Proceedings of the 8th U.S. National Conference on Earthquake Engineering April 18-22, 2006, San Francisco, California, USA Paper No. 320
NONLINEAR STRUCTURE AND FOUNDATION RESPONSE DURING SEISMIC LOADING: DUAL LATERAL LOAD RESISTING SYSTEMS Tara C. Hutchinson, Prishati Raychowdhury and Barbara Chang 1
ABSTRACT In this paper, a model retrofit shear wall is combined with a frame system, and the response of this structure is investigated using nonlinear dynamic time history analyses. A 2D planar model of the structure is designed, considering modern seismic design practice for ductile reinforced concrete moment frames. The effects of foundation rocking, sliding, and settling are considered by incorporating flexibility (elastic and inelastic) at the base of the footings. Varying factors of safety at the base of the footings are used in the modeling, to evaluate the effects of the margin of safety in the foundation on the seismic response. Parameters investigated include: the moment and shear demand at the footings, the inter-story drift ratio, the acceleration amplification, and the energy dissipation at the ductile moment frame joints. Results indicate that if reliably quantified and designed, SFSI has great potential for reducing seismic forces and inter-story drift demands, by providing added energy dissipation to the building-foundation system. In addition, this interaction between the structural system and its supporting soil was observed to generally increase the amount of energy dissipated in designed fuses within the structure (such as strategically placed beam-column joints). Introduction The need to improve our understanding of soil-foundation-structure interaction (SFSI) effects, and especially the need to investigate SFSI on a system level is well known to be an important practical issue in seismic design (e.g. NRC, 2003; EERI, 2002). An integrated approach considering the full structure, surrounding soil, and structure-foundation-soil systems is sorely needed. Such an approach could significantly increase the performance of applied retrofit strategies by specifically designing both the foundation and the structural system to dissipate earthquake-induced demands. From the viewpoint of current practice, the design and strategic placement of ductile structural fuse mechanisms has been an accepted philosophy in earthquake engineering practice for many years. Most commonly energy dissipation is occurring within the structural members (e.g. beam-column joints). However, it is understood, even by practicing geotechnical and structural engineers, that SFSI, if reliably quantified and designed, has great potential for reducing seismic forces and interstory drift demands, by providing added energy dissipation within the building system. Invariably, however, this interaction between the structural system and its supporting soil will modify the 1
Assistant Professor, Graduate Student and Graduate Student, respectively. Department of Civil and Environmental Engineering, University of California, Irvine. Contact author:
[email protected]
amount of load induced into the structural fuses, thereby modifying their ability to dissipate energy. Moreover, the large uncertainty in soil properties, the absence of accepted practical foundation modeling techniques, and insufficient collaboration between structural and geotechnical engineers has hindered the use of nonlinear SFSI as a mechanism for reducing demands on structures in practice. In addition to a reduction of forces and inter-story drift demands, it has long been recognized that the soil-foundation system does provide beneficial energy dissipation properties, particularly through the mode of foundation rocking. This is particularly true for shear wall systems, where little energy dissipation is provided for in the structural element itself. To take advantage of this dissipation of energy, as a mechanism for optimizing structural performance, not only must modeling confidence be strengthened, but optimally designed soil-foundation systems, which limit other undesirable consequences (such as excessive sliding, uplift or settlement), must be investigated. To determine the optimal design for the overall structural systems performance, an integrated analysis approach is needed. Ductile fuse mechanisms could be realized within the soilfoundation or within the superstructure system or both. For moderate to low-rise structures, the incorporation of energy dissipation is of particular importance, since it is well known that variability of spectral response is large within the typical periods of such systems. In particular, these systems tend to have low energy dissipation capacity, due to the highly brittle nature of common components used in their construction (e.g. shear walls). Scope of this Paper In this paper, a model retrofit shear wall is combined with a frame system, and the response of this structure is investigated using nonlinear dynamic time history analyses. A 2D planar model of the structure is designed, considering modern seismic design practice for ductile reinforced concrete moment frames. The effects of foundation rocking, sliding, and settling are considered by incorporating flexibility (elastic and inelastic) at the base of the footings. Varying factors of safety at the base of the footings are used in the modeling, to evaluate the effects of the margin of safety of the foundation on the seismic response. Parameters investigated include: the moment and shear demand at the footings, the inter-story drift ratio, and the energy dissipation at the ductile moment frame joints. Results indicate that if reliably quantified and designed, SFSI has great potential for reducing seismic forces and inter-story drift demands, by providing added energy dissipation to the building-foundation system. Wall-Frame-Foundation System Design and Analysis Wall-Frame-Foundation System Description A prototypical two story, two bay, planar frame connected in series with a rigid, slender shear wall is designed (Figure 1a) and modeled (Figure 1b) using the OpenSEES platform (2005). The 2D planar system is envisioned to perform as the primary lateral resisting system within a conventional 3D building. Loads are estimating by assuming a 3D building, which is supporting surface service loads of 1.3 kPa over tributary bay spans (to the nearest lateral and gravity resisting system) of 4.6 meters. The wall-frame structure is designed by integrating a moderate ductility reinforced concrete frame with a ‘retrofit’ shear wall. A relatively slender shear wall is selected with an aspect ratio (Height:Width) of 3.75. Frame bays are designed with an aspect ratio (Span:Floor Height) of 1.60.
Service as well as seismic loads are estimated based on ASCE 7-02 (2003) and applied, while assuring ductile yielding of forced hinges at the ends of typical beam-column joints. Seismic loading is selected design spectrum for the Bay Area, California. A target soil-structure fundamental period of Tn ~ 0.5 seconds was chosen when designing the system, to represent the period of typical low rise systems, where SFSI is incorporated in the design. For comparison, the fixed base period of the prototype structure is calculated as Tn = 0.2 seconds. The structurefoundation system is designed considering current geotechnical and structural design practice. 2.54
7.62
7.62
Ductile BeamColumn Joint R/C Shear Wall
9.53
Isolated R/C Strip Footing
R/C BeamColumn 4.76 Members Isolated R/C Spread Footings
4.76
Rigid Elastic Beam-Column Elements
Prototype (Dashed)
G.S.
Beams w/ Inelastic Fiber Hinges Spring Array (when occurs)
Nonlinear BeamColumn Elements G.S.
1.00 2.84
1.00
1.00
Dense Dry Sand
(a) (b) Figure 1. Wall-frame-foundation system designed: (a) prototype dimensions (in meters) and (b) idealized FE model. Finite Element Modeling A simplified 2-dimensional finite element (FE) model is constructed of this system, using 1dimensional beam-column elements and arrays of linear and/or nonlinear spring elements (Figure 1b). The skeletal overlain with the prototype model in part (b) shows the idealized FE representation. Element Types and Constitutive Relations – Structural Modeling The frame portion of the model is designed based on ACI 318-02 (2002) prescriptions for ductile moment resisting frames. Beam cross-section dimensions are 40.6 cm height and 30.5 cm width, while square columns of size 50.8 cm are used (Figure 2a). Beam dimensions are selected based on ACI 318-02 minimum sizing and by controlling dead and live load deflections within those suggested in ACI Table 9.5b. Strong column-weak beam design is employed, with the columns having a moment capacity three times that of the beams. Longitudinal reinforcing steel ratios ρl = 1.25% and 1.8% are used for the beams and columns respectively. Table 1 summarizes the material properties used and calculated for the analyses. Concrete in the beams and columns were designed to account for confinement due to transverse hoops using the confinement model proposed by Mander et al. (1988). Shallow footings for the structure were modeled from unconfined concrete and assumed to remain elastic during analysis. The OpenSEES material model of the structural elements used the uniaxial material Concrete01 for both the unconfined and the confined concrete and Steel01 for the steel. Figure 2b presents the unconfined and confined concrete constitutive laws for the concrete, which are based on a Kent-Scott-Park backbone curve. Plasticity is considered at the ends of individual beams (at beam-column joints), using a spread-of-plasticity fiber approach, applied to ‘beamwithHinges’ elements. The fiber section discretizes the cross-section into smaller sub-sections, which are then used to model the stress-strain response of the material. The ‘beamwithHinges’ element places an
elastic portion at the middle of the element and plastic portions at the ends of the element. The plastic hinge length was calculated to be approximately ten percent of the total span of the beam. Columns are modeled with the fiber section and the ‘nonlinearBeamColumn’ element. The ‘nonlinearBeamColumn’ element models plasticity of the element over the entire length of the element. Using stress and strain output at local fibers within each section, moment-curvature response is generated. A comparison of the moment-curvature response for the column and beam elements is provided in Figure 2c. unconfined fibers
unconfined fibers steel fibers (4-#7 bars)
50
500
40
400
30 20 10 0
confined fibers (#3 bars@3" o.c.)
Unconfined Confined (column) Confined (beam)
Moment (kN m)
confined fibers (#4 bars@3" o.c.)
Stress (MPa)
steel fibers (12-#7 bars)
200 100 0
0
0.01
Beam Column
300
0.02
0
0.01
0.02
0.03
0.04
Curvature (rad/m)
Strain
(a) (b) (c) Figure 2. Column and beams for ductile frames: (a) sectional details (note fiber sizes exaggerated for clarity), (b) concrete constitutive laws and (c) moment-curvature response. Table 1. Summary of structural column and beam material parameters. Material Steel 01 Material Unconfined concrete Confined concrete (beams) Confined concrete (columns)
Young’s Modulus 1.99 x 1011 Young’s Modulus 2.16 x 1010 2.16 x 1010 2.16 x 1010
Peak strength (f’c) 2.76 x 107 3.64 x 107 4.14 x 107
Yield strength 4.14 x 108 Strain at peak strength 0.003 0.005 0.007
Ultimate strength 5.52 x 106 2.84 x 107 3.42 x 107
Ultimate strain 0.006 0.02 0.026
Element Types and Constitutive Relations – Soil Modeling A common method for modeling nonlinear response of foundations is the Beam-on-NonlinearWinkler-Foundation (BNWF) class of approaches. Such methods generally combine springs, dashpots, and gap elements, allowing one to capture of the salient features of the rocking foundation, including yielding and uplifting of the foundation, and even settlement (e.g. Harden, 2003; Gajan et al., 2005). In this work, the foundation is modeled using the BNWF approach and considering five different cases of idealized foundations: (i) fixed base (sliding, settling, and rotation at the base restricted), (ii) vertical elastic springs (sliding restricted), (iii) vertical and horizontal elastic springs, (iv) nonlinear, inelastic vertical springs (sliding restricted), and (v) nonlinear, inelastic vertical springs and elastic horizontal springs. Note that case (i), (ii), and (iv) are restrained from horizontal sliding. Each footing is divided into 100 elements, resulting in a footing subgrade supported on 101 vertical springs. Individual springs are considered as onedimensional zeroLength elements, where nonlinearity (when considered) is modeled using the Qzsimple1 material properties (Boulanger, 2004), which can account for vertical settlement and uplift. The Qzsimple1 material has a non-symmetric backbone defined by an ultimate load on the
compression side and a reduced strength in tension as the soil separates from the footing. Additional gap components are added in series with the elastic and plastic components. Inputs to this material are the type of material (clay/sand), the ultimate load capacity, vertical stiffness, the displacement at which 50% of the ultimate load is mobilized, tension capacity, suction, and viscous damping. In the present study, the foundation subgrade is assumed to be dense, dry sand with an 80% relative density. The Youngs Modulus of the sand is assumed based on the specifications given by Das (1999) for dense sand. Vertical and sliding stiffness is selected based on recommendations by Gazetas and Tassoulas (1987) and Gazetas (1991). Vertical load bearing capacity is calculated after Terzaghi (1943), using shape and depth factors after Meyerhof (1951). The basic parameters used for the soil subgrade and the resulting spring values obtained for three different footings are listed in Table 2. For each case, the vertical factor of safety FSv of the strip footing (below the shear wall) is varied to encompass a typical range in design practice (FSv = 3, 5, 7, and 10). Based on corresponding design level (dead and live) service loads, estimated base moments and shears were calculated and design factors of safety against overturning FSo and sliding FSs were estimated. In general, these were very high, with FSo mostly greater than 10 and FSs greater than 30 for the service load condition. To define lower vertical factors of safety, the mass applied to the shear wall is progressively increased to achieve the target FSv. Table 2. Basic parameters for soil subgrade and derived parameters for BNWF model. Cohesion, c (KPa)
Friction angle φ (deg)
Unit weight of soil, γ (KN/m3)
Relative density, Dr (%)
Poisson’s ratio, υ
0
40
16.2
80
0.3
Footing Strip Square
Ultimate load capacity Qult (KN) 2280 1860
Vertical stiffness Kv (KN/m) 88310 55940
Young’s modulus E (KPa) 45000
Horizontal stiffness Kh (KN/m) 79260 45660
Solution Technique Adopted The Newmark method has been used for conducting the transient analysis, with a constant time step and β and γ solution parameters of 0.25 and 0.5, respectively. Five percent Rayleigh damping has been assumed for the structure. The transformation method is used in the analysis as a constraint. This method transforms the stiffness matrix by condensing out the constrained degree of freedoms, while also reducing the size of the system for multi-point constraints. The Reverse Cuthill-McKee algorithm is used to optimize node numbering and reduce the bandwidth of the system matrices. An un-symmetric banded system of equations object is constructed, which is solved during the analysis using the Lapack band general solver. To solve the nonlinear equations, the Newton-Raphson algorithm is used, with a maximum of 40 iterations to a convergence tolerance of 1e-12. Nonlinear Pushover Response and Dynamic Characterization Figure 4(a) shows the nonlinear pushover response of the fixed base, elastic base and nonlinear base wall-frame models. The affect of a softened wall is illustrated by varying the flexural rigidity for the fixed base case (EI, 0.4EI, and 0.2EI). For comparison, part b shows the nonlinear pushover response of the frame only portion of the model (1 bay, 2 story) with the same foundation
conditions. The more significant effect of the foundation on the nonlinear response of the wallframe system is apparent, when compared with the frame only model. Eigenvalue analysis of the wall-frame model indicates the fundamental period is 0.13, 0.19, 0.24, 0.52, and 0.54 seconds for the fixed base (EI), fixed base (0.4EI), fixed base (0.2EI), flexible base (no sliding) and flexible base (sliding) cases, respectively. For comparison, the fundamental period of the frame only model is calculated as 0.41, 0.70, and 0.71 seconds for the same cases. Table 3 summarizes the capacity characteristics in terms of yield drift ratio and corresponding yield strength for the building-frame models, considering the different foundation conditions. In each case, yielding of individual elements (beams, columns, and foundation springs) is monitored and the yield drift is reported as the point at which any element first reaches its yield (shown with circles in Figure 4). Since elements are yielding sequentially in turn, sequential yield points are reported (i.e. Yield Drift 1, Yield Drift 2, etc.). In all conditions, the beam-column joints are reaching their yield curvature prior to the foundation springs or columns. Note that nearly simultaneous yielding of all beam-column joints is occurring for the fixed base model, at approximately 0.13-0.15% total drift, whereas subsequent yielding of elements is delayed for both the elastic and nonlinear base models as the load is redistributed to the foundation. For the elastic and nonlinear base systems, first yielding occurs at 0.33%, which is reasonably close to most code-based design yield amplitudes. Table 3. Summary of capacity characteristics for the different foundation conditions for the framewall-foundation model. Yield Drift1 (%) 0.13 0.33 0.33
Lateral Shear Force / Weight
Fixed Base Elastic Base Nonlinear Base 4.0
Yield Drift2 (%) 0.14 0.34 0.34
Fixed base (elastic wall) Fixed base (0.4*EI) Fixed base (0.2*EI) Elastic base Nonlinear base
3.0 2.0 1.0 0.0 0.0
Yield Drift3 (%) 0.14 0.45 0.44
0.5
1.0
Total Drift (%) (a)
1.5
2.0
Lateral Shear Force / Weight
Case
Yield Drift4 (%) 0.15 0.50 0.50
Fy1 (kN) 288 99 98
Fy2 (kN) 295 102 102
Fy3 (kN) 310 125 119
Fy4 (kN) 317 137 128
Fixed base Elastic base Nonlinear base
1.5
1.0
0.5
0.0 0.0
1.0
2.0
3.0
4.0
Total Drift (%) (b)
Figure 4. Nonlinear pushover response for the different foundation conditions: (a) frame-wallfoundation model (in Figure 1) and (b) frame only (1 bay, 2 story portion of Figure 1). Selection of Ground Motions Ten recorded earthquake motions are selected for use as input into the numerical models. All motions are recorded, with records selected from the Imperial Valley (1979), Landers (1992), Northridge (1994), Kobe (1995), Chi-Chi (1999), San Fernando (1971), North Palm Springs (1986), Whittier Narrows (1987), Loma Prieta (1989), and Duzce (1999) earthquakes. The later five of these motions may be characterized as near-fault, due to the close proximity of the recording to the fault rupture (less than 10 km). Five percent damped elastic response spectrum for each motion are provided in Figure 5, where part (a) presents those motions characterized as near-field, and part (b)
presents those motions characterized as ordinary motions. To illustrate the sensitivity at typical envisioned structural performance levels, each ground motion is amplitude scaled such that the displacement ductility μΔ (=Δmax/Δy, where Δy = yield displacement) is between 2-3, for the fixed base condition. Resulting scaling factors ranged from 0.2-1.6. Peak ground accelerations for the scaled motions ranged from PGA = 0.12 – 0.94g.
4
Imperial Landers Northridge Kobe Chi-Chi FEMA-356
Tflexible Trigid
2 0 0.001
(a)
0.01 0.1 1 Period (sec)
6
SA/PGA
SA/PGA
6
Tflexible Trigid
4 2
(b)
0 0.001
10
San Fernando Palm Springs Whittier Loma Prieta Turkey FEMA-356
0.01 0.1 1 Period (sec)
10
Figure 5. Five percent damped acceleration response spectra for: (a) near fault motions and (b) ordinary (other) motions used in this study. (FEMA 356 design spectrum overlaid). Total Drift (%) 0
0.1
400
Force (KN)
Total Drift (%)
0.2 1
(a) FS=10
200
0.5
0
0
-200
-0.5
-400 -30
-1 -20
-10
0
10
20
-0.4 200
0.1
Force (KN)
1
200
0.5
0
0 -0.5
(c) FS=10
-400 -20
-1 -10
0
10
Displacement (mm)
0.6 1
(b) FS=3 0.5 0
-200 -400 -40
-0.5 -20
0
20
40
60
Total Drift (%) 0.2
400
-200
0.4
Displacement (mm)
20
Acceleration (g) Force (KN)
0
0.2
0
Total Drift (%) -0.1
0
400
Displacement (mm) -0.2
-0.2
Acceleration (g)
-0.1
-0.4
-0.2
0
0.2
0.4
400
1
(d) FS=3
200
0.5
0
0
-200
-0.5
-400 -40
-1 -20
0
20
40
Acceleration (g)
-0.2
Acceleration (g) Force (KN)
-0.3
Displacement (mm)
Figure 6. Global lateral force-displacement response of the wall-frame structure (case iv): Whittier motion (a) FSv = 10 and (b) FSv = 3 and Landers motion (a) FSv = 10 and (b) FSv = 3. Analyses Results and Discussion Time History Response Sample global force-displacement response for the Whittier and Landers motions are shown in Figure 6. These results are shown for the nonlinear foundation case, with sliding restrained (case iv), and for FSv = 10 and 3. These time histories show that although the range of global lateral force absorbed by the system is fairly similar for the different FSv cases, for each motion, the lower FSv = 3 case results in much larger total drift demands (approximately twice that of the FSv = 10 case). This can be attributed to the softer strip footing below the shear wall. For the same two motions, the time history responses of the footing forces and displacements for two motions are shown in Figures 7 and 8. Similarly, response results are shown for the case (iv) foundation condition. Pairs
20
40
60
Time (sec) Shear (KN)
20 10 0
(c) Interior Square Footing
-10 -20 0
20
40
60
Time (sec) Shear (KN)
20 10 0
(e) Exterior Square Footing
-10 -20 0
20
40
Time (sec)
60
FSv=10.0
300 0
(a) Strip Footing -300
-200 0
20
40
0
60
10
Mcap = 44 kN-m Mcap = 38 kN-m
10 0
(d) Interior Square Footing
-10
30
40
50
0 -20
(c) Interior Square Footing
-40
20
40
60
0
10
Time (sec) 20
Mcap = 25 kN-m
0
(f) Exterior Square Footing
-10 -20 0
20
40
Time (sec)
Figure 7. Shear and moment response of foundations – Landers Motion.
Mcap = 144 kN-m
0 -150
(b) Strip Footing
-300 0
10
20
30
40
50
60
0
(e) Exterior Square Footing
-40 0
10
20
30
Time (sec)
30
40
50
Mcap = 44 kN-m Mcap = 38 kN-m
0 -25
(d) Interior Square Footing
-50 0
10
20
30
40
50
Time (sec)
20
-20
20
25
Time (sec)
Mcap = 22 kN-m
10
Mcap = 444 kN-m
150
Time (sec)
20
-20 0
300
Time (sec)
Time (sec) 20
20
Moment (kN-m)
(b) Strip Footing
FSv=3.0
Moment (kN-m)
0
0 -100
600
40
50
Moment (kN-m)
-200
Mcap = 144 kN-m
Shear (KN)
(a) Strip Footing
Mcap = 444 kN-m
100
Shear (KN)
0 -100
200
Shear (KN)
FSv=10.0
Moment (kN-m)
FSv=3.0
100
Moment (kN-m)
200
Moment (kN-m)
Shear (KN)
of each figure, parts (a)-(b), parts (c)-(d) and parts (e)-(f) show responses for each of the strip footing, interior square footing, and exterior square footing, respectively. Note that in the case presented in Figure 8, instability of the structure is observed following the footing exceeding its theoretical moment capacity. These results also further illustrate the amplified response for the softer (FSv = 3.0) footing systems, which is apparent for each of the strip, exterior square, and interior square footings.
Mcap = 22 kN-m
25
Mcap = 25 kN-m 0 -25
(f) Exterior Square Footing
-50 0
10
20
30
40
50
Time (sec)
Figure 8. Shear and moment response of foundations – Whittier Motion.
Response Parameters of Interest in Design Of interest in the design of building systems are response parameters such as the maximum interstory drift, and foundation base forces (moments and shears), to name a few. Figure 9 shows the variation in these three parameters, as a function of the varying foundation conditions. These results are shown for the FSv = 10 condition, and for all ground motions considered. Ground motions are categorized generally as either ordinary or near fault. Figure 9 illustrates that in all cases, considering the foundation flexibility significantly reduces the maximum inter-story drift demands on the structure. Note that when elastic sliding is considered (cases iii and v), maximum inter-story drifts tend to increase. Maximum moments, as represented by the normalized moment M* (= Mjmax/Mimax, where Mjmax = each of cases ii-v and Mimax = case i, the fixed base condition), at the base of the footings are significantly reduced, ranging from approximately 10-30% of the fixed base maximum moments. Similarly trends are observed for the base shear demands; however, there is significantly more scatter in the range of base shear reduction. There is little to no discernable trend between the results considering either a near fault or ordinary ground motion scenario. Of equal importance to the building design, is the magnitude and distribution of energy dissipation in the structure. Figure 9(d) presents a summary of the normalized energy E* (= Ejmax/Eimax, where Ejmax = each of case ii-v and Eimax = case i, the fixed base condition), where energy is calculated as the sum of area under the moment-rotation response for all beam-column plastic hinges. From Figure 9(d), it is observed that in all cases, accounting for foundation flexibility results approximately the same, or more commonly additional energy dissipation from the structural elements, when compared with the fixed base condition (case i). In general, the range of increase in
Fixed- ElasticBase Base
0.10 0.08 0.06 0.04 0.02
Fixed- ElasticBase Base
1.00
0.00
Nonlinear (b) Base
Ordinary Motions Near Fault Motions
0.80 0.60 0.40 0.20 0.00
0
1
2 3 4 Case Number
Fixed- ElasticBase Base
1.00
5
6
0
Nonlinear Base (c)
0.80 0.60 0.40 0.20 0
1
2 3 4 Case Number
5
6
1
2 3 4 Case Number
Fixed- ElasticBase Base
10.00 E* = Ejsum/Eisum
V* = Vjmax/Vimax
Nonlinear (a) Base M* = Mjmax/Mimax
Max Interstory Drift γmax (%)
energy dissipation is between 1 – 9 times that of the fixed base condition. It should be noted that the wall is modeled to remain elastic. Upon considering inelastic wall behavior, the response of the case study system would obviously vary.
5
6
Nonlinear Base (d)
8.00 6.00 4.00 2.00 0.00 0
1
2 3 4 Case Number
5
6
Figure 9. Variation of response parameters as a function of foundation condition: (a) maximum inter-story drift, (b) normalized moment, (c) normalized shear force, and (d) normalized energy (FSv = 10). Conclusions The need to improve our understanding of soil-foundation-structure interaction (SFSI) effects, and especially the need to investigate SFSI on a system level is well known to be an important practical issue in seismic design. To study SFSI on a system level, in this paper, a model retrofit shear wall is combined with a frame system, and the response of this structure is investigated using nonlinear dynamic time history analyses. The effects of foundation rocking, sliding, and settling are incorporated by using a variety of foundation base conditions. Varying vertical factors of safety at the base of the footings are used in the modeling, to evaluate the effects of the margin of safety in the foundation on the seismic response. Results indicate that if reliably quantified and designed, SFSI has great potential for reducing seismic forces and inter-story drift demands, by providing added energy dissipation to the building-foundation system. Moment demands at the base of the foundations were consistently reduced (by as much as 90% of the fixed base moment) by incorporating SFSI. Simulation results also indicate that in general, an increase in energy dissipation is observed in the structural fuses, and this may be as high as nine times that of the fixed base condition. Acknowledgments This work was supported by the Pacific Earthquake Engineering Research Centers program of the National Science Foundation under award EEC-9701568, PEER project number 1092004a.
Helpful suggestions and support of Professors Geoff Martin and Bruce Kutter, doctoral student Sivapalan Gajan, and consulting engineers Mark Moore, and Craig Comartin are appreciated. Any opinions, findings, and conclusions expressed in this paper are those of the authors, and do not necessarily reflect those of the sponsoring organization. References ACI 318-02, 2002, Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02), American Concrete Institute, Farmington Hills, MI. ASCE 7-02, 2003. Minimum Design Loads for Buildings and other Structures. Publisher Structural Engineering Institute (SEI) and the American Society of Civil Engineers (ASCE). Reston, Virginia. Boulanger, R. W., 2004. “The QzSimple1 Material.” Documentation for the OpenSEES platform. Das, B. M., 1999. Principles of Foundation Engineering. Brooks/Cole Publishing Company, California. EERI, 2002. “Securing society against catastrophic earthquake losses: A research and outreach plan in earthquake engineering.” Report no., Earthquake Engineering Research Institute. FEMA 356, 2000. Prestandard and Commentary for the Seismic Rehabilitation of Buildings, American Society of Engineers, Virginia. Gajan, S., Kutter, B. L., and Thomas, J. M., 2005. Physical and Numerical Modeling of Cyclic Moment Rotation Behavior of Shallow Foundations, 16th International Conference on Soil Mechanics and Geotechnical Engineering. Gazetas, G., 1991. “Displacement and soil-structure interaction under dynamic and cyclic loading.” Proceedings of the 10th European Conference on Soil Mechanics and Foundation Engineering, Florence. Gazetas, G. and Tassoulas, J., 1987. “Horizontal stiffness of arbitrary shaped embedded foundations.” ASCE Journal of Geotechnical Engineering, 113(5), 440–457. Harden, C. W., 2003. Numerical modeling of the non-linear cyclic response of shallow foundations. M.S. Thesis, University of California, Irvine. Mander, J. B. and Priestly, M.J.N. and Park, R., 1988. “Theoretical Stress-Strain Model For Confined Concrete,” ASCE Journal of Structural Engineering, 114 (8), 1804-1826. Meyerhoff, G. G., 1951. “The ultimate bearing capacity of foundations.” Geotechnique, 2, 301–332. NRC, 2003. Preventing Earthquake Disasters: The Grand Challenge in Earthquake Engineering, A research agenda for the network for earthquake engineering simulation (NEES). National Research Council of the National Academies, The National Academies Press, Washington, D.C. OpenSEES, 2005, Open System for Earthquake Engineering Simulation - Development platform by PEER, http://opensees.berkeley.edu/ Terzaghi, K., 1943. Theoretical Soil Mechanics. John Wiley, New York.
