FF Phase
180
Degrees
Degrees
180
0
-180
0
-180 S2:FF Coherence Function
1.0
Amplitude
S6:FF Transfer Function
10
0.5
0.5
0.0
0.0 0
5
10
15
S6:FF Coherence Function
1.0
20
Frequency (Hz)
0
5
10
15
20
Frequency (Hz)
Figure 7.19 - Test 2.24 Pile Head:Free-field Transfer Functions 7.6 Pile Group Frequency Response Extending the study of inertial interaction effects to pile group response, a Phase I earthquake shaking test with two comparable 3x3 pile groups but different superstructures will be analyzed. Secondly, the response of two identically configured 3x3 pile groups and superstructures, one of which was first subjected to a static lateral load test carried to large deformations, will be contrasted in a Phase II shaking test.
7.6.1 Test 1.26 Test series 1.2 can be thought of as subjecting two foundations with the same stiffness to different inertial forces. Although the superstructure lumped masses of the S1 and S2 pile groups were identical (406 lbs), the different column heights imparted unique frequency characteristics to the two groups (see Figure 7.20). The input motion consisted
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of the KPI79N00 record with a MHA of 0.42 g, resulting in a free-field soil MHA of 0.64 g. The response spectra of 54 in tall column S1 group (H/B = 3) and the 18 in tall column S2 group (H/B = 1) are displayed in Figure 7.21. The S2 superstructure, pile cap, and cap rocking peak accelerations exceeded the corresponding S1 response quantities.
The
amplitude of spectral accelerations for the pile caps and superstructures of the two groups were similar, but the frequency content was quite different.
The S1 superstructure
responded at 1.5 Hz, and the S2 superstructure at 7 Hz. The pile cap spectra appear to be composites of both free-field and superstructure motions for the respective groups, signifying wave scattering and the necessity of accounting for modified foundation input motions.
Figure 7.20 - Test Series 1.2 Setup
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4.0
4.0 S1 Superstructure
S2 Superstructure
0.0
0.0
Acceleration (g)
4.0
Acceleration (g)
S1 Pile Cap
0.0
4.0 S2 Pile Cap
0.0
4.0
4.0 S1 Pile Cap Rocking
S2 Pile Cap Rocking
0.0
0.0
5000
5000 Pile 8 Axial
µstrain
µstrain
Pile 10 Axial
0
0
10000
10000 Pile 9 Bending
µstrain
µstrain
Pile 6 Bending
0
4.0
4.0
Acceleration (g)
Acceleration (g)
0 Free Field Soil
0.0
Free Field Soil
0.0 0.01
0.1
1
10
0.01
0.1
1
10
Period (sec)
Period (sec)
Figure 7.21 - Test 1.26 Accelerometer and Strain Gage 5% Damped Response Spectra
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Although the S1 group experienced lower peak accelerations, its longer period motion translated into higher superstructure spectral accelerations and much higher forces being transmitted to the piles, as evidenced by the bending and axial strain spectra (computed for the uppermost gages in each pile). To further illustrate this point, Figure 7.22 illustrates bending moment envelopes for piles from the two groups. The S1 piles can be seen to have experienced much larger bending moments near the pile head than the S2 group, consistent with the pile head fixity condition. This test demonstrated the sensitivity of SSPSI to frequency effects (resonance); it is questionable whether pseudostatic methods of analysis could capture such response. 0
1
Depth (ft)
2
S1 - Pile 7 S1 - Pile 5 3
S1 - Pile 9 S1 - Pile 1 S2 - Pile 3
4
S2 - Pile 4 S2 - Pile 6 5
S2 - Pile 12
0.0
0.5
1.0
Bending Moment (K-in)
Figure 7.22 - Test 1.26 Pile Bending Moment Envelopes
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1.5
7.6.2 Test 2.37 In contrast to test series 1.2, test series 2.3 examined the response of two pile groups with different foundation stiffnesses to similar inertial forces. The static lateral preloading of group S1 to large deformations was observed to cause soil-cap yielding and gapping, which would be expected to also extend into the upper segments of the piles, and therefore reduce the group stiffness. This static test will be analyzed in Section 8.7.
Figure 7.23 - Test Series 2.3 Setup The setup for test series 2.3 is shown in Figure 7.23, with the lateral loading cable attached to group S1 (which was removed for earthquake shaking tests). Head masses of 806 lbs were fixed to each group at the top of 36 in tall columns. The KPI79N00 input motion MHA was 0.53 g, resulting in a free-field MHA of 1.07 g. Figure 7.24 depicts the acceleration and strain gage response spectra for the S1 and S2 pile groups. The nonintuitive result from this test is that the “virgin” group exhibited higher peak accelerations
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4.0
4.0 S2 Superstructure
S1 Superstructure
0.0
0.0
4.0
4.0 S2 Pile Cap
Acceleration (g)
Acceleration (g)
S1 Pile Cap
0.0
0.0
4.0
4.0 S1 Pile Cap Rocking
S2 Pile Cap Rocking
0.0
0.0
2000
2000 Pile 8 Axial
µstrain
µstrain
Pile 10 Axial
0
0
6000
6000 Pile 3 Bending
µstrain
µstrain
Pile 1 Bending
0
0
4.0
4.0 Free Field Soil
Acceleration (g)
Acceleration (g)
Free Field Soil
0.0
0.0 0.01
0.1
1
10
0.01
0.1
1
10
Period (sec)
Period (sec)
Figure 7.24 - Test 2.37 Accelerometer and Strain Gage 5% Damped Response Spectra
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than the preloaded group, 40 % higher at the cap and 20 % higher at the superstructure. This result can be explained by recognizing that the preloading did more than degrade the S1 group stiffness, it partially base-isolated the group by soil softening and gapping around the piles and cap. In this fashion, kinematic interaction was unable to transmit the full intensity of the seismic loading to the S1 pile group. Otherwise, superstructure, pile cap, and cap rocking spectral accelerations were similar, except for high frequency noise in the S2 superstructure instrument, possibly due to a loose accelerometer mount. 0
1
Depth (ft)
2
S1 - Pile 2 S1 - Pile 1 3
S1 - Pile 7 S1 - Pile 11 S2 - Pile 5
4
S2 - Pile 3 S2 - Pile 9 5
S2 - Pile 4
0.0
0.5
1.0
1.5
Bending Moment (K-in)
Figure 7.25 - Test 2.37 Pile Bending Moment Envelopes The stronger response of the S2 group induced higher inertial force bending moments in the piles, as seen in the bending strain spectra and in the bending moment envelopes presented in Figure 7.25. The S1 group piles exhibited higher axial strains, perhaps due to decreased group rocking stiffness as a result of the static preloading. The maximum bending moments for S1 piles occurred deeper than for S2 piles, which could be
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a result of the S1 preloading inducing reduced lateral soil-pile resistance in the upper portions of the S1 piles.
7.7 Pile Cap Embedment Effects The contribution of pile cap resistance to pile group static and dynamic response is not well-established, and several test configurations were designed to evaluate these effects. Test series 1.3 was set up to contrast the response of a fully embedded 3x3 pile group and that of a 3x3 group with cap base-soil contact but no cap side-soil contact. Test series 2.5 consisted of two 2x2 pile groups, one with full pile cap embedment, the other with no pile cap side- or cap base-soil contact. In both test series the pile groups had identical column heights and head masses, thereby imparting similar inertial forces to the different foundation conditions. In practice, consolidation settlements are commonly assumed to provide separation between the pile cap base and the soil. Though this configuration was not explicitly modeled, the relative contributions of pile cap base-soil and cap side-soil contact can be evaluated from these tests.
7.7.1 Test 1.37 The layout of test series 1.3 is shown in Figure 7.26; the S3 group is a pile raft foundation which will be described in section 7.9, but was expected to exert no differential effect on structures S1 and S2 in these tests. The S1 and S2 structures consisted of 406 lb head masses atop 18 in tall columns. After both groups were installed, a 6 in deep trench was excavated around the S1 group to relieve all contact between the side of that pile cap and the surrounding soil. Test 1.37 consisted of the KPI79N00 input motion with a MHA
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of 0.45 g, resulting in a free-field MHA of 0.59 g. Figure 7.27 plots the acceleration and strain gage response spectra for the S1 and S2 pile groups. The pile cap, cap rocking, and pile bending responses were very similar for both groups, though the slightly higher foundation stiffness of group S2 with full cap embedment appears to have resulted in an incrementally larger high frequency (8.2 Hz.) response than S1. This response propagated into the pile axial response, which is seen to be much stronger for the S2 group pile than the S1 group pile. Notably this strain contrast was only present for the top gages; all other gages in these two piles had similar values. Finally, examining the bending moment envelopes in Figure 7.28 reveals very similar bending strains in the S1 and S2 piles, except for the case of pile 1, which is positioned at the front center of group S1, and has no corollary S2 pile. Shadowing effects appear to have attenuated bending moments in this pile at mid-depth. The principal conclusion from this test series is that pile cap side-soil contact exerted only a minimal effect on the dynamic response of the pile groups.
Figure 7.26 - Test Series 1.3 Setup
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4.0
4.0 S2 Superstructure
S1 Superstructure
0.0
0.0 4.0
Acceleration (g)
Acceleration (g)
4.0 S1 Pile Cap
S2 Pile Cap
0.0
0.0
4.0
4.0 S1 Pile Cap Rocking
S2 Pile Cap Rocking
0.0
0.0
2000
2000 Pile 10 Axial
µstrain
µstrain
Pile 8 Axial
0
0
2000
2000 Pile 5 Bending
µstrain
µstrain
Pile 4 Bending
0
4.0
Acceleration (g)
Acceleration (g)
0 Free Field Soil
0.0
4.0 Free Field Soil
0.0 0.01
0.1
1
10
0.01
0.1
1
10
Period (sec)
Period (sec)
Figure 7.27 - Test 1.37 Accelerometer and Strain Gage 5% Damped Response Spectra
332
0
1
Depth (ft)
2
S1 - Pile 7 S1 - Pile 5 3
S1 - Pile 9 S1 - Pile 1 S2 - Pile 3
4
S2 - Pile 4 S2 - Pile 6 5
S3 - Pile 11
0.0
0.5
1.0
Bending Moment (K-in)
Figure 7.28 - Test 1.37 Pile Bending Moment Envelopes 7.7.2 Test 2.55 With the recognition that pile cap side-soil contact exerted little influence on the pile group response in test series 1.3, it was perceived that pile groups mobilize cap resistance in rocking, and therefore pile cap base-soil contact could potentially be a more critical component of group stiffness. To explore this concept, test series 2.5 contrasted the response of fully embedded 2x2 group S2 to non-embedded group S1 (Figure 7.29). These two groups had 600 lb head masses mounted on 24 in tall columns, and were subjected to the KPI79N00 motion with a MHA of 0.53 g in test 2.55. Figure 7.30 plots the accelerometer and strain gage response spectra for this test, which had a free-field soil MHA of 1.22 g. The S1 and S2 pile caps had nearly equal peak accelerations, but the higher spectral response of the S1 pile cap, cap rocking, and pile axial strains is consistent with the expected rocking flexibility of this group due to no cap base-soil contact. The
333
S2 superstructure response exceeded the S1 response due to frequency effects; the higher frequency rocking energy at the S1 pile cap did not intensify the superstructure motions. The S2 superstructure motion in turn generated higher S2 pile bending strains, as can be seen in Figure 7.31.
Figure 7.29 - Test Series 2.5 Setup The overall conclusion to be drawn from these tests was that pile cap base-soil contact was a more significant contributor to pile group stiffness than pile cap side-soil contact. But frequency effects remain important; shorter columns or lighter head masses in test 2.55 could have resulted in S1 superstructure response exceeding S2. It is also interesting to consider how these effects would manifest for friction piles as opposed to the end-bearing condition in these tests; stronger rocking response and a greater sensitivity to cap embedment conditions would likely result. Finally, it is important to consider that pile caps in the field are normally surrounded by stiffer soils, either due to dessication or compaction of surface fills, and cap resistance may therefore be more pronounced in the field than for these homogeneous soft model clay deposits.
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6.0
6.0
S1 Superstructure
0.0
S2 Superstructure
0.0
6.0
6.0 S2 Pile Cap
Acceleration (g)
Acceleration (g)
S1 Pile Cap
0.0
0.0
6.0
6.0 S1 Pile Cap Rocking
S2 Pile Cap Rocking
0.0
0.0
2000
2000
Pile 6 Axial
µstrain
µstrain
Pile 1 Axial
0
0
6000
6000
Pile 8 Bending
µstrain
µstrain
Pile 2 Bending
0
0
6.0
6.0
Free Field Soil
Acceleration (g)
Acceleration (g)
Free Field Soil
0.0
0.0 0.01
0.1
1
10
0.01
0.1
1
10
Period (sec)
Period (sec)
Figure 7.30 - Test 2.55 Accelerometer and Strain Gage 5% Damped Response Spectra
335
0
1
Depth (ft)
2
3
S1 - Pile 8 4
S1 - Pile 2 S2 - Pile 3 S2 - Pile 4
5
0.0
0.5
1.0
1.5
2.0
Bending Moment (K-in)
Figure 7.31 - Test 2.55 Pile Bending Moment Envelopes 7.8 Pile Group and Single Pile Subjected to 2-D Shaking Test series 2.4 was devised to subject a 5x3 pile group and a single pile to twodimensional shaking. The single pile head mass, 80 lbs, was selected to provide the same load as the pile group average head load (1200 lbs ÷ 15 piles). This section will highlight the response of the group and single pile to 2-D strong shaking. Group interaction and two-dimensional shaking effects will be analyzed in Chapter 8.
7.8.1 Test 2.46 The setup for test series 2.4 is depicted in Figure 7.32, with the arrow indicating the strong axis of 2-D shaking. The 1200 lb S1 head mass was fixed to a 54 in tall column. Test 1.46 consisted of the KPI79N00 record with a MHA of 0.58 g on the longitudinal axis, and the KPI79N90 record with a MHA of 0.34 g on the lateral axis.
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These motions amplified to free-field MHAs of 1.10 and 0.50 g, respectively. Figure 7.33 reveals that the S2 pile head motions were more severe than the S1 pile group motions at the cap or superstructure. The long period S1 superstructure did not strongly respond to the higher frequency ground motions, and in fact the S1 cap accelerations
Figure 7.32 - Test Series 1.4 Setup exceeded the superstructure accelerations by 60 %.
The longitudinal and lateral
components of structural response were proportional to the longitudinal and lateral input motions. The amplitudes and frequencies of the S1 superstructure and S2 pile head motions drove the pile bending strains, as can be seen from the gage response spectra. The bending moment envelopes for the single and group piles are displayed in Figure 7.34. In the longitudinal direction, S1 exterior pile 10 had a similar peak bending moment
337
8.0
8.0
S2 Pile Head Long
Acceleration (g)
S1 Superstructure Long
0.0 8.0
Acceleration (g)
S1 Superstructure Lat
0.0 8.0 S2 Pile Head Lat
0.0
0.0
8.0 S1 Pile Cap Long
0.0 8.0 S1 Pile Cap Lat
0.0 8000
8000
Pile 1 Bending
µstrain
µstrain
Pile 7 Bending
0
0
Acceleration (g)
Acceleration (g)
8.0 Free Field Soil Long
0.0
8.0
Free Field Soil Lat
0.0 0.01
0.1
1
10
0.01
0.1
1
10
Period (sec)
Period (sec)
Figure 7.33 - Test 2.46 Accelerometer and Strain Gage 5% Damped Response Spectra
338
0
1
Depth (ft)
2
a) Longitudinal S1 - Pile 7
3
S1 - Pile 11 S1 - Pile 12
4
S1 - Pile 9 S1 - Pile 10 5
S2 - Pile 1
0.0
0.5
1.0
1.5
2.0
Bending Moment (K-in) 0
1
Depth (ft)
2
3
b) Lateral S1 - Pile 8 4
S1 - Pile 3 S1 - Pile 5
5
S2 - Pile 2
0.0
0.5
1.0
1.5
2.0
Bending Moment (K-in)
Figure 7.34 - Test 2.46 a) Longitudinal and b) Lateral Pile Bending Moment Envelopes
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to S2 pile 1 near the surface. At intermediate depths, the S2 pile had larger bending moments, displaying an envelope characteristic of its free head condition. At deeper elevations, some of the group pile bending moments exceeded the single pile bending moments.
In the lateral direction, similar trends were observed, though notably the
amplitudes of bending moments in the two directions were similar. This is in contrast to the structural acceleration response, which will be studied in more detail in Section 8.8.
7.9 Pile Raft Foundation Performance Pile rafts are a special class of composite mat-pile foundations designed to control settlements in clays.
There is scant information published on the response of such
foundations to seismic loading. A 3x3 group pile cap was installed over a single pile in test series 1.3 to simulate an element of a larger raft foundation with sparsely placed piles (Figure 7.35). The superstructure head mass was arbitrarily selected, and in retrospect, should have been sized to match the other pile groups in the test, thereby allowing for better comparison of response.
7.9.1 Test 1.37 Figure 7.36 plots the acceleration and strain gage response spectra for structures S2 and S3 in test 1.37 (section 7.7.1 compared the S1 and S2 response in this test). The S2 pile cap was fully embedded with a 406 lb mass on an 18 in tall column; the S2 cap was also fully embedded, with a 162 lb mass on an 18 in tall column. The input and free-field MHAs for the KPI79N00 record were 0.45 and 0.59 g, respectively. The central single pile of the S3 structure provided an axis of rotation for the fairly strong rocking response
340
observed in this group.
These rocking motions caused stronger superstructure
accelerations and higher pile bending moments than experienced by the S2 group. Figure 7.28 presented the bending moment envelopes for test 1.37, where larger bending moments in the upper section of the S3 pile can be identified.
Figure 7.35 - Test Series 1.3 Pile Raft Foundation As previously noted it is difficult to draw conclusions from comparisons of the S2 and S3 response in this test. Both the foundation conditions and the superstructure inertial forces are different, and in fact the S3 rocking behavior does not well represent the expected performance of a pile raft foundation. It may however be possible to derive the pile cap rocking stiffness from this test; that exercise is reserved for Chapter 8.
7.10 Effects of Water/Scour on Pile Group Response Pile foundations are routinely deployed in marine environments for offshore platforms, river crossings, and wharf structures. Scour at the mudline degrades pile lateral resistance over the long term, but there also exists the question of whether limited duration lateral loading events due to wave or seismic forces can induce “dynamic” scour.
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6.0
6.0
S3 Superstructure
S2 Superstructure
0.0
0.0
6.0
6.0 S3 Pile Cap
Acceleration (g)
Acceleration (g)
S2 Pile Cap
0.0
0.0
6.0
6.0 S3 Pile Cap Rocking
S2 Pile Cap Rocking
0.0
0.0
3000.0
3000.0 Pile 11 Bending
µstrain
µstrain
Pile 4 Bending
0.0
0.0
6.0
6.0 Free Field Soil
Acceleration (g)
Acceleration (g)
Free Field Soil
0.0
0.0 0.01
0.1
1
10
0.01
0.1
1
10
Period (sec)
Period (sec)
Figure 7.36 - Test 1.37 Accelerometer and Strain Gage 5% Damped Response Spectra
342
This mechanism is thought to consist of water infilling and being ejected and eroding soil in the soil-pile gap during lateral cyclic or dynamic loading, thereby degrading lateral resistance and inhibiting damping.
Test series 1.4 was designed to investigate
cyclic/dynamic scour by arranging two identical pile groups with the piles exposed at the mudline, and with water impounded around one of the groups.
7.10.1 Test 1.46 The setup for test series 1.4 is shown in Figure 7.37, with a plexiglass chamber around group S2 impounding water 4 in deep. These 2x2 groups supported 24 in tall columns with 406 lb head masses. In addition to earthquake shaking tests, two tests simulating the effects of wave loading were performed.
Test 1.46 consisted of
approximately 60 cycles of manually controlled 1 Hz sine sweep excitation, ramped up to a MHA of 0.26 g. These groups exhibited very strong resonant response during the test, with superstructure transient displacements over 8 in. The time histories for the S1 and S2 pile caps, superstructures, and cap rocking accelerations for this test are shown in Figure 7.38. These response quantities, and the pile bending moment envelopes (which are not shown) are nearly identical, as they were for all tests in this series. There are several possible explanations for this result. After two seismic loading and two wave loading tests, the soil around both pile groups had mounded up, but was constrained by the plexiglass chamber around S2. This condition of restraint may have offset any softened response due to scour. A second explanation for the apparent “non-effect” of scour could be that the short time the water was impounded around the piles did not sufficiently allow for softening of the soil so that
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it could be scoured. In addition, the 60 cycles of wave loading may be too short duration to induce this effect. Another possibility is that the high plasticity model soil may not be erosive. A final explanation could be that cyclic/dynamic scour is insignificant.
Figure 7.37 - Test Series 1.4 Setup 1.0
1.0 S2 Superstructure
0.0
0.0
-1.0
-1.0
1.0
Acceleration (g)
Acceleration (g)
S1 Superstructure
S1 Pile Cap
0.0
-1.0
1.0 S2 Pile Cap
0.0
-1.0
1.0
1.0 S2 Pile Cap Rocking
S1 Pile Cap Rocking
0.0
0.0
-1.0
-1.0 0
10
20
30
40
50
Time (sec)
0
10
20
30
Time (sec)
Figure 7.38 - Test 1.46 Accelerometer Time Histories 344
40
50
7.11 Summary of Experimental Findings In conclusion, the series of shaking table soil-pile model tests was extremely successful. The feasibility of studying SSPSI problems with 1-g scale modeling techniques was demonstrated, and a rich data set was generated that offers many opportunities for detailed study.
A number of interesting problems were investigated, and important
insights to SSPSI were gained. The shaking table performed reasonably well, though some inherent limitations were apparent. The table does not offer strict repeatability, and its high frequency response, particularly at small displacements, imparts distortions. Other table modes of twist, pitch, and roll are present, and serious efforts should be made to correct these instabilities. Nonetheless, as long as the input motions are recorded and characterized, the shaking table offers the possibility to perform high quality scale model testing, well-suited to analytical evaluations and modeling. The model container designed for these tests also appears to have met its performance goals, as evidenced by the positive trends of site response and site coherence. The question of whether soil column bending or any other factors affected the ability of the model to replicate one-dimensional site response will be addressed in more detail in the next chapter. Both free-field and pile group models were subjected to 2-D shaking, and the applicability of 1-D analysis to these results will be examined in chapter 8. Pile group effects for a 5x3 pile group subjected to 2-D shaking will also be investigated in the next chapter.
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Sine sweep tests verified anticipated trends of decreasing pile head and pile group stiffness during the course of testing, and provided an index of degradation of the model soil. Soil-pile nonlinearity that developed during the sine sweeps prevented the calculation of pile head stiffness values from resonant frequencies determined in these tests. Both kinematic and inertial interaction components of SSPSI were observed in the single pile model tests, and the inertial component of response dominated in most cases. Only for single piles with light axial loads did kinematic effects cause maximum bending moments; this result may vary for a pile embedded in a non-uniform soil profile with a strong inter-layer stiffness contrast.
Pile head fixity controlled pile bending moment
patterns, with characteristic bending moment envelopes observed for the single pile (freehead) and pile group (fixed-head) tests. The frequency response and resonant vibration characteristics of the model structures exerted a major influence on their response, which in turn drove foundation bending and axial force demands. Resonance of the superstructure natural period with the ground motion/site period stimulated strong response, and the ability of pseudo-static analysis methods to adequately capture and predict such effects is questioned. Wave scattering effects were observed for pile group foundations, indicating that free-field ground motions are not suitable inputs for pile cap motions. This necessitates the calculation of a “foundation input motion” for substructured analyses, or the use a fully-coupled SSPSI model. In one case, static lateral preloading of a pile group softened the foundation stiffness to the extent that it was partially base isolated and exhibited smaller response than the analagous group that had not been preloaded.
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The influence of pile cap embedment on dynamic response was tested with various cap configurations, and cap base-soil contact was found to be a greater contributor to lateral resistance than cap side-soil contact. Tests with additional cap configurations are necessary to validate this result. The dynamic rocking stiffness of the 3x3 pile cap alone may be computed from the pile raft foundation test results. Experiments designed to evaluate the performance of pile raft foundations and the effect of “dynamic scour” were inconclusive. However these tests do offer the possibility of studying cyclic degradation of lateral resistance under medium term (60+ cycles) loading. In addition to site response, pile group effects, and 2-D shaking, the next chapter will compare pile head stiffness values obtained from the pile head loading tests and system identification analyses with observed dynamic response. Static and dynamic p-y curves will also be computed from the experimental data.
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CHAPTER 8
ANALYSES OF TEST RESULTS
8.1 Introduction This chapter will compare the observed shaking table test results with the performance predicted by both code specifications and common analytical tools. First, the model in-situ soil properties are established for use as inputs to the soil-pile interaction analyses. Then analyses are presented that examine free-field site response of the models, pile head and pile group stiffness, the effects of two-dimensional shaking, and the derivation of experimental p-y curves. In accordance with the scale modeling guidelines introduced in Chapter 5, all analyses presented in this chapter were performed at the model scale.
8.2 Shear Strength Profile Except for very small amplitude vibration problems, soil-pile interaction behavior is primarily a function of large strain soil response, i.e. soil shear strength. In the saturated model clay soil, the applied seismic and pile head loadings could be expected to generate undrained stress-strain soil response, and it was therefore necessary to evaluate the continuous undrained shear strength profile over the full depth of the models.
8.2.1 T-bar Tests T-bar tests were performed to determine the continuous shear strength profile and were supplemented with in-situ vane shear and laboratory undrained triaxial compression tests, used as checks on the T-bar method. The T-bar test procedure was previously 348
described in Section 6.6.3, and is shown being withdrawn from the model soil deposit in Figure 8.1. The T-bar plasticity solution assumes the displacement of a cylinder in an infinite medium, and T-bar readings near the surface underestimate the soil resistance. The T-bar tests were performed before four of five test series in each test phase, to reflect the conditions at the start of the individual test series. The four T-bar test results from the Phase I tests are superimposed on Figure 8.2. The consistency of the T-bar test results is notable, indicating that the soil properties were spatially uniform (in an areal sense, but varying with depth), and temporally showed only a small increase in strength over the six weeks elapsed during these tests. The stiff compacted clay layer at the base inhibited drainage, and surface wetting and covering minimized dessication, resulting in minimal consolidation strength gain during Phase I.
Figure 8.1 - T-Bar Device Being Pulled Out of Soil at Conclusion of Test The four T-bar test results from the Phase II tests are superimposed on Figure 8.3. These results show an appreciable strength gain over the four week course of testing, especially at depth, where the compacted sand layer at the base of the clay provided a
349
drainage path for consolidation. The trend of strength versus depth is consistent for the four tests, indicating that the soil strength properties were spatially (areally) consistent. Undrained Shear Strength (psf) 0
50
100
150
200
250
300
0
12
TBar112 - 11/26/97 Tbar121 - 12/9/97 Tbar130 - 12/12/97 Tbar150 - 1/8/98 Vane Shear Pre-Shake Vane Shear Post-Shake Best Estimate - Phase I
Depth (in)
24
36
48
60
72
Figure 8.2 - Phase I T-Bar and Vane Shear Tests and Undrained Shear Strength Profile
8.2.2 UUTX Tests Model soil specimens were sampled at the beginning and end of Phase I testing from depths of 6 – 18 inches in the model container, and remolded for UUTX testing. Four specimens with a cure age of 56 days (time elapsed since remolding) and four specimens with a cure age of 4 days were tested and the stress-strain plots are shown together as
350
Figure 8.4. The 8 specimens had water contents ranging from 128 – 133 %, and exhibited similar initial stiffness and residual strengths. The specimens that cured 56 days, however, had higher peak strengths, lower failure strains, and higher sensitivity. As the 4 day cure age specimens included the effects of cyclic degradation, sampling disturbance, and remolding, the actual in-situ shear strength could be expected to exceed these values. But the 56 day cure age specimens benefitted from thixotropy “erasing” some of the sample disturbance and remolding effects, and the higher strengths implied by those tests corresponded to the in-situ conditions. Undrained Shear Strength (psf) 0
100
200
300
400
500
600
700
800
0
12
TBar221 - 7/15/98 Tbar232 - 7/29/98 Tbar241 - 8/5/98 Tbar250 - 8/12/98 Vane Shear - Post Shake Best Estimate - Series 2.2
Depth (in)
24
36
48
60
72
Figure 8.3 - Phase II T-Bar and Vane Shear Tests and Undrained Shear Strength Profile
351
300 Cure Age 56 days
Deviatoric Stress (psf)
Cure Age 4 days
200
100
0 0
0.025
0.05
0.075
0.1
Strain
Figure 8.4 - Model Soil UUTX Laboratory Test Results 8.2.3 Vane Shear Tests Vane shear tests were conducted in Phases I and II to better establish the in-situ soil strengths and calibrate the T-bar test results. The vane shear tests were performed in accordance with ASTM D-2573 using a vane 4 ¼ in tall x 3 3/8 in diameter, rotated at 6 degrees/minute. Peak strengths obtained by the vane shear tests are superimposed on Figure 8.2 and 8.3; Phase I results include tests conducted both before and after shaking table tests, indicating minor strength degradation due to shaking. The vane shear test results strongly correlate to the T-bar test trends of strength versus depth, but are consistently smaller in magnitude. This discrepancy was thought to be due to the difference in the “shearing velocity” applied in the two test procedures. For the vane shear tests, the rotational shearing velocity at the blade/soil interface was computed as 0.003 in/sec; for the T-bar tests, the bar withdrawal shearing velocity was calculated to range from 1.4 to 2.8 in/sec. A study was conducted at U.C. Berkeley to investigate the effects of shearing velocity on the
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model soil (Biscontin, 1998). She performed laboratory miniature vane shear tests on remolded samples of the model clay soil obtained from the test container. The results are summarized in Figure 8.5, showing that a model soil peak strength increase on the order of 30 - 70% could be expected between the vane shear and T-bar test shearing velocities. This factor brings the observed vane shear and T-bar test results into closer agreement. 1.8
Batch 1 - Maximum
Normalized Undrained Shear Strength
1.6
Batch 2 - Maximum Batch 3 - Maximum
1.4
1.2
Batch 1 - Minimum Batch 2 - Minimum
1
0.8
0.6
0.4
0.2
0 0.0001
0.001
0.01
0.1
1
Velocity (in/sec)
Figure 8.5 - Effect of Strain Rate on Laboratory Vane Shear Testing of Model Soil 8.2.4 Best Estimate Strength Profiles The best estimate undrained shear strength profiles were developed from the T-bar, vane shear, and UUTX test data, and are also shown on Figures 8.2 and 8.3 for the Phase I and Phase II tests, respectively. The best estimate Phase I strength profile may be applied to all tests during that Phase. The best estimate Phase II profile was specifically constructed for use as input to the single pile analyses in test series 2.2, and reflects the lower strengths existing at the early stages of consolidation. Best estimate soil strength
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profiles for later Phase II test series have also been developed to reflect further consolidation strength gain.
8.3 Shear Wave Velocity Profile The site stiffness or shear wave velocity profile is a required input for wavepropagation site response analyses. Both laboratory and in-situ tests were performed to evaluate the in-situ stiffness profile.
Previously established relations (Section 5.2.4)
between model soil water content/shear strength and shear wave velocity were also considered in establishing the shear wave velocity profile.
8.3.1 Phase I Hammer Blow Tests In-situ hammer blow tests were performed with the intention of generating vertically propagating shear waves that could be detected by the vertical arrays of accelerometers in the soil column. By identifying shear wave arrivals at each instrument, and knowing the instrument positions, differential travel times and shear wave velocities could then be computed. The Phase I test procedure consisted of striking the steel base plate of the model soil container with a sledgehammer. The accelerations recorded in a 5 instrument downhole array during 6 sequential hammer blows are shown in Figure 8.6.
The
acceleration FFTs reveal the high frequency content and broad-band nature of these excitations. Manual identification of wave arrivals and numerical cross-correlation of signal pairs yielded inconsistent results for Phase I tests, but suggested near-surface shear wave velocities in the range of 100 ft/sec.
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0.1
0.003 Elev 0
0 -0.1 0.1
0 0.003 Elev -6
-0.1 0.1
Acceleration (g)
Acceleration (g)
0
0 -0.1 0.1
0 0.003 Elev -24
0 0.003 Elev -48
0 -0.1 0.1
0 0.003 Elev -74
0 -0.1
0 0
3
6
9
12
15
Time (sec)
0
20
40
60
80
100
Frequency (Hz)
Figure 8.6 - Test 1.13 Base Impact Shear Wave Velocity Test Time Histories and FFTs 8.3.2 Phase II Hammer Blow Tests The Phase II hammer blow test procedure was modified to improve the generation and detection of shear waves in the model soil. Surface geophysics test techniques were employed by striking a wooden plate coupled to the soil surface, as previously shown in Figure 6.28. Higher data sampling rates and vertically denser accelerometer arrays were also used to improve the signal fidelity. Hammer blow test results for a container devoid of piles is shown in Figure 8.7. The left column of Figure 8.7 depicts the unfiltered wave arrivals at the 9 accelerometers, growing weaker with depth. The right hand column plots the same waves filtered at 50 Hz, with one arrival tracked through the soil column and
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UNFILTERED
FILTERED
0.2
0.2 Elev 0
0
0
-0.2 0.2
-0.2 0.15 Elev -8
0
0
-0.2 0.2
-0.15 0.1
0
0
-0.2 0.2
-0.1 0.1
Elev -30
0
0
-0.2 0.2
-0.1 0.1
Acceleration (g)
Acceleration (g)
Elev -18
Elev -48
0 -0.2 Elev -60
0 -0.1 0.05
0
0
0.2
-0.05 0.03 Elev -66
0
0
-0.2 0.2
-0.03 0.01
Elev -72
0
0
-0.2 0.2
-0.01 0.005 Elev -75
0
0
-0.2
-0.005 0
0.1
0.2
0.3
0.4
0.5
Time (sec)
0
0.1
0.2
0.3
0.4
0.5
Time (sec)
Figure 8.7 - Test 2.10 Surface Impact Shear Wave Velocity Test; Stack 1 Blow 1 Unfiltered and Filtered Time Histories with Shear Wave Arrivals Identified
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identified by dashed lines. Note that the filtered signals are plotted to different scales and the low signal to noise ratio of the deeper instruments calls into question the reliability of those measurements. The presence of piles in close proximity to the accelerometer array affected some test results, as the piles provided alternate travel paths for wave energy, and artificially increased the apparent shear wave velocities.
8.3.3 Baseline Shear Wave Velocity Profiles Baseline shear wave velocity profiles were adapted from the best estimate shear strength profiles for the two test Phases, recognizing the direct relationship between undrained shear strength and shear wave velocity, as proposed by Dickenson (1994) for Bay Mud and shown experimentally for the model soil (Section 5.2.4). The Phase I baseline shear wave velocity profile is shown in Figure 8.8, and was scaled to have a shear wave velocity of 105 ft/sec in the upper two feet. This value was derived from the results of bender element tests performed on a model soil specimen sampled from the test container (Section 8.4) and was in agreement with the limited hammer blow test results. The Phase II shear wave velocity profile inferred from the shear strength profile is shown in Figure 8.9, along with the shear wave velocity profile deduced by the hammer blow test. The two are in very good agreement except near the surface and at the base of the container; this trend was consistently obtained for all Phase II hammer tests. The very short travel times for the two near surface accelerometers are likely the result of higher velocity surface waves obscuring the shear waves, thereby corrupting information in the top two intervals. The low velocity in the base layer is thought to be fictitious and a
357
0
0
12
12
24
24
Depth (in)
) n i( 36 h tp e D
Hammer Blow Profile 36
48
48
60
60
72
72
0
100 200 300 Shear Wave Velocity
400
Inferred Profile
0
300
600
900
Shear Wave Velocity (fps)
Figure 8.9 - Phase II Hammer Blow Test and Inferred Shear Wave Velocity Profiles
Figure 8.8 - Phase I Shear Wave Velocity Inferred Profile
result of the low energy signal and wave reflections at the clay/sand interface and from the steel base plate. A shear wave velocity of several hundred feet/sec would be expected for medium dense sands at this confining pressure, and pile installations reaching refusal at that elevation substantiate the dense state of that layer. Strong shaking accelerometer time histories showed very high correlation between the instrument in the sand layer and the one in the clay above it, refuting the possibility that liquefaction occurred in the sand. In any event, the site response and soil-pile interaction analyses were formulated to be insensitive to the properties of the base sand layer, as will be shown in Section 8.5. The overall stiffness of the model soil column could be expected to decrease in response to strong shaking, and increase with periods of rest due to thixotropy. Figures
358
Sine Sweep Soil Column Resonant Frequency (Hz)
1.6
3 1.2
2 0.8
1 0.4
0
0
359
kpi259
kpi258
sin256
kpi255
sin254
kpi253
sin252
sin247
kpi246
sin245
kpi244
sin243
sin238
kpi237
sin236
kpi235
sin234
sin227
kpi226
sin225
kpi224
sin223b
sin218
kpi217
kpi216
sin215
kpi214
kpi213
3 0.6
2 0.4
1 0.2
0 0
5
Test Event
Figure 8.10 - b) Phase II Soil Peak Acceleration vs. Site Resonant Frequency sin159
kpi158
kpi157
kpi155
ybi153
sin152
sin148
wav147
wav146
sin145
kpi144
sin143
ybi142
sin141
sin138
kpi137
sin136
ybi134
sin133
sin127
kpi126
ybi124
sin123
ybi118
sin116
ybi115
Maximum Soil Acceleration (g)
0.8
sin114
4
Maximum Soil Acceleration (g)
4
sin212
Sine Sweep Soil Column Resonant Frequency (Hz) 5 1
Frequency
Acceleration
Test Event
Figure 8.10 - a) Phase I Soil Peak Acceleration vs. Site Resonant Frequency Illustrating Trends of Soil Degradation and Recovery
Frequency 2
Acceleration
8.10a and 8.10b plot the history of site resonant frequency derived from sine sweep tests in parallel with the history of peak acceleration during earthquake shaking tests for Phases I and II. These charts illustrate decreases in site resonant frequency after strong shaking events, and increases after rest periods. Therefore a methodology was conceived to describe test-specific shear wave velocity profiles for the entire test series. This method consisted of scaling the baseline shear wave velocity profile developed for each phase to have the same first mode frequency as the observed sine sweep resonant frequency for the specific test. This somewhat simplistically implies that stiffness degradation and recovery effects occurred uniformly across the entire depth, which would not be expected due to shear strain concentrations. However, this method, with one further modification, will be shown in Section 8.5 to have yielded very good results.
8.4 Model Soil Modulus Degradation and Damping Modulus degradation and damping curves are input parameters for the equivalentlinear site response analyses used to simulate the observed model soil site response. An advanced laboratory testing apparatus described by Gookin (1998) was utilized to perform cyclic triaxial tests and bender element shear wave velocity tests on a model soil specimen sampled from the test container, remolded, and allowed to cure for 5 days to match the time elapsed between shaking tests. A shear wave velocity of 105 ft/sec was measured in the bender element shear wave velocity tests, corresponding to a shear modulus Gmax of 16 ksc. The model soil modulus degradation and damping data points are depicted in Figure 8.11, with a best estimate curve fit to the data. For comparison, modulus degradation and damping curves recommended by Sun et al. (1988) for Young Bay Mud and Vucetic and
360
Dobry (1991) for cohesive soils as a function of plasticity index are also shown in the figure. It is interesting to note that the model soil damping data fit the Bay Mud curve extremely well, though the model soil modulus degradation occurs at significantly smaller strains than Bay Mud. A second specimen was tested immediately after remolding and exhibited similar modulus degradation and damping behavior, but with a Gmax of only 6.7 ksc, illustrating that the model soil experienced pronounced thixotropy. 1.0
0.8
G/Gmax
0.6
0.4 PI = 200 0.2
PI = 0 0.0 1E-6
1E-5
1E-4
1E-3
0.01
0.1
0.3
1 Hz Test Data PI = 0
0.1 Hz Test Data Best Estimate Young Bay Mud
Damping Ratio
0.2
Vucetic & Dobry
0.1 PI = 200
0.0 1E-6
1E-5
1E-4
1E-3
0.01
Shear Strain
Figure 8.11 - Model Soil Modulus Degradation and Damping Curves
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0.1
8.5 Container Performance and Observed Free Field Response The most important component of an SSPSI analysis is obtaining the “correct” freefield site response, as any error in that computation will propagate into and amplify error in the soil-pile analysis; this is true for both uncoupled and coupled analysis techniques. It is therefore essential to be able to conduct accurate free-field site response analyses of the model soil columns, both with and without piles and pile groups present. Analytical reproduction of the observed site response also serves to indicate that the model container is effective in minimizing boundary effects, and that the potential soil column bending mode and/or twist motions are not distorting the site response.
In addition, the
applicability of one-dimensional site response analyses to cases of two-dimensional shaking can be evaluated for several tests.
The following section will compare the
observed site response with the free-field response predicted by the program SHAKE91 (Idriss et al., 1991). The model container is shown during strong shaking in Figure 8.12.
The site
specific shear wave velocity profiles and material specific modulus degradation and damping curves previously introduced were used as input parameters for the SHAKE91 analyses. The analyses focused on the Phase II tests, as the accelerometer arrays were denser and better positioned away from structures than in Phase I. With some uncertainty as to the properties of the base sand layer, the SHAKE91 model was configured to use the acceleration recorded in the clay layer just above the sand as input to the simulation at that layer (“within” motion). Trial simulations confirmed the insensitivity of the SHAKE91 results to the base sand layer properties, and the strong sensitivity of the results to variations in the shear wave velocity profile and the modulus degradation and damping
362
curves. In fact, the trial simulations were found to consistently underpredict the observed site response, and a parametric study of stiffness profiles was performed to achieve a better match to the experimental results. It was found that increasing the shear wave velocity values by 30 % from the test-specific stiffness profiles consistently resulted in optimized matches to the observed data. This suggested that the stiffness profile derived from the sine sweep test resonant frequencies was not in fact the small strain stiffness of the soil.
As observed in Section 7.4, the sine sweep tests generated moderate
accelerations in the soil, and a SHAKE91 analysis substantiated the development of shear strains sufficient to degrade the site average shear wave velocity from 142 ft/sec to 98 ft/sec, or 30 %. Therefore a 30 % increase in the site shear wave velocity profile was adopted for every SHAKE91 simulation reported in this section to compensate for the soil nonlinearity induced by the sine sweep tests.
Figure 8.12 - Model Soil Container in Motion During Strong Shaking, Test Series 1.5
363
The recorded motions for the Phase II tests are shown in Figures 8.13 – 8.18 as solid lines, with the corresponding SHAKE91 simulation as dashed lines.
Overall, the
agreement is quite good. The following observations can be made about the SHAKE91 simulations of the test data: •
The predicted MHA at the soil surface nearly always matched the observed value, with only 1 case overpredicted and 2 cases underpredicted, all to a small degree.
•
The SHAKE91 simulations were effective in capturing nuances of site response; a good example is provided by the spectral transformation between elevations –30 and –18 in test 2.13 (Figure 8.13a).
•
The response at the predominant input motion and site periods (0.12 and 0.35 sec, respectively) was accurately predicted by the analyses.
•
The amplitude of response at the site period was nearly always overpredicted, raising the possibility that the equivalent linear method is inherently biased, and that nonlinear analyses might be more effective for these strong shaking events.
•
The amplitude of response in the high frequency range was frequently underpredicted, particularly for tests 2.44, 2.46, and 2.55. This may reflect the proximity of the accelerometer array to the model structures in test series 2.4 and 2.5, and feedback energy from the structures being recorded by the accelerometers. This phenomena was observed in several field case studies presented in Chapter 3.
•
Another possible explanation for the underprediction of high frequency energy in the models was the strong twist motions imparted by the shaking table, which would not be accounted for in the SHAKE91 analyses, but cannot be isolated from the test data.
364
•
The quality of response predictions with “distant” structures (test series 2.2 and 2.3) and without structures (test series 2.1) was similar.
•
In some cases high frequency response was better predicted for low amplitude shaking (tests 2.13 and 2.16) than for strong shaking (tests 2.14 and 2.17). The overprediction of response at the site period was consistently higher for strong shaking than for low amplitude shaking.
•
The one dimensional site response analysis predicted 1-D and 2-D shaking with the same level of accuracy, as test 2.13 and 2.14 (1-D shaking) simulations were of similar quality as those for test 2.16 and 2.17 (2-D shaking).
•
There was no direct evidence that soil column bending distorted the site response.
•
Efforts to optimize SHAKE91 input parameters to more accurately predict the amplitudes of response at the site and input motion periods resulted in shifting the periods, not the amplitudes of response.
In conclusion, the SHAKE91 simulations of the observed model soil response were very successful, and the model soil-container system can be judged to adequately reproduce free-field site response.
The small deviations between the observed and
predicted behavior may be acceptable for pure site response analyses, but the propagation of these errors into the SSPSI analysis requires further study.
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1
2 Elev 0
Elev 0
0 1
0 2 Elev -8
Elev -8
0 1
0 2 Elev -18
0 2
Elev -30
0 1
5% Damped Spectral Acceleration (g)
5% Damped Spectral Acceleration (g)
0 1
Elev -18
Elev -48
0 1
Elev -60
0 1
Elev -30
0 2
Elev -48
0 2
Elev -60
0 2 Elev -66
0 1
Elev -66
0 2
Elev -72
0 1
Elev -72
0 2 Elev -75
Elev -75
0
0 0.01
0.1
1
10
Period (sec)
0.01
0.1
1
10
Period (sec)
(a) (b) Figure 8.13 - a) Test 2.13 and b) 2.14 Stack 1 Site Response vs. SHAKE91 Predicted Spectra
366
1
2 Elev 0
Elev 0
0 1
0 2 Elev -8
Elev -8
0 1
0 2 Elev -18
0 2
Elev -30
0 1
5% Damped Spectral Acceleration (g)
5% Damped Spectral Acceleration (g)
0 1
Elev -18
Elev -48
0 1
Elev -60
0 1
Elev -30
0 2
Elev -48
0 2
Elev -60
0 2 Elev -66
0 1
Elev -66
0 2
Elev -72
0 1
Elev -72
0 2 Elev -75
Elev -75
0
0 0.01
0.1
1
10
Period (sec)
0.01
0.1
1
10
Period (sec)
(a) (b) Figure 8.14 - a) Test 2.16 and b) 2.17 Stack 1 Site Response vs. SHAKE91 Predicted Spectra
367
2
4
Elev 0
Elev 0
0 2
0 4
Elev -8
Elev -8
0 2
0 4
Elev -18
0 4
Elev -30
0 2
5% Damped Spectral Acceleration (g)
5% Damped Spectral Acceleration (g)
0 2
Elev -18
Elev -48
0 2
Elev -60
0 2
0 4
Elev -48
0 4
Elev -60
0 4
Elev -66
0 2
Elev -30
Elev -66
Elev -72
0 2 Elev -75
0
0 4
Elev -72
0 4 Elev -75
0 0.01
0.1
1
10
Period (sec)
0.01
0.1
1
10
Period (sec)
(a) (b) Figure 8.15 - a) Test 2.24 and b) 2.26 Stack 1 Site Response vs. SHAKE91 Predicted Spectra
368
4
2
Elev 0
Elev 0
0 4
0 2
Elev -8
Elev -8
0 4
0 2
Elev -18
Elev -18
0 4 Elev -30
0 2
5% Damped Spectral Acceleration (g)
5% Damped Spectral Acceleration (g)
0 2
Elev -48
0 2
Elev -60
Elev -30
0 4
Elev -48
0 4
Elev -60
0 4
0 2
Elev -66
Elev -66
0 4
0 2
Elev -72
Elev -72
0 4
0 2
Elev -75
Elev -75
0
0 0.01
0.1
1
10
Period (sec)
0.01
0.1
1
10
Period (sec)
(a) (b) Figure 8.16 - a) Test 2.35 and b) 2.37 Stack 1 Site Response vs. SHAKE91 Predicted Spectra
369
3
4 Elev 0
Elev 0
0 3
0 4 Elev -8
Elev -8
0 3
0 4 Elev -18
0 4
Elev -30
0 3
5% Damped Spectral Acceleration (g)
5% Damped Spectral Acceleration (g)
0 3
Elev -18
Elev -48
0 3
Elev -60
0 3
Elev -30
0 4
Elev -48
0 4
Elev -60
0 4 Elev -66
0 3
Elev -66
0 4
Elev -72
0 3
Elev -72
0 4 Elev -75
Elev -75
0
0 0.01
0.1
1
10
Period (sec)
0.01
0.1
1
10
Period (sec)
(a) (b) Figure 8.17 - a) Test 2.44 and b) 2.46 Stack 1 Site Response vs. SHAKE91 Predicted Spectra
370
3
4 Elev 0
Elev 0
0 3
0 4 Elev -8
Elev -8
0 3
0 4 Elev -18
0 4
Elev -30
0 3
5% Damped Spectral Acceleration (g)
5% Damped Spectral Acceleration (g)
0 3
Elev -18
Elev -48
0 3
Elev -60
0 3
Elev -30
0 4
Elev -48
0 4
Elev -60
0 4 Elev -66
0 3
Elev -66
0 4
Elev -72
0 3
Elev -72
0 4 Elev -75
Elev -75
0
0 0.01
0.1
1
10
Period (sec)
0.01
0.1
1
10
Period (sec)
(a) (b) Figure 8.18 - a) Test 2.53 and b) 2.55 Stack 1 Site Response vs. SHAKE91 Predicted Spectra
371
8.6
Pile Head Loading Tests Pile head loading tests attempt to replicate the inertial component of SSPSI, though
the extension of static or cyclic loading derived pile head stiffness values to seismic response is not well substantiated. Therefore a series of pile head loading tests was performed on individual model piles to provide estimates of pile head stiffness to be compared with the observed seismic response of analogous piles in the same model. One static lateral load test was performed during test series 1.1, and static lateral, lateral impact, forced vibration, static axial, and cyclic axial tests were performed during test series 2.2. The following sections will also compare the experimental results with the performance predicted by code, practice, and common analytical tools.
8.6.1 Static Lateral Loading Tests As described in Section 4.2.1, static lateral loading tests have been the principal basis for the analysis of piles under all modes of lateral loading, including SSPSI. Model piles were laterally loaded in tests 1.11 and 2.20 to large deformations, and the pile head loaddeflection and the pile deflected shape and bending moment diagrams at maximum loading are shown in Figure 8.19. The pile deflected shape was obtained by double integration of the bending moment diagram, which was directly calculated from the measured strain gage data. Both the pile bending moment and deflected shape are characteristic of the freehead loading condition of the model piles. Pile head secant stiffness values were estimated at 0.25 in deflection, which corresponds to the ATC-32 recommended tolerable lateral deflection of 2 in divided by the geometric scaling factor. These secant stiffnesses are also
372
plotted on Figure 8.19, with 310 lb/in and 340 lb/in obtained for the Phase I and II piles, respectively. 250 K = 340 lb/in
K = 310 lb/in
Load (lbs)
200 150 100 50 0 0
0.5
1
1.5
2
0
0.5
Deflection (in)
1
1.5
2
Deflection (in)
0
12
Depth (in)
24
36
Test 2.20
Test 1.11 48
Test Data
Test Data
COM624P
COM624P
60
72 0
0.5
1
1.5
2
0
0.5
Deflection (in)
1
1.5
2
Deflection (in)
0
12
Depth (in)
24
36
48
60
72 -0.5
0
0.5
1
1.5
2
2.5
Bending Moment (K-in)
-0.5
0
0.5
1
1.5
2
2.5
Bending Moment (K-in)
Figure 8.19 - Static Lateral Load Tests 1.1 and 2.2 vs. COM624 Predicted Deflection and Bending Moments, with Secant Pile Head Stiffnesses
373
Also depicted on Figure 8.19 is the performance predicted by the lateral pile analysis computer program COM624P. The input data to these analyses consisted of the model pile physical properties, the best estimate soil strength profiles, and the default p-y curves for soft clay proposed by Matlock (1970). The agreement between the experimental and analytical results is quite good for test 1.11. Test 2.20 loading conditions were such that the cable and pulley system applied the lateral load at 20 degrees from the horizontal (Figure 6.25); this raked load was input as lateral and axial components in COM624P, but may account for the less accurate prediction of bending moments. These results suggest that Matlock’s soft clay p-y criteria are a suitable model for the nonlinear model soil-pile interaction under static loading. The accuracy achieved at this basic level of analysis for this simple load case instills confidence for analyses of problems of increasing complexity, including SSPSI.
8.6.2 Pile Head Impact Test A common technique for obtaining the natural frequency of vibration of structures consists of performing a snap-back (or ringdown) test, which consist of quickly releasing the structure from some imposed, initial lateral displacement, and measuring the ensuing free vibrations of the structure as it attempts to rebound to its original position. The free vibration response is described by: u& (0) + ζ ω n u (0) sin ω D t u (t ) = e −ζ ω n t u (0) cos ω D t + ωD where
2 ω D = ωn 1−ζ
374
(8.1)
(8.2)
This method was modified for the model soil-pile system as it was feared that the initial imposed displacement would open a soil-pile gap that would interfere with the free vibration response. The pile head was subjected to 3 lateral blows delivered in slow succession by a rubber mallet, to damp high frequency “ring”. The acceleration response of the pile head for each blow is shown in Figure 8.20 as acceleration time histories and FFTs. The peak accelerations appear to be “clipped” near + 2.5 g, particularly for blow 3, indicating that the instrument went out of range. The peak amplitude of the FFTs occurs at 31.7 Hz for the first two blows, and 24.7 Hz for the third blow, indicative of the system softening with repeated excitations. The dashed lines delineate the segments extracted for analysis of the free vibration response of the pile. Figure 8.21 presents equation 8.1 fit to the three segments, with the frequency and damping parameters of the solution indicated on the plots. With the known pile head mass of 6.5 lbs and measured frequency response at 34 Hz, the pile head stiffness can be computed from
ωn =
k m
(8.3)
as approximately 770 lb/in, more than double the secant stiffness values obtained from the static lateral load tests. Double integration of the accelerometer records indicated that the peak displacements were on the order of 0.05 in, consistent with initial tangent stiffness values on Figure 8.19. The damping values of 5 % obtained from the free vibration analysis are low as a function of load level, and will be compared with the system identification results in Section 8.10.
375
0.04
2.5 Blow 1
0
0.02
0
-2.5 2.25
2.5
2.75
3
3.25 0.04
Acceleration (g)
2.5 Blow 2
0
0.02
-2.5
0 9.75
10
10.25
10.5
10.75
2.5
0.04 Blow 3
0.02
0
0
-2.5 13.75
14
14.25 Time (sec)
14.5
14.75
0
20 40 Frequency (Hz)
60
Figure 8.20 - Test 2.20e Pile S6 Head Impact Frequency Response 0.5 Blow 1
0
f = 34.2 Hz, damping = 5 % -0.5
Acceleration (g)
0.5 Blow 2
0
f = 33.6 Hz, damping = 5 % -0.5 0.5 Blow 3
0
f = 33.7 Hz, damping = 5 % -0.5 0
20
40
60
Time Step
Figure 8.21 - Test 2.20e Pile S6 Head Impact Test Free Vibration Response
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8E+5 Input FFT
Output FFT
4E+5
0E+0 1E+7 Input Power Spectral Density
Output Power Spectral Density
1E+6 1E+5 1E+4 1E+3 1E+2
1E+7
1E+1 Cross Spectral Density
Transfer Function Magnitude
1E+6 1E+5
1
1E+4 1E+3
0.1
1E+2 1E+1
1E-2
180
Degrees
Amplitude
1E+1
Transfer Function Phase
Coherence Function
0
-180 0
10
20
30
40
Frequency (Hz)
0
10
20
30
Frequency (Hz)
Figure 8.22 - Test 2.20d Pile S5 Forced Vibration Spectral Analysis
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40
8.6.3 Pile Head Forced Vibration Tests Forced vibration pile head loading tests were performed on a single pile as described in Section 6.6.2. Three tests were made on the same pile at increasing levels of intensity, but the electrodynamic shaker was not powerful enough to excite the pile at its resonant frequency, and lost control at high frequencies. Figure 8.22 illustrates the spectral analysis for the acceleration input of the shaker and the acceleration output of the pile head; the fall-off in input energy is readily apparent above 25 Hz. Although the transfer function estimate suggests a peak above 30 Hz, the extremely low input and output energy in that frequency range invalidates these results. For future tests of this type, equipment capable of delivering and controlling higher frequency energy must be employed.
8.6.4 Pile Head Static Axial Loading Test Axial pile response is a critical component of SSPSI, as pile group rocking stiffness is a function of single pile axial stiffness. The axial load test is also the most commonly performed pile head loading test, as it can be directly interpreted to determine the pile axial capacity. The pile load-deflection diagram is shown in Figure 8.23, with pile head and pile tip deflections plotted. Davisson (1972) proposed a method commonly used in practice to interpret the failure load of the pile from the load-deflection diagram. This method consists of first constructing the elastic compression line at a slope of QultLpile/ApileEpile, then constructing a parallel failure line separated by a deflection of 0.01875 + d/120 in (model scale). The intersection of the failure line with the load deflection diagram defines the failure load, in this case 200 lbs. For endbearing piles that transfer axial load through the tip and not through skin friction, the data can be directly
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expressed as a tip pressure-deflection (Q-z) diagram, as shown in Figure 8.24. An axial secant stiffness of 4500 lb/in is plotted, for use as input to the pile group dynamic analyses. 0.0
Failure
0.1
Deflection (in)
Pile Head Pile Tip 0.2
Elastic Compression Line Davisson's Failure Criterion
0.3
0.4 0
100
200 Axial Load (lbs)
300
400
Figure 8.23 - Test 2.20a Pile S1 Static Axial Load-Deflection and Failure Criterion 400
Tip Pressure (psf)
K = 4500 lb/in 300
200
100
0 0
0.05
0.1
0.15
0.2
0.25
Pile Tip Deflection (in)
Figure 8.24 - Test 2.20a Pile S1 Static Axial Tip Pressure-Deflection (Q-z) Curve 8.6.5 Pile Head Cyclic Axial Loading Test The rocking response of pile groups to seismic loading and the mobilization of pile axial resistance is cyclic/dynamic in nature, and therefore cyclic axial head loading tests were also performed. This test procedure was previously described in Section 6.6.2 and shown in Figure 6.27. The pile head cyclic load-deflection diagram is shown in Figure 8.25, and depicts accumulated deflections under stress-controlled cyclic loading. The
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static axial loading secant stiffness is also plotted on the figure, illustrating the potential unconservativeness of applying static loading values to cyclic loading conditions.
0
Pile Head Deflection (in)
Kstatic 0.1
0.2
0.3
0.4
0.5 -200
0
200
400
Axial Load (lbs)
Figure 8.25 - Test 2.20b Pile S3 Cyclic Axial Load-Deflection Response Bea et al. (1980) studied rate and cycling effects of axially loaded piles and showed the effects of cycling on increasing deflections. The experimental data has been plotted in the same format of normalized deflection versus number of cycles in Figure 8.26, and is in good agreement with Bea’s results. It can also be noted that the observed load cycling effects were more severe for higher load levels. Pile Head Deflection at Load Cycle N --------------------------------------------------Pile Head Deflection at Load Cycle 1
2.0 Load Level 105 lbs Load Level 200 lbs
1.8
Load Level 240 lbs Load Level 290 lbs
1.6
Load Level 380 lbs 1.4
1.2
1.0 1
2
3
4
5 6 7 Number of Load Cycles
8
9
10
11
Figure 8.26 - Axial Load Cycling Effects for Test 2.20b Pile S3
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In the discussion of the static axial load test results and the development of an axial secant stiffness, it was assumed that all axial load was transferred through the pile tip, and skin friction was negligible. The cyclic axial tests provide a unique opportunity to derive the pile skin friction, by analyzing a tension cycle of loading where all load must be transferred through skin friction. The first tension cycle at the highest load level was analyzed and is shown as Figure 8.27. Details of this derivation are given by Reese Distribution of Axial Load
Pile Head Load -Deflection 0.05
0
12
0.1
Depth (in)
Deflection (in)
24 0.15
0.2
36
48 0.25
60
0.3
72 -200
0
200
400
-250
-200
Axial Load (lbs)
-150
-100
-50
0
50
Load (lbs)
Distribution of Pile Load Transfer 0
Pile T-Z Curves
4
depth z = 2
12
Load Transfer (psf)
3
Depth (in)
24
36
48
z=4 2
z=8
1 60
z = 12 z = 16 72
0 -6
-5
-4
-3
-2
-1
0
1
Load (psf)
0
0.01
0.02
0.03
0.04
0.05
Deflection (in)
Figure 8.27 - Derivation of Pile S3 T-z Curves from Cyclic Axial Test Tensile Loading Segment
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(1979). First, five time steps to be analyzed are designated by the symbols on the pile head load-deflection diagram. The distribution of axial load for a given time step is calculated from the strain gage data, and the load transfer is computed as the slope of the load distribution curve divided by the pile circumference. The pile movement z can be obtained at any depth knowing the pile head deflection and the elastic compression (or extension) of the pile. Proper T-z curves normalize the load transfer by the soil shear strength. The analytical results indicate that the pile was in fact transferring little load through skin friction, and the endbearing assumption is therefore valid for these models. T-z curves are not codified to the degree that p-y curves are, and therefore do not offer a point of comparison to the test results.
8.7 Pile Group Effects Analytical methods describing pile group effects were presented in Section 3.1.5, and a number of experimental programs were described in Chapter 4 that investigated pile group interaction. These studies have focused on aspects of pile group load distribution, load “shadowing”, group efficiency, and group dynamic response. This test program has obtained an extensive data set of pile group performance under seismic loading that lends itself to detailed future study of these topics. This section will review the results of a static lateral load test performed on a 3x3 pile group, and contrast the static lateral group stiffness with the group seismic response, as was considered for the single piles. Figure 8.28 depicts the load cell and 21 strain gage time histories for the static lateral load test; these gages were fixed to three piles in the line of loading in front, center, and rear positions of the group. The test was carried to very
382
large deformations (Figure 6.26), and 5 gages overloaded, obscuring the peak bending moments for all three piles. The pile group load-deflection diagram is shown in Figure 8.29, with the pile group load normalized by the number of piles. This yields the average load per pile-deflection diagram, which provides a point of comparison to the single pile load-deflection and secant stiffness diagrams. The pile group average per pile secant stiffness is estimated at a deflection of 0.25 in to be 250 lb/in, producing a static group efficiency factor of 0.8 and a lateral group stiffness of 2250 lb/in. This high efficiency is deceptive, as the high initial stiffness is followed by yielding behavior, which is consistent with the global rocking/overturning mode of the group. For design purposes, it would be necessary to recognize this softer group response with a lower efficiency factor and a lower group stiffness value. As a point of comparison, the dynamic group efficiency factor for a 3x3 group consisting of fixed-head piles in soft soil is given by Kaynia and Kausel (1982), as a function of frequency. Referring to Figure 3.28, and interpolating between the curves for pile spacing of 2d and 5d, the static group efficiency (dimensionless frequency ao = 0) is read equal to 0.35. Attempts to simulate the static lateral group test with the computer codes GROUP and FLPIER were not successful. GROUP is a well-established analytical tool used in practice that should be readily able to analyze this test. However the program aborted the analysis when internally-specified failure critreria were exceeded for pile plunging and pullout failure. With full pile head fixity to the cap, GROUP predicted that the model pile group would undergo a rigid body rotation, with front row piles failing in bearing and rear row piles failing in tension. This deformation mode is in agreement with the observed 6 degree rotation of the cap during the test and pile bending moment diagrams.
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2000 Strain Gages 1500
Load Cell
Microstrain / Load (lbs)
1000
500
0
-500
-1000
-1500 overloaded -2000 0
100
200
300
400
500
600
700
800
900
1000
Time Step
Figure 8.28 - Test 2.31 Pile Group Static Lateral Load Test Load vs. Strain Gage Response
250 K = 340 lb/in
Kgroup = 250 lb/in
Average Load Per Pile (lbs)
200
150
100
50
Pile Group Single Pile
0 0
δ = 0.25 in
1
2
3
4
Pile Head / Pile Group Deflection (in)
Figure 8.29 - Test 2.31 Pile Group Average Head Load vs. Test 2.20g Single Pile Load-Deflection Curves and Secant Stiffnesses
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5
Efforts to override or “trick” the program to proceed to full solution were unsuccessful. Modeling the pile to cap fixity as pinned connections actually permitted the program to converge to a solution, as the front and rear pile movements did not exceed failure limits. But the pile group load-deflection was underpredicted by a factor of 2, and the pinned head condition cannot be considered a realistic assumption. The computer code FLPIER was also utilized, and it makes the interesting assumption that the pile cap does not contribute to the lateral resistance of a pile group under lateral loading. That is perhaps one reason why the pile group deflections were grossly overpredicted by FLPIER.
8.8 2-D Shaking Effects Earthquake engineering analyses of three-dimensional problems are often reduced to one-dimensional analysis for modeling simplicity and computational efficiency. While earthquake ground motions have 3 components, it is common practice to conduct site response analyses with either the strong component of motion or to resolve the two horizontal components to a strong axis motion. In addition, topographic, soil layer, or bedrock orientation deviations from horizontal may make it necessary to model the -z plane in two dimensions.
For structural response, combination rules for multiple
components of ground motion have been proposed (Menun and Der Kiureghian, 1998), and are codified in the UBC, ATC-32, Caltrans BDS, etc. These combination rules reflect the fact that we cannot know a priori the relative orientation of a structure to an earthquake (though not an issue for 1-D site response).
SSPSI problems have also
typically been modeled with one-dimensional analyses, though some 3-D and axisymmetric finite element solutions were introduced in Chapter 3.
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Beam-on-elastic or –Winkler
foundation models have only been formulated to consider the resistance to 1-D static, cylic, or dynamic loadings. A special consideration for SSPSI is that 2-D shaking engages the full perimeter of soil resistance around a pile. The resistance to loading in a direction that hasn’t been previously loaded would be expected to be higher than in a direction that has been previously loaded and yielded, softened, or gapped.
A 2-D loading history would
therefore activate different zones of the perimeter soil resistance, and theoretically offer higher resistance than the 1-D assumption. Conversely, yield in one direction may have the effect of softening the response in an orthogonal direction for subsequent load cycles. For larger diameter piles, other components of resistance may be activated, including side shear resistance and suction behind the pile. Test series 2.4 and 2.5 were performed with two components of the KPI79 input motion to investigate the effects of 2-D shaking on single piles and pile groups. The KPI79 record N00 and N90 components are fairly typical in that the N90 weak axis MHA is roughly 40 % of the N00 strong axis MHA. The components are well-correlated, and the weak axis record has some long period motions late in the record. The longitudinal and lateral free-field acceleration components recorded during strong shaking test 2.46 are plotted in Figure 8.30, indicating the orientation of the surface free-field response. Figure 8.31 depicts a soil-pile gap opened around single pile S2 in Test 2.46. The shaking axes are also shown on the figure; the pile clearly responded in the direction corresponding to the vector sum of the two components of motion. It can be judged that the pile preferentially followed the gap, and did not exhibit as strong off-axis motion as in the free-field (Figure 8.30). Figure 8.32 plots the longitudinal versus lateral acceleration
386
response of pile S2; the predominant direction of motion can be seen to coincide with the gap depicted in Figure 8.31. To consider the difference between a 1-D idealization and the actual 2-D response, the recorded longitudinal component was compared with the record rotated 22 degrees. The acceleration time histories of the original and the rotated record are also shown in Figure 8.32, along with the corresponding response spectra. The rotated record exceeds the original component by only a very small degree. Longitudinal Acceleration (g)
1.5
0
-1.5 -1.5
0
1.5
Lateral Acceleration (g)
Figure 8.30 - Longitudinal and Lateral Components of Free-Field Surface Ground Motion During 2-D Shaking Test 2.46
Figure 8.31 - Gap Developed Around Single Pile S2 During 2-D Shaking Test 2.46
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RECORDED 2.5
Acceleration (g)
Longitudinal Acceleration (g)
2.5
0
-2.5
0
-2.5 -2.5
0
2.5
0
2
4
6
8
10
Time (sec) ROTATED 22 DEGREES 9 Damping = 5%
Acceleration (g)
Longitudinal Acceleration (g)
2.5
0
-2.5
6
3
0 -2.5
0
2.5
0.01
0.1
Lateral Acceleration (g)
1
10
Period (sec)
Figure 8.32 - Test 2.46 S2 Two Dimensional Shaking Response RECORDED 0.8
Acceleration (g)
Longitudinal Acceleration (g)
1
0
-1
0
-0.8 -1
0
1
0
2
4
6
8
10
Time (sec) ROTATED 0 DEGREES 3 Damping = 5%
Acceleration (g)
Longitudinal Acceleration (g)
1
0
-1
2
1
0 -1
0
1
0.01
Lateral Acceleration (g)
0.1
1
Period (sec)
Figure 8.33 - Test 2.46 S1Two Dimensional Shaking Response
388
10
Figure 8.33 depicts the same analysis for the superstructure mass mounted atop the 5x3 group S1 during test 2.46. In this case, the long period superstructure followed the primary axis of shaking, as the strong inertial motion of the 1200 lb head mass was not influenced by smaller off-axis accelerations. In test series 2.5, the more lightly loaded superstructures were observed to respond to the off axis motion late in the KPI79 record. The preliminary conclusion that can be drawn from these tests is that superstructure inertial forces may have the effect of resolving 2-D excitation to strongly directional components. In the case of pile S2, initial gapping created a preferential path for the pile to follow in subsequent cycles. In the case of pile group S1, the superstructure inertial motion damped out the off-axis excitation. In both cases the soil-pile resistance was engaged principally on a single axis, and the full perimeter effect was not observed. This supports the notion of using 1-D SSPSI analyses, preferably with a mulicomponent combination rule to scale input motions.
8.9
Experimental P-Y Curves Section 3.1.2 introduced the beam-on-Winkler-foundation model, with the inclusion
of p-y springs to map the nonlinear lateral soil-pile interaction. The field tests from which these p-y curves originated were described in Section 4.2.1. This section will derive p-y curves from the static and seismic experimental data and compare them to the standard curves used in practice, those recommended by the American Petroleum Institute. Favorable comparison between the experimental and recommended curves gives confidence in the model soil performance and the applicability of the p-y model to the static and seismic analyses.
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P-y curves can be calculated from a known bending moment distribution along the pile M(z) according to basic equations of beam theory: 2
p = d 2 M ( z)
(8.4)
2 d y =M 2 pile EI dz
(8.5)
dz
and
The pile deflected shape ypile is obtained by double integrating the pile bending moment diagram and the soil-pile force p is obtained by double differentiating the bending moment diagram. These operations require some combination of boundary conditions that may include the deflection, moment, or rotation at the pile head or the pile tip. And for seismic events, the pile deflected shape ypile must be subtracted from the soil deflected shape ysoil to correctly describe the relative soil-pile displacement. Ting (1987), Gohl (1991), and Wilson (1998) have all described the derivation of dynamic p-y curves from experimental data. A primary challenge is fitting continuous curves to the discrete data points (strain gage readings), and these and other researchers have typically used cubic spline or polynomial fitting functions. The double integration procedure is straightforward, but double differentiation is fraught with potential error. Ting (1987) introduced a method of “Lagrange multipliers”, which Gohl (1991) adapted. The analysis presented herein follows the method of “weighted residuals” originated by Wilson (1998). This differentiation scheme involves minimizing weighted residuals, as is often used in finite element approximations. For complete details, refer to Wilson (1998). For the static lateral load tests, the boundary conditions of integration included the pile head displacement measured by a linear potentiometer and the assumption that the pile
390
tip displacement was equal to zero. A fifth order polynomial was fit through the strain gage data points to describe the pile bending moment diagram. For the seismic tests, the soil deflection profile was obtained by high pass filtering and double integrating the accelerometers and fitting a third order polynomial through the computed soil deflections. For the pile analysis, the boundary conditions of integration included pile tip (relative) displacement assumed equal to zero, and the slope of the pile at the tip was constrained to follow to slope of the soil deflected shape. This latter boundary condition was found to yield superior results to other implementations. Again, a fifth order polynomial was fit through the strain gage data points to describe the pile bending moment diagram. The weighted residual method was slightly modified to fit separate polynomials to the p values computed in the upper and lower segments of the pile. Finally, the p and y time histories were bandpass filtered to remove low and high frequency noise. The p-y curve calculation was performed in Matlab, and included data visualization of the soil, pile, and superstructure acceleration, displacement, and force profile time histories. This animation of the p-y analysis proved an invaluable tool for debugging the complex programming and gaining insight into the p-y behavior. With p and y time histories computed along the entire length of the pile, p-y curves could then be computed at any depth.
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8 depth = 2d
depth = 3d
depth = 4d
depth = 5d
depth = 6d
depth = 7d
depth = 8d
depth = 9d
0
-8 8
Soil Resistance P (lb/in)
0
-8 8
0
-8 8
0
API Test Data -8 -1.2
0
1.2
Deflection Y (in)
-1.2
0
Deflection Y (in)
Figure 8.34 - Test 1.11 Pile 6 Experimental vs. API Static P-Y Curves
392
1.2
8 depth = 2d
depth = 3d
depth = 4d
depth = 5d
depth = 6d
depth = 7d
depth = 8d
depth = 9d
0
-8 8
Soil Resistance P (lb/in)
0
-8 8
0
-8 8
0
API Test Data -8 -1.2
0
1.2
Deflection Y (in)
-1.2
0
Deflection Y (in)
Figure 8.35 - Test 2.20g Pile 6 Experimental vs. API Static P-Y Curves
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1.2
8.9.1 Static P-Y Curves Figure 8.34 compares the experimentally-derived p-y curves for test 1.11 to the API recommended static p-y curves. P-y curves calculated at depths ranging from 2 to 9 pile diameters for the entire loading history are presented.
The API curves were
computed from the Phase I best estimate undrained shear strength profile, and assigned values of εc = 0.02 and J = 0.5 to the model soil (see Section 3.1.2). Figure 8.35 presents the data from test 2.20g. In both cases, the agreement is quite good. The initial stiffness and ultimate strength are well-captured, and the shape of the backbone curve provides a good fit to the data. At depths < 2d, the p-y curve is unstable, as the polynomial is not constrained at the end point. At depths > 9d, the relative soil-pile deflection approaches zero and the p-y curve becomes infinitely stiff. At greater depths where near zero bending moment was recorded, the soil-pile force approaches zero and the p-y curve reduces to a point at the origin. These static test results are consistent with theory and code, and provide some validation for the model soil and scale modeling design.
8.9.2 Dynamic P-Y Curves After the p-y curve methodology was successfully implemented for the static tests, it was applied to the seismic test data. It is useful to extract a segment of the p-y time histories to focus on the loading range of interest. Figure 8.36 depicts the time window of the p-y analysis in terms of the p time history. Figure 8.37 presents the p-y curves at depths of 2 – 9 pile diameters for pile 1 (head mass = 160 lbs) during test 1.15. Piles with lighter head masses and therefore lower inertial interaction did not as effectively mobilize
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P (psi)
12
0
-12 0
2
4
6
8
10
Time (sec)
Figure 8.36 - Test 1.15 Pile 1 P-Y Analysis Window 8 depth = 2d
depth = 3d
depth = 4d
depth = 5d
depth = 6d
depth = 7d
depth = 8d
depth = 9d
0
-8 8
Soil Resistance P (lb/in)
0
-8 8
0
-8 8
0
API Test Data -8 -0.3
0
0.3
Deflection Y (in)
-0.3
0
0.3
Deflection Y (in)
Figure 8.37 - Test 1.15 Pile 1 Experimental vs. API Cyclic P-Y Curves
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P (psi)
8
0
-8 0
2
4
6
8
10
Time (sec)
Figure 8.38 - Test 1.18 Pile 1 P-Y Analysis Window 8 depth = 2d
depth = 3d
depth = 4d
depth = 5d
depth = 6d
depth = 7d
depth = 8d
depth = 9d
0
-8 8
Soil Resistance P (lb/in)
0
-8 8
0
-8 8
0
API Test Data -8 -0.5
0
0.5
Deflection Y (in)
-0.5
0
0.5
Deflection Y (in)
Figure 8.39 - Test 1.18 Pile 1 Experimental vs. API Cyclic P-Y Curves
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p-y resistance. The p-y curve fit to the API cyclic curves is very good, both in terms of initial stiffness and ultimate strength. Hysteretic and degrading behavior is well illustrated, particularly at depths of 3 – 6d. Figure 8.38 shows the analysis window for the same pile subjected to stronger shaking in test 1.18, and Figure 8.39 depicts p-y curves at depths 2 - 9d. The very low stiffness observed at 3d and 4d indicates the pile is traversing the gap previously opened during test 1.15. One shortcoming of the analysis is that it does not properly capture p=0 while the pile is traversing a gap. This is because the polynomial is shifting from a maximum to a minimum while traversing the gap, and passes through zero, rather than equaling zero for the entire excursion. This effect is exacerbated near the surface where the polynomial is unconstrained, and can be seen in this test at a depth of 2d where very high values of p are calculated.
8.10 System Identification System identification can be defined as the process of deducing a model of a real system from its known inputs and outputs. This technique is being more frequently used in earthquake engineering to identify the vibration properties of both structures and soil deposits. Some examples are provided in the work of Beck (1978), Safak (1991), Glaser (1993), Fenves and Desroches (1994), and Stewart (1996).
Both parametric and
nonparametric methods have been introduced. The parametric approach represents the system response in the discrete time domain and estimates the parameters of the model by least-squares procedure to minimize the error between the model and recorded output.
397
Safak (1991) shows that the model discrete time transfer function can be represented by a rational polynomial: H ( z) =
b1 z − + b 2 z − + ... + b 2 J z − 1 + a1 z −1 + a 2 z − 2 + ... + a 2 J z − 2 J 1
2
2J
(8.6)
where J is the filter order of the model, equal to twice the number of modes being considered. This model can be described by a linear difference equation which relates the input x(t) and the output y(t): y(t) + a1y(t-1) +…+ a2Jy(t-2J) = b1x(t-d-1) + b2x(t-d-2) + b2Jx(t-d-2J)
(8.7)
where d is the time delay between input and output. This type of model is referred to as an ARX model, for autoregresive with extra input (Ljung, 1995). The poles of the discrete time transfer function are identified as the roots of the denominator of H(z): 1 + a1z-1 + a2z-2 + … + a2Jz-2J = 0
(8.8)
The poles of the discrete time transfer function are related to the poles in the Z domain by
sj=
1 ln z j ∆t
(8.9)
where ∆t is the sampling interval. Fenves and Desroches (1994) show that the modal frequencies and damping ratios can be computed from the transmissibility function complex conjugate poles: * 2 s j , s j = −ζ j ω j ± iω j 1 − ω j
and
ω j = s j s*j ζ j=−
( )
Re s j
398
ωj
(8.10) (8.11)
(8.12)
The purpose of applying system identification techniques to the experimental data was to evaluate single pile and pile group modal frequencies and damping ratios, and compute pile head and pile group stiffnesses for comparison with estimates derived from static tests, theory, and code recommended values. In addition, a recursive estimate RARX model was employed (see Stewart, 1996 for details) to consider the time variation of stiffness and damping of the model structures, and examine the assumption of linearity. The input for the system identification analyses was the free field surface acceleration record, and the output was the pile head or pile group superstructure acceleration. With this signal pair, the model estimated flexible base frequency and damping parameters. The Matlab System Identification Toolbox was used to perform the analyses, and the analysis progressed as follows and is illustrated in Figure 8.40: 1. The signals were decimated to 50 Hz to remove extraneous high frequency noise. 2. Using a single mode model, the variation of error with time delay was calculated, and a delay value was selected to minimize the error (delay ranged from 0 – 4 time steps). 3. Using the minimum error delay, the variation of error with number of modes was calculated, and a model degree was selected that was large enough to provide a good fit to the data, but would not overconstrain the model (3 – 5 mode models were used). 4. The model was computed with the selected delay and number of modes. 5. The zeroes and poles of the model were plotted to make sure all the poles lay within the unit circle in the complex plane, defining a stable model. Congregation of the zeroes and poles at the perimeter of the circle signifies the model is overconstrained, and cases with zero-pole cancellation were also rejected.
399
6. The autocorrelation of the residuals and the cross correlation of the residuals and input was checked to see if they were within acceptable confidence limits (99 %). 7. The model and recorded output were compared, and the residual plotted. 8. The parametric transfer function was compared with the non-parametric transmissibility function to ensure the fundamental frequency response was captured by the model.
Table 8-1 summarizes the results of the system identification analyses for the single piles in both Phase I and Phase II tests. The test numbers are appended with the pile number, which are listed in order of decreasing head mass for each test. The first mode frequencies will be compared with other estimates in Section 8.11, but can be observed here to follow reasonable trends. Figure 8.40 includes a plot of the RARX analysis describing the time variation of frequency of test 1.15 pile 1. The RARX analyses were found to be very sensitive, and in this case the computed frequency variation in the first two seconds and last five seconds cannot be real. The analysis does indicate an initial frequency of approximately 6 Hz, which can be seen to decrease to below 4 Hz in direct response to strong shaking. Damping calculations with the RARX method proved less stable, and are not presented here. The values of damping computed by the parametric analysis shown in Table 8-1 are generally a function of load level. For a given pile, higher accelerations usually resulted in higher damping ratios. Damping ratios of 5 – 15% were calculated for lower level excitations, and some values in excess of 20 % were computed for very strong shaking (ybi115s3 is deemed an invalid result).
400
3
1 Autocorrelation of Residuals
Zeroes and Poles 0 0
0
20
40
60
80
100
0.4 0 Cross Correlation of Residuals and Input -3
-0.4 -3
0
3
-100
-50
0
50
100
lag
1 Recorded Output Model Simulation
Acceleration (g)
0
-1 0.2
Residual
0
Frequency (Hz)
-0.2 10 Time Variation of Frequency 5
0 0
4
8
12
16
20
Time (sec)
Amplification
10 Transmissibility Function Transfer Function 5
0 0
5
10
15
Frequency (Hz)
Figure 8.40 - Test 1.15 Pile 1 System Identification
401
20
25
Table 8–1 System Identification Single Pile Flexible Base Frequency and Damping test frequency (Hz) damping ybi115s1 3.77 10.34% ybi115s2 6.51 8.65% ybi115s3 9.23 34.21% ybi115s4 9.95 5.30% ybi118s1 3.52 10.14% ybi118s2 5.24 10.93% ybi118s3 8.26 17.83% ybi118s4 8.14 11.79% kpi224s2 2.65 19.09% kpi224s4 3.88 12.27% kpi224s8 5.61 10.90% kpi224s7 7.30 8.03% kpi224s6 6.68 14.43% kpi226s2 1.87 29.92% kpi226s4 2.67 21.09% kpi226s8 4.60 13.03% kpi226s7 6.11 11.13% kpi226s6 6.20 8.00% kpi244s2 5.46 11.54% kpi246s2 3.41 21.91%
The pile group system identification results are summarized in Table 8-2 for the Phase II tests only. The test numbers are appended with the structure number. For a point of comparison, the fixed base frequencies are computed for each structure from the superstructure mass and the column stiffness. The period lengthening effects of the flexible base are considerable, evidenced by the significant differences between the fixed and flexible base frequencies. Using fixed base frequencies for analysis of these pile groups could be expected to introduce major analytical errors. In test series 2.3, the S1 structure was first subjected to static lateral loading before shaking tests, and as observed in Section 7.6.2, this may have served to soften and base-isolate the structure. This is borne out by the system identification analysis, which computes lower frequencies and damping for S1 than S2 in tests 2.35 and 2.37. The lower frequencies and damping ratios calculated in test series 2.4 matches the observed long period motions experienced by that
402
S1 structure. There was some difficulty in achieving stable models for the test series 2.5 data, and the very high damping values computed therein may not be wholly reliable. Table 8–2 System Identification Pile Group Frequency and Damping test / column fixed base flexible base flexible base structure mass (lbs) stiffness (lb/in) frequency (Hz) frequency (Hz) damping kpi235s1 806 4061 7.02 2.27 17.10% kpi235s2 806 4061 7.02 2.49 21.44% kpi237s1 806 4061 7.02 1.98 30.93% kpi237s2 806 4061 7.02 2.20 38.71% kpi244s1 1200 1422 3.41 1.53 9.11% kpi246s1 1200 1422 3.41 1.37 18.19% kpi253s1 600 1768 5.37 1.66 36.28% kpi253s2 600 1768 5.37 1.94 23.86% kpi255s1 600 1768 5.37 1.46 47.17% kpi255s2 600 1768 5.37 1.37 35.19%
8.11
Pile Head Stiffness The analyses presented in this chapter have developed a number of estimates of pile
head lateral stiffness, which will be contrasted with theoretical solutions in this section. In the Foundation Engineering Handbook (Fang, 1991), Gazetas presents the following equation for pile head lateral dynamic stiffness: 0.21
K HH
Ep = d × E s × E s
(8.13)
Sanchez-Salinero (1982) performed a study of static and dynamic stiffnesses of single piles and presented chart solutions for theories proposed by Novak (1974). This model forms the basis of the DYNA4 computer code used in practice for the analysis of piles under dynamic loading.
From the chart solutions, the dynamic lateral stiffness can be
determined: K xx = 0.0017 ×
403
EI p 3 R
(8.14)
Blaney et al. (1976) used the boundary element method to compute pile head lateral stiffnesses, and suggested the following approximate formula for cases of slender piles with Es/Ep < 0.005: 0.75
K HH
EI p E = 2× 3 × s R E p
(8.15)
ATC-32 includes chart solutions for free and fixed head pile stiffnesses assuming an increasing soil modulus with depth. The free head lateral stiffness is computed as: K δ = 0.41 ×
EI p EI p f
(
)
(8.16)
0.6
where f is the coefficient of variation in subgrade modulus with depth. With the known model soil and pile properties, these four methods compute the pile lateral dynamic stiffness as: Table 8-3 Estimates of Pile Lateral Dynamic Stiffness Reference
Lateral Stiffness (lb/in)
Gazetas (1991) Novak (1974) Blaney et al. (1976) ATC-32 (1996)
10,179 1434 1260 146
The tremendous variation in these estimates reflects the fact that these researchers may be modeling different phenomena. Gazetas starts from the problem of machine vibrations and assumes linear elastic soil response, but cautions that for soil-pile nonlinearities developed during lateral pile loading, a strain-compatible soil modulus should be input to the analysis. Novak and Blaney’s theories also assume visco-elasticity, but their Winkler and boundary element methods yield somewhat more reasonable (and
404
similar) results. The ATC-32 stiffness value is very sensitive to the specification of f, which may be reduced at prototype scale calculations. The low value computed by this method reflects the fact that it a conservative (built-in factor of safety) secant stiffness approximation of nonlinear response. If computed at the prototype scale, these values are somewhat attenuated but maintain the same trends. Table 8-4 computes pile head stiffness values from pile head masses and frequencies of vibration identified from sinesweep and earthquake FFTs and system identification of the earthquake records. In addition, a secant stiffness value from the static lateral load test is listed. For the lightly loaded piles 3 and 4 which were dominated by kinematic interaction, the frequency identified from the sine sweep or earthquake FFT reflects the predominant frequency of the input motion, rather than the structural response. In these and other cases, system identification provides a more accurate estimate of response frequencies as the parametric transfer function was iterated to provide a good fit to the nonparametric transmissibility function. The first point to be made is that the soil-pile system predominant frequencies declined over the course of testing, as the system progressively softened. In the case of pile 3 that was dominated by kinematic interaction, the system identification analyses were able to extract the system response from the free-field dominated record. The values obtained for pile 4 are fictitious, as the soil-pile resistance was not mobilized. The other pile head stiffness computations ranged from approximately 200 – 730 lb/in, with the lower values obtained for cases of strong soil-pile nonlinearity (large head mass, strong shaking), and the higher values for near-elastic response (lighter head mass, sinesweep). These two bounding cases are illustrated by the response of pile 1 during test 1.18, and
405
pile 2 in test 1.14, respectively. The static lateral load test secant value provided an intermediate estimate to the observed stiffnesses, and the ATC-32 recommendation provided a conservative lower bound value for these moderate shaking events. Table 8-4 Test Series 1.1 Single Pile Head Stiffness Estimates Test
Pile 1
Pile 1
Pile 2
Pile 2
Pile 3
Pile 3
Pile 4
Pile 4
f (Hz) K (lb/in) f (Hz) K (lb/in) f (Hz) K (lb/in) f (Hz) K (lb/in) Static lateral load test 111
310.0
Sinesweep 114
4.40
316.5
8.47
733.0
2.23
12.7
2.23
YBI 115 MHA = 0.26 g
3.80
236.1
6.25
399.1
2.05
10.7
2.05
3.3 2.8
YBI 115 System Identification
3.77
232.3
6.51
433.0
9.23
217.6
9.95
65.7
Sinesweep 116
3.64
216.6
8.00
653.9
2.01
10.3
2.01
2.7
YBI 118 MHA = 0.42 g
3.80
236.1
4.45
202.3
2.00
10.2
2.00
2.7
YBI 118 System Identification
3.52
202.5
5.24
280.5
8.25
173.8
8.14
44.0
Table 8-5 presents pile head stiffnesses for test series 2.2 computed from sinesweep and earthquake FFTs, and system identification analyses. In addition, stiffness values computed from the impact/free vibration test and the static lateral load test are included. Test series 2.2 was marked by very strong shaking events resulting in significant soil-pile nonlinearity and therefore well-degraded stiffness values. The initial impact/free vibration test recorded high frequency soil-pile response, resulting in upper bound stiffness calculations, but still not approaching those values recommended by Novak or Blaney. The frequency response of the initial sinesweep test calculated stiffnesses from approximately 210 – 440 lb/in. Again, the lightly loaded pile S6 was dominated by kinematic interaction and did not mobilize discernable soil-pile resistance. The KPI 2.24 test resulted in stiffness values of approximately 80 – 280 lb/in, and are a direct function of inertial head mass. The KPI 2.26 test drove the piles to even softer response, with stiffness values below 60 lb/in obtained. The static load test secant stiffness provided a potentially unconservative estimate of pile head stiffness for these very strong shaking
406
events, while the ATC-32 recommended value provided a marginally acceptable lower bound estimate. Table 8-5 Test Series 2.2 Single Pile Head Stiffness Estimates Test
Pile 2
Pile 2
Pile 4
Pile 4
Pile 8
Pile 8
Pile 7
Pile 7
Pile 6
Pile 6
f (Hz) K (lb/in) f (Hz) K (lb/in) f (Hz) K (lb/in) f (Hz) K (lb/in) f (Hz) K (lb/in) Impact 220e blows 1, 2
31.67
666.1
Impact 220e blow 3
24.67
404.2
Test 220e free vibration
34.20
776.8
Static lateral load test
340.0
Sinesweep 223
3.59
210.7
4.31
227.8
6.26
KPI 224 MHA = 0.5 g KPI 224 System ID
320.3 10.35
437.8 10.35
71.1
2.19
78.4
3.44
145.1
3.44
96.7
2.65
114.8
3.88
184.6
5.61
257.2
8.25
278.2
8.25
45.2
7.28
216.6
6.68
Sinesweep 225
2.26
83.5
3.77
174.3
5.80
275.0 10.19
29.6
424.4 10.19
KPI 226 MHA = 1.6 g
1.44
33.9
2.25
62.1
3.38
93.4
69.0
7.13
207.8
8.19
44.5
KPI 226 System ID
1.87
57.2
2.67
87.4
4.60
Sinesweep 227
1.51
37.3
3.38
140.1
3.82
173.0
6.11
152.6
6.20
25.5
119.3
9.26
350.4 10.02
66.7
Table 8.6 lists pile head stiffness values obtained from test series 2.4, which consisted of a single pile and a 3x3 group subjected to 2-D shaking. Again, initial stiffness determined in the sinesweep test was quickly degraded by soil-pile nonlinearity developed during strong shaking. The system identification frequencies of tests 2.44 and 2.46 are considered the upper and lower bound stiffnesses of the system, ranging from 95 - 245 lb/in. Table 8-6 Test Series 2.4 Single Pile Head Stiffness Estimates Test
Pile 1
Pile 1
f (Hz)
K (lb/in)
Sinesweep 243
3.81
118.6
KPI 244 MHA = 0.69 g
3.42
95.6
KPI 244 System Identification
5.46
243.7
Sinesweep 245
3.60
105.9
KPI 246 MHA = 1.1 g
3.33
90.6
KPI 246 System Identification
3.41
95.0
Sinesweep 247
3.47
98.4
8.12 Conclusions
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The analyses of the shaking table test data have attempted to address an assortment of topics relating to the SSPSI problem, and the following conclusions can be drawn: •
The development of site-specific shear strength and shear wave velocity profiles required considerable judgement and interpretation of a variety of source data. Multiple measures of shear strength, for example, proved invaluable in deciphering the site conditions.
Understanding the site loading history
contributed to an accurate assessment of the shear wave velocity profile. •
The calculation of material-specific modulus degradation and damping curves provided precise inputs to and enabled successful site response analyses.
•
The simulations of the model free-field response with SHAKE91 were fairly accurate, and the model soil-container system can be judged to have adequately reproduced free-field site response. The small errors between the observed and predicted behavior may be acceptable for pure site response analyses, but the propagation of these errors into the SSPSI analysis requires further study. Elimination of shaking table twist motions may improve the high frequency response, and nonlinear analyses may offer the possibility of better estimates of response at the site period.
•
The suite of pile head loading tests provided estimates of pile head lateral and axial stiffness. COM624P achieved very good predictions of the static lateral pile load tests. Increased deflections under axial load cycling were observed to agree with published data.
T-z analysis demonstrated that the piles were
transferring load almost exclusively through end-bearing.
408
•
Pile group effects were not thoroughly analyzed, though a group efficiency factor of 0.8 was calculated from the static lateral group test. The end-bearing group was observed to engage in a near rigid body rotation, which may constitute a potential seismic response mode for relatively stiff piles in soft soil.
•
The influences of 2-D shaking were seen to be minimal, as structural inertial forces tended to resolve the motion to a strong axis for the simple single degree of freedom models tested. For single piles, full perimeter soil resistance was not engaged, as the piles preferentially followed gaps developed in previous cycles.
•
The derivation of p-y curves from the static and seismic test data was quite successful, and the experimental curves compared very well to those recommended by API. P-y curve initial stiffness and ultimate strength trends with depth were in agreement with API static and cyclic curves. Degrading behavior due to hysteresis and gapping was observed, softening the near-surface response below API stiffness values, indicating gapping is an important analytical feature to model.
•
The application of system identification techniques yielded good estimates of single pile and pile group flexible base frequencies and damping factors. The pile group flexible base frequencies differed significantly from the fixed base case, and damping ratios from 10 –20 % were observed. Damping for the single piles and groups was computed to be a function of load level, and single pile values ranged from 10 – 20 %.
•
Estimates of pile head stiffness and experimentally-derived values differed over a wide range, from 100 – 700 lb/in, and were a function of soil-pile nonlinearity.
409
The methods examined for computing dynamic stiffness from elastic theory provided unrealistically high estimates of stiffness for the model tests. Appropriately selected secant stiffness values provided more realistic descriptions of the observed soil-pile response to moderate intensity shaking. ATC-32 chart solutions provided marginally acceptable lower bound estimates of stiffness for very strong shaking events.
The following chapter will summarize the principal finding of these studies, consider the results in the context of codes and practice, and provide recommendations for future study.
410
CHAPTER 9
SUMMARY AND CONCLUSIONS
9.1 Scope of Research A significant number of cases of damage to piles and pile-supported structures during earthquakes have been observed, but few instrumented records of the response and performance of such structures during earthquakes have been obtained. Much of the observed damage to piles during earthquakes has been due to the effects of liquefaction and lateral spreading, though some important cases of seismically-induced pile failures in clay have been observed in the Mexico City and Loma Prieta earthqukes. A thorough review of field and laboratory experimental programs designed to investigate SSPSI has revealed that most efforts have focused on liquefaction problems, leaving a gap in our understanding of SSPSI in cohesive soils. The state-of-the-practice and current building code recommendations reflect the lack of consensus on how to evaluate SSPSI effects. Currently available analytical methods for SSPSI problems range from simple static analyses to derive pile head secant stiffnesses for input to dynamic structural models, to complete dynamic pile group interaction analyses. Many analytical tools consider visco-elastic response, and others model soil-pile nonlinearity with p-y curves, but nearly all have the common feature of uncoupling the site response, soil-pile interaction, and superstructure response components of SSPSI. To expand the database of pile performance during strong shaking, a series of scale model shaking table tests of model piles in soft clay was performed. This research effort had the goals of providing insight into a variety of SSPSI topics, and generating a data set
411
with which to calibrate an advanced SSPSI analysis tool being developed at U.C. Berkeley (Lok, 1999), as well as data suitable for evaluation of other analytical tools and methods.
9.2 Research Findings and Recommendations Principles of scale model similitude were used to derive a set of model scaling relationships that were used in a method of “implied prototypes” to relate model and prototype behavior. Consideration was given to the dynamic and nonlinear nature of soilpile interaction in developing the model soil and model piles for the testing program. A specialized flexible wall test container was designed to allow the soil to respond in the same fashion as the free-field, unencumbered by boundary effects. The performance of the shaking table was generally seen to be good, with reasonable reproduction of 1-D and 2-D input motions. Unwanted twist, pitch, and roll motions were present, however, and exerted unquantifiable influence on the model response. These spurious motions were, however, principally of high frequency content, and did not appear to significantly affect soil-pile-superstructure performance. The trends of model site response were consistent with free-field behavior; the motions amplified from base to surface and were coherent across the site. Vertical accelerations observed at the soil surface may have been due to a combination of surface wave reflections, table pitch and roll motions, and a soil column bending mode. Qualitative analysis of the single pile and pile group response yielded a number of interesting results. The single piles were seen to respond with components of inertial and kinematic interaction, though the inertial components produced upper bound bending moments. This result may suggest that developing pile demands from consideration of
412
inertial loading only may be acceptable for cases where site stiffness contrasts or ground failure (lateral spreading) do not exert significant soil loads or deformations on the piles. The response of pile groups was highly frequency dependent, which calls into question the applicability of applying pseudo-static analyses to such problems. Pile cap and free field motion variations illustrated wave scattering effects and the necessity of developing modified foundation input motions for substructuring analyses. Moderate effects of pile cap embedment were observed, particularly in contributing to pile group rocking stiffness, though further study is warranted in this area. A group that had been first subjected to large deformation static lateral loading was seen to have lesser seismic response than an identical group that had not been pre-loaded, suggesting that pre-loading remolded the near-field soils and base-isolated the group. A 5x3 pile group and single pile with the same average load per pile were subjected to 2-D shaking, and the single pile was seen to have greater bending moment demands than the group piles. This was attributable to the long period motion and resulting lack of resonance of the pile group superstructure, which did not impart large inertial loads to the foundation. Finally, tests evaluating pile raft performance and the effects of impounded water scouring the soil-pile gap and degrading resistance were somewhat inconclusive, but can be revisited with improved test designs. Site characterization included laboratory and in-situ testing to establish the undrained shear strength and shear wave velocity profiles. T-bars tests were adapted from centrifuge testing, and produced continuous profiles of strength versus depth.
The
strength determined in the T-bar tests was found to include a shearing velocity rate effect, which was quantified in relation to vane shear testing.
Hammer blow tests were
performed from the base and surface of the model container to determine the site shear
413
wave velocity profile. The latter method was found to yield good results except near the surface, where surface wave interference obscured the shear waves, and at depth, where the wave energy attenuated and reflected.
Piles in very close proximity to the
accelerometer arrays were found to artificially increase the apparent wave velocity by proving alternate travel paths for the wave energy. Model-soil-specific dynamic modulus degradation and damping curves as a function of strain level were derived from testing with an advanced cyclic triaxial testing apparatus with internal strain and shear wave velocity measurements. SHAKE91 was successfully used to simulate the model free-field response, indicating that the model soil-container system adequately reproduced free-field site conditions.
The small errors between the observed and predicted behavior may be
acceptable for pure site response analyses, but the propagation of these errors into the SSPSI analysis requires further study. The suite of pile head loading tests provided estimates of pile head lateral and axial stiffness. COM624P achieved very good predictions of the static lateral pile load tests. Increased deflections under axial load cycling were observed to agree with data published by Bea et al. (1980). T-z analysis demonstrated that the model piles were transferring load almost exclusively through end-bearing, as was intended. Pile group effects were not thoroughly analyzed, though a group efficiency factor of 0.8 was calculated from the static lateral group test. This value may be unconservative considering the group yield behavior at higher load levels. The end-bearing group was observed to engage in a near rigid body rotation, which may constitute the seismic
414
response mode in soft soils. Although group effects were not analyzed in great detail, the data developed here should provide a good basis for such analyses in subsequent studies. The influences of 2-D shaking were seen to be minimal, as structural inertial forces tended to resolve the motion to a strong axis for the simple single degree of freedom models tested. For single piles, perimeter soil resistance was not engaged, as the piles preferentially followed gaps developed in previous cycles. These findings support the notion of using 1-D SSPSI analyses for simple and regular structures, preferably with a multi-component combination rule to scale input motions. The derivation of p-y curves from the static and seismic test data was quite successful, and the experimental curves compared very well to those recommended by API. P-y curve initial stiffness and ultimate strength trends with depth were in good agreement with API static and cyclic curves. Degrading behavior due to hysteresis and gapping was observed, softening the near-surface response below API stiffness values, indicating that gapping is an important feature to analytically model. These findings also serve as a back-analysis validation of using p-y curves for SSPSI problems. The application of system identification techniques yielded estimates of single pile and pile group flexible base frequencies and damping factors. Single pile and pile group frequencies were consistent with sine sweep and seismic response. The pile group flexible base frequencies differed significantly from the fixed base case, and damping ratios from 10 – 20 % were observed. Damping for the single piles and groups was computed to be a function of load level, and single pile values ranged from 10 – 20 %. Estimates of pile head lateral stiffness and experimentally-derived values differed over a wide range, from 100 – 700 lb/in, and were a function of loading level and
415
consequent soil-pile nonlinearity. The methods examined for computing dynamic stiffness from elastic theory provided unrealistically high estimates of stiffness for the model tests. Appropriately selected secant stiffness values from the static lateral load tests provided more realistic descriptions of the observed soil-pile dynamic response for moderate levels of shaking. ATC-32 chart solutions provided marginally acceptable lower bound pile head stiffness estimates for very strong shaking events.
9.3 Recommendations for Future Research The recommendations for future research are threefold as they relate to: (1) further analysis of the existing data set, (2) modified test procedures for shaking table testing with the flexible container, and (3) other possible future research .
9.3.1 Data Mining The data set generated in this research effort provides a rich information base for extensive study of SSPSI. Much work remains to be performed in the analysis of group interaction in both the static and seismic tests. The rocking response of the pile raft foundation and cap contributions to dynamic group response may also be investigated. The procedures developed for the derivation of experimental p-y curves can be applied to the many single pile and group pile cases. The implications of response prediction with the range of pile head stiffness values observed can be studied. Nonlinear site response analyses may provide improved estimates of the model soil site amplification. Most importantly, the single pile and pile group seismic response can be simulated with the wide range of existing and developing analytical tools.
416
9.3.2 Improved Test Procedures First and foremost, the shaking table performance should be further improved, particularly by eliminating twist, pitch, and roll motions, which exert unknown effects on the model performance. If possible, tests with other scaling factors should be conducted in a “modeling of models” approach to further validate the scaling relationships. A stiff cohesive soil base layer impeding drainage and arresting consolidation is recommended, to ensure more stable model conditions. Model pile strain gaging quality control can be slightly improved, though the model soil fly ash provides a harsh (chemical) environment and some gage failures are inevitable. The positioning of soil accelerometers should be such that in a given test, one array is distant from the model structures; one or two dense vertical arrays is recommended. Multiple surface vertical accelerometers are useful for tracking the soil column deformation modes. Surface hammer blow shear wave velocity tests are promising for determining Vs profiles, and may be improved by using an accelerometer trigger on the hammer and stacking records as practiced in geophysics. Pile group effects may be better detected by constructing a pile cap or load frame with load measurement devices at each pile head, or in each pile row. Forced vibration tests should be implemented for both single piles and pile groups with equipment capable of delivering higher loadings and higher frequencies. From the testing standpoint, the model response to a suite of ground motions with different frequency characteristics would provide a broader understanding of SSPSI. A given model may be excited with several different ground motions at low amplitude, but only one large amplitude shake can be performed before site degradation occurs. An
417
alternative procedure could consist of exciting the model with progressively increasing intensisties of the same motion, rather than just low and high amplitude shakes. It may also be possible to shake on one axis, then the other, so that soil-pile nonlinearities would be minimized from one test to the next. Other strategies may include changing model frequency response by changing pile head masses from test to test. The shaking table capabilities for 2-D and 3-D shaking should be utilized, as this type of data provides unique and realistic performance assessments. In addition, it may be useful to vary the orientation of the model structures to the principal axes of shaking.
9.3.3 Future Shaking Table Research Topics The capability that has been developed at U.C. Berkeley to study SSPSI with scale model shaking table testing is a unique and valuable resource, and demands to be applied to further investigations. Some possible topics for future study include the following: •
battered pile supported structures, attracting large head loads,
•
large diameter drilled shafts, possibly constructed of scale model concrete,
•
friction pile axial, t-z, and rocking response,
•
pile raft foundations, including seismically induced settlements,
•
multi-mode structures and/or structures supported by multiple pile groups,
•
ductile columns, designed to yield and thereby reduce foundation demands,
•
layered site profiles, including impedance contrast and surficial fill cases,
•
variable pile group spacing, and
•
influence of pile cap base contact on dynamic lateral and rocking stiffnesses.
418
Continued study of these and other SSPSI topics can contribute to advancing the state-of-knowledge, which then can hopefully be translated into advancing the state-ofpractice.
419
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457
APPENDIX A
Similitude for Model Tests in a 1-g Gravitational Field (Iai, 1989) Geometric Scaling Factor λ
8
Soil Density Scaling Factor λp
1
Model Soil Shear Wave Velocity (Vs)m Prototype Soil Shear Wave Velocity (Vs)p Soil Strain Scaling Factor λε = λ / [(Vs)p/(Vs)m]
100 282.8
2
1 prototype:model
x ρ
length
λ
8
density of saturated soil strain of soil
λp λε
1
ε t ε0
time
σ σ'
total stress of soil
D
(λλε)
1 0.5
2.83
λε
1
λλp
8
λλp λλp/λε
8
tangent modulus of soil
Ks
bulk modulus of the solid grains of soil
λλp/λε
8
p
pressure of pore water and/or external water
k
permeability of soil
u
displacement of soil and/or structure
strain of soil due to creep, temperature, etc. effective stress of soil
λλp 0.5 (λλε) /λp λλε 0.5
8 8 2.83 8
(λλε)
2.83
1
1
u
velocity of soil and/or structure
u
acceleration of soil and/or structure
w
average displacement of pore water relative to the soil skeleton
w
rate of pore water flow
n Kf
porosity of soil bulk modulus of pore water and/or external water
λλp/λε
EI
flexural rigidity (per unit breadth of the beam)
λ λp/λε
EA
longitudinal rigidity (per unit breadth of the beam)
λ λp/λε
64
inclination of the beam
λε
1
M
bending moment of the beam (per unit breadth of the beam)
3
λ λp
S
shear force of the beam (per unit breadth of the beam)
λ λp
F ρf
axial force of the beam (per unit breadth of the beam)
λ λp
64
density of pore water and/or external water
λp
1
ρb
density of the beam ( mass per unit length and breadth of the beam)
λλp
8
T
traction acting on the soil specified on the boundary
8
u
displacement of the soil and/or the beam specified on the boundary
λλp λλε
p
pressure of pore water and/or external water specified on the boundary average displacement of pore water, on the boundary, relative to the soil skeleton
λλp λλε
8
w θ
inclination of the beam specified at the boundary
λε
1
M
bending moment of the beam specified at the boundary (per unit breadth)
3
λ λp
S
shear force of the beam specified at the boundary (per unit breadth)
λ λp
F
axial force of the beam specified at the boundary (per unit breadth)
i
hydraulic gradient of external water specified at the boundary
θ
λλε 0.5
2.83
1
1
4
458
8
(λλε)
2
2 2
2 2
8 4096
512 64
8 8 512 64
λ λp
64
λp
1
APPENDIX B
Model Pile Design Spreadsheet
Geometric Scaling Factor:
8
Prototype Input Parameters Prototype Pile OD: Prototype Pile Wall: Prototype Pile Length: Prototype Soil Shear Strength: Prototype Soil Vs: E Steel: E Concrete: % Concrete EI Contribution:
16 inches 0.50 inches 44 feet 1000 psf 1000 fps 29000 ksi 4000 ksi 50%
Prototype Pile Computed Properties Prototype Pile L/D Ratio: Prototype Pile d/t Ratio: Prototype Epile/Gsoil: Prototype EIpile/Esoil*D^4: Area Steel: Steel Moment of Inetria: Steel Flexural Rigidity EI: Area Concrete: Concrete Moment of Inertia: Concrete EI: Composite Concrete/Steel EI: Total Mass/ft length: Prototype First Mode Period: Model Input Parameters Model Pile OD: Model Pile Wall: Model Pile E: Model Pile Density: Model Soil Vs: Model Pile Computed Properties Model Pile Cross Sectional Area: Model Pile Mass/ft length Model Pile Moment of Inertia: Model Pile EI: Model Pile L/D Ratio: Model Pile d/t Ratio: Model Pile First Mode Period: Model Epile/Gsoil: Model EIpile/Esoil*D^4:
33 32 1392 96 0.1691 0.0353 147405 1.2272 0.1198 34515 181920 266.93 0.7386
2 0.028 10000 40.00 100
0.0012 0.0482 4.0673E-06 5.8568 36.0 71.4 0.0273 3840 101
ft^2 ft^4 k-ft^2 ft^2 ft^4 k-ft^2 k-ft^2 lbs/ft seconds
inches inches ksi pcf fps
ft^2 lbs/ft ft^4 k-ft^2
seconds
459
Target % difference 5.5517 5% 33.0 9% 32.0 123% 0.2611 90% 1392 176% 96 5%
APPENDIX C Analysis of Seismic Response of Cylindrical Tank Container Properties: radius R, height H, wall thickness h, soil unit weight γ, soil mass m, depth z: 3.5. ft
R
H
7. ft
0.064. in γ
h
94.
lb
2 π. R . H. γ
m
3
m = 12.661 ton
z
0. ft , 1. ft .. H
ft Container dynamic respose modeled as flexible wall tank with three response components: hydrodynamic convective, hydrodynamic impulsive, and hydrostatic.
Convective Response: modal frequency fc, modal mass mc, modal height hc λ
from the zeroes of the Bessel function derivative:
fc
mc
hc
1.841
1 . .g. H λ tanh λ. . R R 2π
fc = 0.654 Hz
2. m . R . H tanh λ. 2 . R λ 1 λH
mc = 0.227 m
R.
H
λ
tanh λ.
H 2. R
hc = 0.742 H
Response Maxima: Peak ground acceleration xmax, amplification factor αc, pseudoacceleration Ac: xmax
0.8. g
αc
1
Ac
αc. xmax
Ac = 0.8 g
kip
1000. lbf
Wall pressure pc, base shear Qc, base moment Mc, normal stress σc, shear stress τc, hoop stress θc:
Cc( z )
pc( z )
z cosh λ. R 2 . 2 H λ 1 cosh λ. R Cc( z ) . γ. R . Ac
Qc
mc. Ac
Qc = 4.6 kip
Mc
mc. hc. Ac
Mc = 23.883 kip. ft
Mc
σc τc
Qc π. R. h
θc( z ) pc( z ) psi 0.077 0.088 0.124 0.194 0.32 0.537 0.905 1.53
σc = 808.047 psi
2 π. R . h
pc( z ) .
τc = 544.692 psi R h
θc( z ) psi 50.517 57.668 81.146 127.597 210.173 352.252 594.058 3 1.004. 10
Impulsive Response: modal frequency fi, effective modal mass mi, effective modal height hi, peak ground acceleration xmax, amplification factor αi, pseudoacceleration Ai : fi
1. Hz
mi
0.763. m
hi
αi
0.422. H
2.5
Ai
αi. xmax
Ai = 2 g
Wall pressure pi, base shear Qi, base moment Mi, normal stress σi, shear stress τi, hoop stress θi:
Ci( z )
pi( z )
(H
Ci( z ) . γ. R . Ai
pi( z ) psi
z 0.186. ft
0.133 . z ). e ft
Qi
mi. Ai
Qi = 38.643 kip
Mi
mi. hi. Ai
Mi = 114.15 kip. ft
τi
4.254 4.392 4.408 4.247 3.837 3.081 1.855 0
Mi
σi
3
σi = 3.862 10
2.
π. R h Qi . π R. h
θi( z )
3
τi = 4.576 10 R h
pi( z ) .
θi( z ) psi 3
2.792. 10
3
2.882. 10
3
2.893. 10
3
2.787. 10
3
2.518. 10
3
2.022. 10
3
1.217. 10 0
Hydrostatic Response: wall pressure ph, hoop stress θh: ph( z ) ph( z ) psi 4.569 3.917 3.264 2.611 1.958 1.306 0.653 0
γ. ( H
z ).g θh( z )
ph( z ) .
R
θh( z )
h
psi 3
2.999. 10 3 2.57. 10 3
2.142. 10
3
1.714. 10 3 1.285. 10 856.771 428.385 0
psi
psi
Total Dynamic Response:
Conservatively sum components (ABSSUM): Wall pressure p, base shear Q, base moment M, normal stress σ, shear stress τ, hoop stress θ: p( z ) psi 8.901 8.396 7.796 7.053 6.115 4.923 3.413 1.53
p( z )
pc( z )
pi( z )
ph( z )
θ( z )
θc( z )
θi( z )
θh( z )
Q
Qc
M
Mc
σ
Qi
σc τ
Mi σi
τc
Q = 43.242 kip M = 138.033 kip. ft 3
σ = 4.67 10
psi 3
τi
τ = 5.121 10
8 0 6 z ft 4 z ft 2
0
0
2
4
6
8
0
10
p( z ) ph( z ) , psi psi
8
θ( z ) psi 6
3
5.841. 10 3 5.51. 10 3
5.116. 10
3
4.628. 10 3 4.013. 10 3
z ft 4 z ft 2
3.231. 10 3 2.24. 10 3
1.004. 10
0
0
1000
2000
3000 θ( z ) θh( z ) , psi psi
4000
5000
6000
psi
