der, N.A. (2012): Economic MEMS based 3-axis water proof accelerometer for dynamic ...... 6.12 Positioning of PPT during dry pluviation . . . . . . . . . . . . . . . . 148 .... This chapter provides an introduction to the research presented in this thesis,.
Dynamics of pile-supported structures in seismically liquefiable soils
By
Domenico Lombardi
A dissertation submitted to the University of Bristol in accordance with the requirements of the degree of Doctor of Philosophy in the Faculty of Engineering
Department of Civil Engineering University of Bristol
January 2014
Abstract Failure of pile-supported structures are still observed in liquefiable soils after most major earthquakes. As a result, the behaviour of pile foundations during liquefaction phenomena remains a constant source of attention to the earthquake engineering community. In this context, the present research attempts to investigate the effects of soil liquefaction on the dynamic behaviour of pile-supported structures. Firstly, the thesis reports a field investigation carried out in the region affected by liquefaction events observed after the 2012 Northern Italy earthquake sequence. The collected information are used to gain insight into the mechanism governing the onset of liquefaction in the real field. The thesis also presents a series of multi-stage cyclic triaxial tests that aim to investigate both pre and post-liquefaction behaviours of two types of silica sands. These findings are subsequently used to develop a new set of p − y curves which are capable of capturing the strain-hardening behaviour observed in the experiments. The main component of the present research consists of an experimental investigation carried out using a shaking table. A preliminary study is reported in which tests are performed to investigate the effects of artificial boundaries of the model container on the response of the enclosed soil. It is found that the use of absorbing boundaries, which are made of conventional foams, is capable of reducing reflections and generation of body waves from the artificial boundaries, which in turn minimise the so called boundary effects. Subsequently, four physical models consisting of two single piles and two 2×2 pile groups are tested on a shaking table. The dynamic response is conveniently identified in terms of two modal parameters, namely: fundamental period and damping ratio. The experimental results suggest that the fundamental period of the pile-supported structures may increase considerably due to the soil softening caused by liquefaction. On the other hand, the damping ratio of these structures increase to values in excess of 20%. Based on the these findings, it is noted that the seismic demand imposed by the shaking on the models may vary with the excess pore water pressure generation, which in extreme case may lead to full liquefaction conditions. In particular, it is observed that the highest acceleration demand, and consequently maximum inertia force, experienced by the models occur during the transient to liquefaction. Finally, a series of numerical analyses are performed using the Winkler approach with the proposed p − y curves. The numerical results show that the models correctly replicated the distribution of the maximum bending moments measured after the onset of liquefaction but consistently underestimated the maximum moments by a factor ranging from 2 to 3. It is also found that the capacity spectrum method can be used as a simple and convenient tool for assessing the seismic demand. i
List of publications Peer-Reviewed Journal 1. Lombardi, D., Bhattacharya, S. (2014). Modal analysis of pilesupported structures during seismic liquefaction. Earthquake Engineering & Structural Dynamics. Vol. 43(1), pp 119-138. DOI: 10.1002/eqe.2336. 2. Bhattacharya, S., Murali Krishna, A., Lombardi, D., Crewe, A.J., Alexander, N.A. (2012): Economic MEMS based 3-axis water proof accelerometer for dynamic geo-engineering applications, Soil Dynamics and Earthquake Engineering, Vol. 36, pp 111-118. DOI:10.1016/j.soildyn.2011.12.001. 3. Bhattacharya, S., Lombardi, D. (2012): On the seismic behaviour of pile foundations in liquefiable soils. Italian Geotechnical Journal. 46(1), pp 23-34. (in Italian).
Book Chapters 1. Bhattacharya, S., Lombardi, D., Dihoru, L., Dietz, M., Crewe, A.J., Taylor, C.A. (2011): Chapter 8 titled ’Model Container Design for Soil-Structure Interaction Studies’ in the book Role of Seismic Testing Facilities in PerformanceBased Earthquake Engineering (Fardis, Michael N.; Rakicevic, Zoran T. (Eds.), Published by Springer ISBN 978-94-007-1976-7.
Volume of Conference Proceedings • Lombardi, D., Bhattacharya, S. (2012). Shaking table tests on rigid soil container with absorbing boundaries. Proc. 15th World Conference on Earthquake Engineering, September 24-28 2012, Lisbon, Portugal. • Lombardi, D., Bhattacharya, S. (2012). Application of MEMS accelerometer for liquefaction studies. Proc. Proc. 9th International Conference on Urban Earthquake Engineering/ 4th Asia Conference on Earthquake Engineering. March 6-8, 2012, Tokyo Institute of Technology, Tokyo, Japan. • Lombardi, D., Dash, S.R., Bhattacharya, S. (2011). Inclusion of axial load on bending response of pile in liquefiable soils. Proc. 8th International Conference on Urban Earthquake Engineering, March 7-8 2011, Tokyo Institute of Technology, Tokyo, Japan.
ii
• Lombardi, D., Durante, M.G., Dash, S.R., Bhattacharya, S. (2010). Fixity of piles in liquefiable soils. Proc. 5th International Conference on Recent Advances in Geotechnical Engineering and Soil Dynamics, May 24-29 2010, San Diego, California, US. • Lombardi, D., Dash, S.R., Bhattacharya, S. (2010). Simplified dynamic analysis of pile supported structures in liquefiable soils. Proc. 7th International CUEE & 5th ICEE joint Conference, March 3-5 2010, Tokyo Institute of Technology, Tokyo, Japan.
iii
Acknowledgements The last three years have been an exciting journey for me both professionally and personally. This would not have been possible without the support and existence of numerous people, for whom I would like to pay my sincerest gratitude. The writing up of this dissertation reminded me many of the scientific and personal challenges encountered during my studies. The person who has made it possible for me to succeed throughout these challenges and my academic career is my mentor and friend, Professor Subhamoy Bhattacharya, to whom I can never fully express the extent of my gratitude. This work would not have been possible without his guidance, support and encouragement. I could not have imagined having a better mentor for my PhD and I am forever indebted to him for providing me the opportunity to be part of an amazing scientific community that is at the forefront of the geotechnical earthquake engineering research. I am also thankful to my co-supervisor Dr Nicholas Alexander for his enthusiastic and technical guidance throughout this research. The experimental investigation presented in Chapter 4 would not have been possible without the collaboration with academic and research staff from the Department of Civil Engineering at Yamaguchi University, Japan. In particular, I owe considerable appreciation to Professor Masayuki Hyodo for giving me the privilege to be part of a vibrant research group. I am also thankful to Dr Takashi Kaneko for providing me hands-on training in the use of the experimental apparatus, and Shohei Noda, Tomoya Kuroiwa and Masahide Otsubo (University of Tokyo) for their company and unforgettable dinners spent with them. My sincere appreciation is extended to Mr Mehdi Rouholamin, Mr Masoud Shadlou and Dr Murali Krishna (Indian Institute of Technology Guwahati, India) for their invaluable assistance in the preparation and execution of the shaking table tests. I am especially grateful to Mehdi also for his precious support with the numerical analysis. Over the past years, I had privilege to collaborate with a number of esteemed academics who strengthen my research confidence and persistence. In particular I would like to express my deepest gratitude to Professor Takashi Tazoh (Shimizu Corporation & Toyama Prefectural University, Japan), Professor Kohji Tokimatsu (Tokyo Institute of Technology, Japan), Professor David Muir Wood (University of iv
Dundee), Professor Fabrizio Scarpa (Univeristy of Bristol), Dr Suresh Dash (Indian Institute of Technology Bhubaneswar, India), Professor Yu Huang (Tongji University Shanghai, China). I would like to thank Professor Armando Lucio Simonelli (University of Sannio, Italy) and Professor Giuseppe Lanzo (University ’La Sapienza’, Italy) for their assistance during the site investigation in the regions struck by the 2012 Northern Italy earthquake. I am thankful to my friends and collegues Matteo, Elisa, Nicolas, James, Hisham, Ignazio, Riccardo, George, Appo, Shima, and my housemates Laurence and Robert. I am lucky to have an amazing family, they are not mentioned yet since they deserve their own part. I would like to thank my fiance, Pamela, for her patience and support while I worked day and night for month on end. I would like to extend my warmest thanks to my parents Dolores and Nino for giving me the opportunity to follow my dreams, and my sister, Caterina for her love. It is to them that I dedicate this thesis, with the hope that this work makes you proud. This study was supported by the Bristol Centenary Postgraduate Research Scholarship offered by the University of Bristol. I would also like to extend my sincere appreciation to Il Circolo Cultural Italian Association (London) and the Centre of Urban Earthquake Engineering of Tokyo Institute of Technology for providing external funding.
v
Declaration I declare that the work in this dissertation was carried out in accordance with the requirements of the University’s Regulations and Code of Practice for Research Postgraduate Programmes and that it has not been submitted for any other academic award. Except where indicated by specific reference in the text, this work is my own work. Work done in collaboration with, or with the assistance of others, is indicated as such. I have identified all material in this dissertation which is not my own work through appropriate referencing and acknowledgement. Where I have quoted from the work of others, I have included the source in the references/bibliography. Any views expressed in the dissertation are those of the author.
Domenico Lombardi
Date:
vi
List of Symbols Roman symbols A
Coefficient for loading condition in API code
ax
Horizontal acceleration
Ct
Coefficient in Eurocode 8
cu
Undrained shear strength
C1 , C2 and C3
Coefficients in API code
Df
Depth of fixity
Dr
Relative density
D50
50% finer size
E E∗ e ecr
Young’s modulus Complex elastic modulus Void ratio Critical void ratio
emax
Maximum void ratio
emin
Minimum void ratio
G Gmax Gs g Heq Hs
Shear modulus of soil Maximum Shear modulus of soil Specific gravity Gravity acceleration Equivalent static lateral force (i.e. base shear force) Depth of soil
I
Moment of inertia of pile cross section
J
Coefficient in API code
vii
Ki
Elastic later stiffness
ks
Coefficient of subgrade reaction
kx
Coefficient of horizontal acceleration
K0
Coefficient of lateral earth pressure at rest
M
Diagonal mass matrix
M(x)
Bending moment function
MS
Strain scaling factor
Mw
Moment magnitude
mp
p-multiplier
N NS Ndyn (N 1)60
Static axial load Stress scaling factor Dynamic axial load SPT equivalent clean sand blow count
p
Soil resistance
p0
Effective mean principal stress
pu
Ultimate lateral bearing capacity in API code
q
Deviator stress
qcyc
Cyclic deviator stress
rd
Correction factor for assessment of τmax
Sr
residual strength of the liquefied soil
ru
Excess pore water pressure ratio
Sxy
Cross Power Spectral Density of the input and output signals
Sx
Power Spectral density of the input signal
T
Fundamental period
viii
Uc
Coefficient of uniformity
V(x)
Shear force function
Vp
Shear wave velocity of P waves in medium
Vs
Shear wave velocity of S-waves in medium
v X XR y yto Z
Specific volume Depth below soil surface in API code Depth of reduced soil resistance in API code Pile deflection Take-off displacement Impedance of the medium
Greek symbols γ
Unit weight of the soil layer
γ0
Effective soil weight
γto
Take-off strain
∆u
Excess pore water pressure
εa
Axial strain
ζ
Damping ratio
η
Characteristic length
λw
Wavelength
ν
Poisson’s ratio
ρ
Density of the material
σa0
Axial effective stress
σc0
Confining stress
σr0
Radial effective stress
ix
σxo
Horizontal effective overburden stress and vertical stresses,
0 σzo
Vertical effective overburden stress
σ10
Major principal stress
σ20
Intermediate principal stress
σ30
Minor principal stress
τ
Shear stresses
τmax
Maximum shear stresses
Φ
Matrix of eigenvectors
φ
Angle of internal friction
Ω2
Diagonal matrix of eigenvalues
Abbreviations BNWF : Beam on Nonlinear Winkler Foundation CSL: Critical State Line CRR: Cyclic Resistance Ratio CSR: Cyclic Stress Ratio CSSM : Critical State Soil Mechanics DSSI : Dynamic Soil-Structure Interaction FFT : Fast Fourier Transform FOS : Factor of safety against liquefaction FRF : Frequency Response Function MEMS : Micro Electro Mechanical System PGA: Peak Ground Acceleration PI : Plasticity Index PPT : Pore Pressure Transducers
x
PSD: Power Spectral Density SDOF : Single Degree Of Freedom SPT : Standard Penetration Test SSI : Soil-Structure Interaction
xi
Contents Abstract
i
List of Publications
ii
Acknowledgements
iii
Declaration
v
List of Symbols 1 Introduction 1.1 Outline of the chapter . . . . 1.2 Introduction . . . . . . . . . . 1.3 Scope of the present research . 1.4 Organization of the thesis . .
vi
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1 1 1 7 8
2 Literature Review 2.1 Outline of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Undrained behaviour of cohesionless soils . . . . . . . . . . . . . . . . 2.3.1 Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Undrained post-liquefaction . . . . . . . . . . . . . . . . . . . 2.4 Current understanding of pile failures during seismic liquefaction . . . 2.5 Dynamic Soil-Structure Interaction . . . . . . . . . . . . . . . . . . . 2.5.1 Load-Deflection p−y curves for DSSI modelling in non-liquefiable soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 p − y curves for DSSI modelling in liquefiable soils . . . . . . . 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 10 10 10 15 17 23 25
3 Site 3.1 3.2 3.3 3.4
40 40 40 42 44 44 48 50
3.5
investigation Outline of the chapter . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . Seismicity of the area and historical liquefaction events Fault type and ground motion . . . . . . . . . . . . . . 3.4.1 May 20, 2012 event . . . . . . . . . . . . . . . . 3.4.2 May 29, 2012 event . . . . . . . . . . . . . . . . Elastic acceleration response spectra . . . . . . . . . .
xii
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28 33 38
CONTENTS 3.6
3.7 3.8 4 Soil 4.1 4.2 4.3 4.4
4.5 4.6 4.7 4.8 4.9
Field survey . . . . . . . . . . . . . . . . . . . 3.6.1 SantAgostino . . . . . . . . . . . . . . 3.6.2 San Carlo . . . . . . . . . . . . . . . . 3.6.3 Assessment of Liquefaction potential in 3.6.4 Mirabello . . . . . . . . . . . . . . . . Observed damage to historic buildings . . . . Conclusion . . . . . . . . . . . . . . . . . . . .
. . . . . . the . . . . . .
. . . . . . . . . . . . . . . . . . San Carlo . . . . . . . . . . . . . . . . . .
element testing Outline of the chapter . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Multi-stage cyclic triaxial apparatus . . . . . . . . . . . . Stress states in free-field and triaxial apparatus . . . . . 4.4.1 Free-field conditions . . . . . . . . . . . . . . . . 4.4.2 Laboratory conditions . . . . . . . . . . . . . . . Preparation of the specimen . . . . . . . . . . . . . . . . Materials used in the tests . . . . . . . . . . . . . . . . . Test procedure and experimental program . . . . . . . . Test results . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Undrained Cyclic Behaviour . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.1 Undrained Cyclic Behaviour . . . . . . . . . . . . 4.9.2 Post-liquefaction undrained monotonic behaviour
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5 Geotechnical model container 5.1 Outline of the chapter . . . . . . . . . . . . . . . . . . . . 5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Requirements for geotechnical model container . . . . . . . 5.3.1 Stress similarity . . . . . . . . . . . . . . . . . . . . 5.3.2 Strain similarity . . . . . . . . . . . . . . . . . . . . 5.3.3 Propagation of shaking to the soil deposit . . . . . 5.3.4 Reflection and generation of body waves from the boundaries . . . . . . . . . . . . . . . . . . . . . . . 5.4 Basic concept of wave propagation . . . . . . . . . . . . . 5.5 Experimental investigation . . . . . . . . . . . . . . . . . . 5.5.1 Earthquake simulator . . . . . . . . . . . . . . . . . 5.5.2 Soil material . . . . . . . . . . . . . . . . . . . . . . 5.5.3 Absorbing material . . . . . . . . . . . . . . . . . . 5.5.4 Testing program and instrumentation set-up . . . . 5.6 Experimental results . . . . . . . . . . . . . . . . . . . . . 5.7 Development of new geotechnical model container . . . . . 5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Experimental investigation (shaking 6.1 Outline of the chapter . . . . . . . 6.2 Introduction . . . . . . . . . . . . . 6.3 Experimental apparatus . . . . . . xiii
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. . . . . . . . . Area . . . . . . . . .
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53 54 56 59 61 63 66
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68 68 68 69 71 71 73 75 78 81 83 83 104 104 104
106 . 106 . 106 . 108 . 108 . 109 . 110 . . . . . . . . . .
110 113 115 115 118 118 120 123 130 133
table tests) 135 . . . . . . . . . . . . . . . . . . . 135 . . . . . . . . . . . . . . . . . . . 135 . . . . . . . . . . . . . . . . . . . 136
CONTENTS 6.3.1 Earthquake simulator . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Geotechnical soil container . . . . . . . . . . . . . . . . . . . 6.3.3 Models of Pile-supported structures . . . . . . . . . . . . . . 6.3.4 Soil properties . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Instrumentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Strain Gauges . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Pore-water pressure transducers . . . . . . . . . . . . . . . . 6.4.4 Instrumented impact hammer . . . . . . . . . . . . . . . . . 6.4.5 Signal Conditioning and Data acquisition system . . . . . . 6.4.6 Testing programme . . . . . . . . . . . . . . . . . . . . . . . 6.5 System identification techniques . . . . . . . . . . . . . . . . . . . . 6.5.1 Assessment of modal parameter from free decay . . . . . . . 6.5.2 Assessment of modal parameter from shaking table tests . . 6.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Dynamic properties of the models evaluated before the shaking table tests . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Results from second stage . . . . . . . . . . . . . . . . . . . 6.7 Acceleration, velocity and displacement time histories . . . . . . . . 6.8 Bending moment profiles . . . . . . . . . . . . . . . . . . . . . . . . 6.9 Soil layer response . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10 Response spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Numerical modelling 7.1 Outline of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Modelling of pile and soil-structure interaction . . . . . . . . . . . . 7.4 Numerical analysis procedure . . . . . . . . . . . . . . . . . . . . . 7.4.1 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Pseudo-static analysis . . . . . . . . . . . . . . . . . . . . . 7.4.3 Nonlinear Static Analysis (or Pushover analysis) . . . . . . . 7.5 Capacity spectrum method . . . . . . . . . . . . . . . . . . . . . . . 7.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Simplified pseudo-static analysis and assessment of maximum bending moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Literature review . . . . . . . . . . . . . . . . . . . . 8.1.2 Site investigation . . . . . . . . . . . . . . . . . . . . 8.1.3 Multi-stage cyclic triaxial tests . . . . . . . . . . . . 8.1.4 Shaking table tests to study boundary effects . . . . 8.1.5 Shaking table test to investigate dynamic behaviour supported structure models during liquefaction . . . . 8.1.6 Numerical modelling . . . . . . . . . . . . . . . . . . xiv
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136 136 137 140 141 144 146 147 148 149 149 153 153 154 156
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157 162 169 176 186 193 200
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201 201 201 203 206 207 208 214 219 224
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234 234 234 235 235 236
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8.2
Areas for future research . . . . . . . . . . . . . . . . . . . . . . . . . 239
References
240
xv
List of Tables 2.1 2.2
Non-dimensional static p − y curves for soft clays from API (2000) . . 32 Non-dimensional cyclic p − y curves for soft clays from API (2000) . . 32
3.1
List of historical Italian earthquakes occurred in the area of the 2012 Emilia seismic sequence. The occurrence of liquefaction is also highlighted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1 4.2
Index properties of Redhill 110 and Toyoura sands . . . . . . . . . . . 80 Summary and loading conditions of the tests carried out in this study ∗ Tests carried out in tension . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 5.2 5.3 5.4 5.5
Earthquake simulator specifications (Crewe 2007) . . . . . . . . . . Mechanical properties of the absorbing material . . . . . . . . . . . Specification of piezoelectric accelerometers . . . . . . . . . . . . . . Summary of the tests carried out in this study . . . . . . . . . . . . Reduction in energy, RE, computed at two depth and for two different levels of acceleration . . . . . . . . . . . . . . . . . . . . . . . . . .
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116 121 121 123
. 130
6.1 6.2 6.3 6.4 6.5 6.6
Mechanical properties of Aluminium alloy L114-T4 6082-T4 . . . . . 138 Dimensions and mechanical properties of the physical models . . . . . 138 Characteristics of C2A-06-125-lW-35 0 strain gauges . . . . . . . . . . 146 Characteristics of Instrumented impact hammer (model 086C01, PCB)148 Characteristics of Instrumented impact hammer (model 086C01, PCB)158 Resonance frequencies shear wave velocity and shear modulus of the soil deposit, assessed from the Power spectral functions . . . . . . . . 193
7.1 7.2
Estimated values for take-off displacement, yto . . . . . . . . . . . . p − multiplier amplitudes and comparison between measured and numerical undamped frequencies of the models . . . . . . . . . . . . Input parameters used in the pseudo-static analysis . . . . . . . . . Computed values of elastic lateral stiffness, Ki , and equivalent fundamental period, Teq . . . . . . . . . . . . . . . . . . . . . . . . . . p − multiplier amplitudes and comparison between measured and numerical undamped frequencies of the models . . . . . . . . . . . . p − multiplier amplitudes and comparison between measured and numerical undamped frequencies of the models . . . . . . . . . . . . Input parameters considered in the simplified analysis and computed maximum bending moments . . . . . . . . . . . . . . . . . . . . . .
7.3 7.4 7.5 7.6 7.7
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. 205 . 208 . 210 . 219 . 225 . 226 . 229
List of Figures 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19
Effects of liquefaction on acceleration seismic demand . . . . . . . . Schematic of capacity spectrum method (adapted from Fajfar et al. 1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elastic displacement response spectra recommended by EC8, Part 5, Annex A. (EC8 1998a) . . . . . . . . . . . . . . . . . . . . . . . . . Capacity curve (adapted from (El Naggar 2012)) . . . . . . . . . . .
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3
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5
. .
6 7
Schematic representation of forces acting at contacts between grains . Coulomb’s failure criterion . . . . . . . . . . . . . . . . . . . . . . . . Different dilatancy behaviour of sand with different degree of packing Typical behaviour of specimens of loose and dense sands tested in direct shear apparatus (redrawn after Casagrande 1975) . . . . . . . . Critical State Line (CSL). (a) q − p0 plane; (b) semi-log v − p0 plane . Undrained behaviour of loose and dense sands depicted in the state diagram (modified from Castro & Poulos 1977) . . . . . . . . . . . . Comparison of pre and post liquefaction behaviours of sand subjected to undrained monotonic loading . . . . . . . . . . . . . . . . . . . . . Simplified stress-strain curves for modelling post-liquefaction monotonic undrained behaviour . . . . . . . . . . . . . . . . . . . . . . . . Schematic of loading conditions acting on a typical pile-supported structure subjected to seismic-induced liquefaction. . . . . . . . . . . Beam on elastic foundation approach (Winkler 1867) . . . . . . . . . p − y for sand recommended by API 2000 . . . . . . . . . . . . . . . Initial coefficient of subgrade reaction versus relative density recommended by API 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . Coefficients C1 , C2 and C3 versus angle of internal friction recommended by API 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . Static p − y curve for soft clay recommended by API 2000 . . . . . . Cyclic p − y curve for soft clay recommended by API 2000 . . . . . . p − multiplier versus excess pore water pressure ratios for post liquefaction cyclic loading of sand (from Boulanger et al. 2003) . . . . . Values of p−multiplier versus (N 1)60 for liquefied p−y curves (modified from Brandenberg et al. 2007) . . . . . . . . . . . . . . . . . . . Undrained residual shear strength versus equivalent clean sand blow count (modified from Cubrinovski & Bradley 2008) . . . . . . . . . . p−y curves for liquefied soils according to p−multiplier and residual strength approaches (redrawn from Goh & O’Rourke 1999) . . . . . .
11 11 12
xvii
13 14 17 19 21 24 27 29 30 31 33 33 34 35 36 36
LIST OF FIGURES 2.20 p − y curves measured from dynamic centrifuge tests carried out by Boulanger et al. (2003). API curves are depicted in dotted lines . . . 37 2.21 Schematic of Dash’s method for scaling the p − y curves from stressstrain curve of the soil . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1 3.2
3.3 3.4 3.5 3.6
3.7 3.8
3.9
3.10 3.11 3.12
3.13
3.14
3.15
Map of Northern Italy and locations of epicentres of the earthquake sequence (http:/iside.rm.ingv.it/) . . . . . . . . . . . . . . . . . . . Italian seismic hazard map, in terms of peak ground acceleration (PGA) referred to horizontal ground and bedrock with return period of 475 years (Ordinanza PCM del 28 Aprile 2006 n.3519, All.1b . . Acceleration time histories of the mainshock and following aftershocks, recorded at Mirandola station on May 20th, 2012 . . . . . . Ground motion of the mainshock recorded at Mirandola station on 20th of May and associated power spectral densities . . . . . . . . . Particle acceleration trajectories computed from acceleration time history recorded on 20th May event . . . . . . . . . . . . . . . . . . Acceleration time histories of the 29th May event and associated power spectral densities for the North-South, East-West and vertical component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Particle acceleration trajectories computed from acceleration time history recorded on 20th May event . . . . . . . . . . . . . . . . . . Comparison between computed and predicted (by Italian Building Code (NTC 2008)) horizontal elastic response spectra (5% damping) for: (a) First mainshock (May 20, 2012); (b) Second mainshock (May 29, 2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison between computed and predicted (by Italian Building Code (NTC 2008)) vertical elastic response spectra (5% damping) for two main events . . . . . . . . . . . . . . . . . . . . . . . . . . . Locations of the surveyed site for liquefaction reconnaissance . . . . Cemetery of SantAgostino (Site 1). Large amount of ejected grey silty sand covered the pavement . . . . . . . . . . . . . . . . . . . . Cemetery of SantAgostino (Site 1). (a) Observed damages in the parking and external wall of located on the North-East side of the cemetery; (b) Typical sand boil observed at the site. See lens cap for scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evidence of liquefaction at San Carlo. (a) Site 2: courtyard covered by a 2 cm thick layer of ejected grey silty sand (location: Via Galileo Galilei); (b) Site 3: considerable amount of ejected sand covered the main roads of San Carlo (location: Via A. Gramsci) . . . . . . . . . Typical liquefaction induced damages observed in San Carlo. (a) Site 4: cracks on road pavement and relative settlements of footpath (location: Via A. Gramsci); (b) Site 5: Observed damage at footpath (location: Piazza Augusto Pola) . . . . . . . . . . . . . . . . . . . . Large soil fracture observed in San Carlo at Site 6. (a) Close-up of soil fracture and characteristic dimensions; (b) Grey silty sand flowed over the top surface confirming occurrence of liquefaction . . . . . .
xviii
. 41
. 43 . 46 . 47 . 48
. 49 . 50
. 52
. 53 . 54 . 55
. 56
. 57
. 58
. 59
LIST OF FIGURES 3.16 Preliminary results of liquefaction potential in the San Carlo Area (Site 7, A,B,C). The liquefaction potential is expressed in terms of Factor of Safety (FOS), which is evaluated by using the Eurocode 8 approach (EC8 1998b) and the simplified analysis by Idriss & Boulanger (2008)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.17 Typical manifestation of liquefaction occurrence at Mirabello. (a) Sand boil observed at Mirabello stadium, i.e. Site 10. (b) Uneven settlement of footpath and ejected grey silty sand observed at Mirabello stadium, i.e. Site 10 in Figure 3.10 . . . . . . . . . . . . . . . . . . . 3.18 Liquefaction induced damages observed on the main road (Corso Italia, i.e. Site 8) in Mirabello municipality; (a) buckled footpath caused by lateral spreading (b) Building declared unsafe due severe uneven settlement induced by the liquefaction of soil foundation . . . 3.19 Cathedral of San Paolo at Mirabello (Site 8). (a) Main building and bell tower of San Paolo Cathedral; (b) Detail of damaged faade of the Cathedral; (c) Photograph of San Paolo cathedral taken before the seismic sequence. (source: http://www.comune-italia.it/comunemirabello.html) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.20 Church in the suburb of Mirandola . . . . . . . . . . . . . . . . . . . 3.21 Estense fortress at San Felice sul Panaro . . . . . . . . . . . . . . . . Multi-stage cyclic triaxial apparatus (a) photograph of the apparatus used in this study; (b) schematic diagram of the triaxial apparatus . 4.2 Representation of geostatic stress condition existing in a soil element in the free-field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Mohr’s circle depicting the stress path of a soil element subjected to one-dimensional shaking (redrawn from Kramer 1996) . . . . . . . . 4.4 Stress conditions in the triaxial sample at different stages of the test 4.5 (a) Rubber membrane rolled over the split mould; (b) cone shaped funnel used during dry pluviation . . . . . . . . . . . . . . . . . . . 4.6 (a) Wooden mallet; (b) specimen kept together by a negative pressure of 10 kPa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 (a) triaxial cell mounted on the triaxial frame and filled by water; (b) loading frame is finally attached to the triaxial cell . . . . . . . . . 4.8 (a) Microscopic photographs of (a) Redhill 110; (b) Toyoura sand . 4.9 Particle size distributions for Redhill 110 and Toyoura sand. It has been also indicated the grain size distribution of liquefaction-prone sand according to Japanese Seismic Code for Harbor Structures . . 4.10 Loading path applied in the multi-stage cyclic triaxial test . . . . . 4.11 Typical effective stress path from of loose specimen of RedHill sand 110 (test ID: RH-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Typical behaviour of loose specimen of Redhill 110 sand (test ID: RH − 1) subjected to undrained cyclic loading. (a) Time history of excess pore water pressure ratio, ru , and axial strain, εa ; (b) Stressstrain hysteresis curve . . . . . . . . . . . . . . . . . . . . . . . . .
61
62
63
64 65 66
4.1
xix
. 70 . 72 . 73 . 75 . 76 . 77 . 78 . 79
. 80 . 82 . 84
. 85
LIST OF FIGURES 4.13 Typical effective stress path of dense specimen of Redhill sand 110 (test ID: RH-10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.14 Typical behaviour of dense specimen of Redhill 110 (test ID: RH-11) sand subjected to undrained cyclic loading. (a) Time history of excess pore water pressure ratio, ru , and axial strain, εa ; (b) Stress-strain hysteresis curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.15 Typical effective stress of loose sample of Toyoura sand (test ID: TY-4) 88 4.16 Typical behaviour of loose specimen of Toyoura sand (test ID: TY-4) sand subjected to undrained cyclic loading. (a) Time history of excess pore water pressure ratio, ru , and axial strain, εa ; (b) Stress-strain hysteresis curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.17 Typical effective stress path of dense sample of Toyoura sand (test ID: TY-11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.18 Typical behaviour of dense specimen of Toyoura sand (test ID: TY11) sand subjected to undrained cyclic loading. (a) Time history of excess pore water pressure ratio, ru , and axial strain, εa ; (b) Stressstrain hysteresis curve . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.19 Cyclic stress ratio versus number of cycles required to cause 5% of DA axial strain (a) Samples with Dr of 30 and 40%; (b) Samples with Dr of 50, 70 and 90% . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.20 Cyclic stress resistance versus relative density . . . . . . . . . . . . . 94 4.21 Post-liquefaction stress-strain responses and excess pore water pressure ratio versus axial strain obtained from samples of Redhill 110 sand subjected to undrained monotonic compression loading . . . . . 95 4.22 Comparison of post-liquefaction stress-strain responses, and excess pore water pressure ratio versus axial strain, obtained from samples of Redhill 110 sand consolidated at three different effective confining stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.23 Post-liquefaction stress-strain responses and excess pore water pressure ratio versus axial strain obtained from samples of Toyoura sand subjected to undrained monotonic compression loading . . . . . . . . 97 4.24 Comparison between idealised bi-linear model and typical post-liquefaction monotonic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.25 (a) Shear strain required to mobilise 1 kPa of shear stress, γto , versus relative densities; (b) Post-liquefied shear modulus G1 versus the relative density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.26 (a) Effects of relative density on post-liquefied shear modulus at large strains G2 ; (b) G2 /Gmax versus the relative density . . . . . . . . . . 101 4.27 Post-liquefaction undrained monotonic response in extension. (a) Redhill 110 sand (RH-11); (b) Toyoura sand (TY-4) . . . . . . . . . . 103 5.1 5.2
Schematic of soil mass subjected to horizontal shaking and representations of shear and normal stresses generated during shaking . . . . 109 Shear-beam idealisation of infinite lateral extent stratum overlying a bedrock subjected to one-dimensional shaking . . . . . . . . . . . . . 110
xx
LIST OF FIGURES 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18 5.19 5.20 5.21 6.1 6.2 6.3 6.4
Example of flexible model container used on the shaking table at the University of Bristol . . . . . . . . . . . . . . . . . . . . . . . . . . Laminar container used in the centrifuge available at the University of Cambridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic of wave propagation within a soil container having absorbing boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photograph of the shaking table and small geotechnical model container used for the experimental investigation . . . . . . . . . . . . Geotechnical model container used in the tests . . . . . . . . . . . . kN Instron 3343 K 2887 testing machine (model 3343) used for the mechanical characterization of the absorbing material . . . . . . . . Typical stress-strain behaviour obtained from compression tests . . Schematic of the instrumentation layout . . . . . . . . . . . . . . . Comparison of the transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC2 (output) and ACC-1 (input) . . . . . . . . . . . . . . . . . . . . . Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC3 (output) and ACC-1(input) . . . . . . . . . . . . . . . . . . . . . Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC4 (output) and ACC-1(input) . . . . . . . . . . . . . . . . . . . . . Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC5 (output) and ACC-1(input) . . . . . . . . . . . . . . . . . . . . . Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC7 (output) and ACC-1(input) . . . . . . . . . . . . . . . . . . . . . Comparison of transmissibilities relative to different boundary arrangements subjected to 0.5g acceleration, and estimated from signals recorded by accelerometers ACC-2 (output) and ACC-1(input) . . . Comparison of transmissibilities relative to different boundary arrangements subjected to 0.5g acceleration, and estimated from signals recorded by accelerometers ACC-5 (output) and ACC-1(input) . . . Steel ’Channel’ sections employed for the construction of container . Close-up of connections between ’channel’ sections and bottom steel plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rubber matting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geotechnical model container used in the shaking table program . . Geotechnical model container mounted on the shaking table . . . . Pile-supported structure models . . . . . . . . . . . . . . . . . . . . Steel plates bolted on the wood base . . . . . . . . . . . . . . . . . Installation of SP1 model into steel plates attached to the bottom wood base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xxi
. 111 . 112 . 115 . 117 . 118 . 119 . 120 . 122
. 124
. 125
. 126
. 127
. 128
. 129
. 129 . 131 . 132 . 132 . 133 . 137 . 138 . 139 . 139
LIST OF FIGURES 6.5 6.6 6.7
6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 6.18 6.19 6.20 6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28 6.29 6.30 6.31
(a) Dry pluviation apparatus; (b) Pluviation of dry sand into the soil container . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Plan view and cross section of physical models and instrumentation layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 SETRA accelerometers: (a) SETRA mounted on the pile cap of model SP1; (b) SETRA accelerometers mounted on the shaking table for monitoring input motion . . . . . . . . . . . . . . . . . . . . . . . . . 144 Close-up of ADXL chip mounted on the breakout board . . . . . . . . 145 Construction of new casing for MEMS accelerometer . . . . . . . . . 146 Example of C2A-06-125-lW-350 strain gauge mounted on the aluminium tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 RDP 628-type strain gauge amplifier modules mounted on the RDP 600 rack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Positioning of PPT during dry pluviation . . . . . . . . . . . . . . . . 148 : (a) Instrumented impact hammer model 086C01; (b)Kistler (model 5134A) power supply/coupler . . . . . . . . . . . . . . . . . . . . . . 149 Impact test carried out on model GP1 before saturation of soil deposit150 Application of white noise excitation in three different phases and corresponding excess pore water pressure ratios . . . . . . . . . . . . 152 Factors of safety against liquefaction achieved in the three stages of the shaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Flow chart illustrating the modal analysis procedures used for the assessment of the modal parameters . . . . . . . . . . . . . . . . . . . 156 Results from free vibration tests of model SP1 . . . . . . . . . . . . . 159 Results from free vibration tests of model SP2 . . . . . . . . . . . . . 160 Results from free vibration tests of model GP1 . . . . . . . . . . . . . 161 Results from free vibration tests of model GP2 . . . . . . . . . . . . . 162 Frequency response functions, both measured and fitted estimated for model SP1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Frequency response functions, both measured and fitted estimated for model SP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Frequency response functions, both measured and fitted estimated for model GP1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Frequency response functions, both measured and fitted estimated for model GP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Variation of natural frequency and damping ratios of the four physical models subjected to a white noise input . . . . . . . . . . . . . . . . . 169 Acceleration time histories recorded on the pile caps of the four models170 Response of model SP1 expressed in terms of acceleration, velocity and displacement time histories . . . . . . . . . . . . . . . . . . . . . 171 Response of model SP2 expressed in terms of acceleration, velocity and displacement time histories . . . . . . . . . . . . . . . . . . . . . 172 Response of model GP1 expressed in terms of acceleration, velocity and displacement time histories . . . . . . . . . . . . . . . . . . . . . 173 Response of model GP2 expressed in terms of acceleration, velocity and displacement time histories . . . . . . . . . . . . . . . . . . . . . 174 xxii
LIST OF FIGURES 6.32 Bending moment time histories recorded along instrumented pile of model SP1 and acceleration time histories recorded on the model pilecap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.33 Bending moment time histories recorded along instrumented pile of model SP2 and acceleration time histories recorded on the model pilecap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.34 Bending moment time histories recorded along instrumented pile of model GP1 and acceleration time histories recorded on the model pile-cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.35 Bending moment time histories recorded along instrumented pile of model GP2 and acceleration time histories recorded on the model pile-cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.36 Maximum bending moment envelope recorded in model SP1 . . . . . 6.37 Maximum bending moment envelope recorded in model SP2 . . . . . 6.38 Maximum bending moment envelope recorded in model GP1 . . . . . 6.39 Maximum bending moment envelope recorded in model GP2 . . . . . 6.40 Schematic of laterally loaded pile and Beam on Elastic Foundation idealisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.41 Acceleration, velocity and displacement time histories recorded by MEMS accelerometer embedded in the soil layer (a) measured at 1000 mm from soil surface; (b) measured at 600 mm from soil surface . . . 6.42 Power spectral density (PSD) evaluated during Phase 1 from data recorded on the table and in the soil (a) 1 m depth; (b) -0.6 m depth 6.43 Power spectral density (PSD) evaluated during Phase 2 from data recorded on the table and in the soil (a) 1 m depth; (b) -0.6 m depth 6.44 Power spectral density (PSD) evaluated during Phase 3, before liquefaction, from data recorded on the table and in the soil (a) 1 m depth; (b) -0.6 m depth . . . . . . . . . . . . . . . . . . . . . . . . . . 6.45 Power spectral density (PSD) evaluated during Phase 3, after liquefaction, from data recorded on the table and in the soil (a) 1 m depth; (b) -0.6 m depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.46 Computed acceleration response spectra estimated before and at full liquefaction obtained considering an average damping ratio of the models of 3% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.47 Computed velocity response spectra estimated before and at full liquefaction obtained considering an average damping ratio of the models of 3% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.48 Computed displacement response spectra estimated before and at full liquefaction obtained considering an average damping ratio of the models of 3% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 7.2
7.3
177
178
179
180 181 182 183 184 185
188 189 190
191
192
196
198
199
Numerical models used in the analysis . . . . . . . . . . . . . . . . . 202 Typical p − y curves used in the numerical analysis; (a) Schematic of p − y curves obtained from different methods; (b) Examples of proposed p − y curves computed for different numerical models . . . . 206 Pseudo acceleration computed for different damping ratios . . . . . . 210
xxiii
7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19
Numerical models used in the pseudo-static analysis during the transient conditions and computed bending moment profiles . . . . . . . . Comparison of computed and measured maximum bending moments during the transient to liquefaction . . . . . . . . . . . . . . . . . . . Comparison of computed and measured maximum moments in the pile at full liquefaction condition . . . . . . . . . . . . . . . . . . . . . Comparison of the pushover curves obtained for model SP1 . . . . . . Comparison of the pushover curves obtained for model SP2 . . . . . . Comparison of the pushover curves obtained for model GP1 . . . . . Comparison of the pushover curves obtained for model GP2 . . . . . Comparison of acceleration displacement spectra response computed during transient and full liquefaction condition . . . . . . . . . . . . . Capacity spectrum method computed during transient to liquefaction Capacity spectrum method computed during transient to liquefaction Capacity spectrum method computed at full liquefaction by using p − multiplier method . . . . . . . . . . . . . . . . . . . . . . . . . . Reduction of natural frequency as a function of the excess pore water ratio ru . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Increase of damping ratio as a function of the excess pore water pressure ratio ru . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic cantilever idealization for condition prior and at full liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison between computed and experimental bending moment developed before the onset of full liquefaction . . . . . . . . . . . . . Comparison between computed and experimental bending moment developed at full liquefaction . . . . . . . . . . . . . . . . . . . . . . .
xxiv
211 212 213 215 216 217 218 220 221 222 223 224 227 228 230 231
Chapter 1 Introduction 1.1
Outline of the chapter
This chapter provides an introduction to the research presented in this thesis, namely effects of seismically-induced liquefaction on the dynamic behaviour of pilesupported structures. The scope of the present research and the organization of the thesis are also presented.
1.2
Introduction
One of the critical aspects of any seismic design is represented by the assessment of the seismic demand imposed by the earthquake on the structure. The current seismic design codes are based on the assumption that the action exerted by an earthquake can be realistically represented by an equivalent static force (i.e. base shear force) that is proportional to the mass of the structure and the acceleration imposed by the earthquake shaking. This type of approach, which is also referred to as force-based design, requires firstly the assessment of the dynamic properties of the structure, namely fundamental period and damping ratio. Subsequently these are employed for the calculation of the pseudo acceleration by means of an idealised response acceleration spectrum which can also take into account any site-amplification effects induced by the presence of soft soil deposits and inelastic structural response. Furthermore, the current seismic codes recognise that the role of soil-structure interaction (SSI) may also have detrimental effects on the seismic response. For example, Eurocode 8 Part 5, Annex D (EC8 1998a) states: ‘For the majority of common building structures, the effects of SSI tend to be beneficial, since they reduce the bending moments and shear forces in the various members of the superstructure. For the structures listed in Section 6 the SSI effects might be detrimental’. 1
1. Introduction The structures listed in Section 6 of Eurocode 8, Part 5 are (EC8 1998a): • Where P-delta (2nd order) effects play a significant role; • Structures with massive or deep-seated foundations, such as bridge piers, offshore caissons, and silos; • Slender tall structure, such as towers and chimneys; • Structure supported on very soft soils, with average shear wave velocity, Vs , max less than 100 m/s, such as soils in ground type S1 (Deposits consisting or containing a layer at least 10 m thick of soft clays/silts with high plasticity index (PI>40) and high water content). It should be pointed out that these recommendations are in contrast with the past misconception that considered the effects induced by soil-structure interaction always beneficial since they lead to a reduction in spectral accelerations and, on this basis, they may be safely neglected in the design process. In addition, the role of damping on the SSI can be very important as correctly addressed by the EC8, which recommends that ‘damping should be considered as an additional ground property in the cases where effects of soil-structure interaction are to be taken into account’, and ‘internal damping, caused by inelastic soil behaviour under cyclic loading and radiation damping, caused by seismic waves propagating away from the foundation, should be considered separately’. Over the past decades, significant improvements have been made in the field of earthquake engineering and new recommendations have been gradually introduced in the design codes. However, despite the extensive research, the effects of soil liquefaction on the seismic performance of pile supported structures are still uncertain and vaguely addressed by many seismic codes. For example the Eurocode 8, Part 5, Section 5.4.2 states (EC8 1998a): ‘The side resistance of soil layers that are susceptible to liquefaction or to substantial degradation shall be ignored’. This may suggest that the fundamental period required for the assessment of the pseudo acceleration should be calculated assuming that the structure behaves as a free-standing system for the entire depth of liquefaction. Based on this assumption, the fundamental period of the structure would increase considerably as the soil liquefies. In addition, it has been also recognised that the damping ratio at full liquefaction may increase up to values higher than 20%. Evidently, the combined effect of lengthening in period and increase in damping ratio caused by liquefaction would have an important repercussion on the assessment of the seismic demand. In fact, as schematically illustrated in Figure 1.1, considering 2
1. Introduction the shape of the acceleration response spectra suggested by current codes, the spectral acceleration that the structure would experience during soil liquefaction could be significantly lower than that experienced prior to the onset of liquefaction. This result suggests that, in a conventional force-based design approach, the reduction in acceleration demand would reduce the seismic demand imposed on the structure. Therefore, based on these observations, the occurrence of liquefaction phenomena may have beneficial effects in a conventional force-based design approach. It is noted that the above considerations are made on the assumption that the soil deposit has a level ground surface and it is not subjected to severe lateral deformation (i.e. lateral spreading phenomena) that are likely to occur in gently sloping areas or in proximity to free-surfaces.
Before liquefaction T1
Liquefaction
1
KRot.
Acceleration Response Spectra
KLat.
T1
T2
1
2
T2
1
2
2
T1
T2
Fundamental period
Figure 1.1: Effects of liquefaction on acceleration seismic demand However, collapse and/or severe damage of pile supported structures are still observed in liquefiable soils after major earthquakes (Bhattacharya et al. 2011, My3
1. Introduction lonakis et al. 2006, Bhattacharya 2006, Tokimatsu & Asaka 1998, Hamada 1992, Yoshida & Hamada 1991). Most design codes employ large factors of safety against both gravity and inertia loads, yet the occurrence of pile failures as a consequence of liquefaction phenomena evidently contradict the above mentioned consideration, i.e. liquefaction reduce the the seismic demand imposed by the earthquake. The above considerations suggest that it might be questionable whether the safety of the structure should be assessed in terms of strength, or in other words ultimate bending moment and shear force, of the various elements of the structure. Therefore, one of the main arguments of this thesis is represented by the need to change the attention from ‘strength’ to ‘performance’ especially when liquefaction is likely to occur as consequence of the earthquake. This is also pointed out by Priestley (2003), who stated: ‘increasing the strength does not automatically improve safety at the design level of seismic response. If strength increase is obtained merely by increasing the flexural reinforcement ratios while keeping member dimensions constant, then the displacement capacity of the structure will actually decrease as the strength increases, as a result of reduced ultimate curvature capacity. Since displacement capacity is more fundamental to damage control than is strength, it was argued that safety may well be improved by reducing, rather than increasing strength... It is generally accepted that damage can be related to material strain, and that material strains can be related to maximum response displacement, but not to response acceleration. It would thus seem important for design procedures to emphasize the importance of estimating peak displacement response’. Although different parameters can be used to describe the seismic performance, it has been recognised that the structural behaviour of any structure can be fully identified in terms of four quantities, namely, stiffness, strength, displacement and ductility (Fajfar et al. 1999). Generally, in a conventional design approach, two of these quantities are considered as input parameters whereas the remaining two can be estimated from the design. It is noted that the various design approaches select different input quantities. For example in a typical force-based design approach, the input quantities are represented by the stiffness (in the form of fundamental period) and ductility (or damping ratio). These are subsequently used for the assessment of the base shear force from which the strength and displacement experienced by the structure can be determined. However, in recent years, alternative design approaches are emerging. One of the most promising is the displacement performance-based design. This considers as input parameters displacement and ductility of the structure and output of the
4
1. Introduction
Spectral acceleration
design strength and stiffness (i.e. fundamental period). Differently from the forcebased design, which can be also interpreted as a strength-based design approach, in a displacement-based design approach the performance of the structure is commonly estimated in the form of displacement capacity. Specifically, the performance of the structure can be graphically predicted by comparing the capacity of the structure with the demand imposed by the earthquake. The intersection of the two curves approximates the response and performance of the structure for that earthquake (Freeman 1998). This graphical procedure is generally referred to as Capacity Spectrum Method (Freeman et al. 1975, Freeman 1998). A typical capacity spectrum method has been schematically depicted in Figure 1.2, in which the horizontal axis plots the spectral displacement and the vertical axis the spectral acceleration whereas the radial lines from the origin denote the fundamental periods.
demand spectrum
acceleration demand & capacity
capacity spectrum (from pushover curve)
displacement demand
displacement capacity
Spectral displacement
Figure 1.2: Schematic of capacity spectrum method (adapted from Fajfar et al. 1999) The seismic demand can be conveniently represented by displacement response spectra of the earthquake under consideration Freeman (1998). It should be pointed out that in the displacement response spectra, the spectral displacement increases progressively in the medium and long period range. For example, Figure 1.3 shows the elastic response spectra recommended by Eurocode 8 (EC8 1998a). It is noted 5
1. Introduction
Spectral displacement
that TE ranges between 4.5 and 6 s depending on the ground type. As a consequence of this, the lengthening of the period experienced by the structure during soil liquefaction may lead to a significant amplification of the seismic demand in the form of spectral displacement. In conclusion, such an approach would appropriately consider the detrimental effects induced by liquefaction phenomena.
TB TC
TD
TE
TF Fundamental period
Figure 1.3: Elastic displacement response spectra recommended by EC8, Part 5, Annex A. (EC8 1998a) The capacity of a structure can be conveniently expressed in the form of base shear force versus top displacement obtained from a standard non-linear static analysis (i.e. pushover). However, it should be pointed out that in order to plot the pushover curve in the capacity spectrum shown in Figure 1.2, the base shear force needs to be converted into spectral acceleration by using the mass of the structure as scaling factor. The pushover analysis is also advocated by Eurocode 8 for verifying the structural performance of newly designed and of existing buildings (i.e. EC8, Part 1, Section 4.3.3.4.2; (EC8 1998a)). In addition to this, results from pushover analysis can be also employed to represent the different performance levels for seismic design as illustrated in Figure 1.4.
6
1. Introduction
Base shear force
CAPACITY CURVE Non-structural damage
Structural damage
Collapse
Elastic limit
Top displacement Figure 1.4: Capacity curve (adapted from (El Naggar 2012))
1.3
Scope of the present research
This research aims to investigate the dynamic behaviour of pile-supported structures during seismically-induced liquefaction phenomena considering different perspectives and looking at different scales of analysis. The main objectives of the present research can be summarised as follows: • To carry out a comprehensive literature review on the undrained behaviour of cohensionless soils before and after the onset of liquefaction; • To review the current understanding of pile failures during liquefaction phenomena; • To review simplified approaches for modelling dynamic soil-structure interaction; • To examine the mechanism governing the onset of liquefaction in the real field; • To characterise, by means of multi-stage cyclic triaxial tests, pre and post liquefaction behaviours of two silica sands, namely Redhill 110 and Toyoura sand; • To investigate the dynamic response of a soil container for geotechnical physical modelling with absorbing boundaries, which consisted of conventional foams; 7
1. Introduction • To quantify the amount of energy dissipated by different artificial boundaries and select the optimum foam to be used in the subsequent experimental tests; • To perform a series of shaking table tests at normal gravity, which aim to investigate the dynamic performance of four physical models. The models comprise two single piles and 2 × 2 pile groups; • To assess the variation of the natural frequency and damping ratio of the models at different stages of excess pore water pressure generation and ultimately at full liquefaction condition (i.e. excess pore water pressure equals to in-situ vertical effective stress); • To quantify the seismic response of the models in terms of acceleration, velocity and displacement responses and maximum bending moment envelopes along the piles; • To develop a simplified numerical models using a new set of p − y curves, which model the soil-structure interaction according to the widely used beam on nonlinear Winkler foundation approach (Winkler 1867); • To study the effects of soil liquefaction on the seismic demand exerted on the models.
1.4
Organization of the thesis
The present thesis is divided into 8 chapters. After the introduction to the subject of the present study, the chapters are divided as follows: Chapter 2 provides background of the research presented in this thesis. Chapter 3 reports a field investigation carried out in the areas affected by liquefaction phenomena observed after the 2012 Northern Italy earthquake sequence. Chapter 4 presents an experimental investigation conducted by means of multi-stage cyclic triaxial tests, which aims to study resistance to liquefaction and post-liquefaction behaviours of two silica sands, namely: Redhill 110 and Toyoura sands. Chapter 5 identifies the main requirements for an ideal geotechnical model container and presents results from an experimental study performed to investigate the effects of different boundary arrangements on the dynamic response 8
1. Introduction of the soil deposit. Finally, the chapter describes the development of the goetechnical model container used in the subsequent shaking table tests. Chapter 6 presents an experimental investigation conducted at normal gravity on small scale models representing typical pile-supported structures. These consisted of two single piles and two 2 × 2 pile-groups tested on a shaking table. The experimental results provide valuable insights into the variation of natural frequency and damping ratio at different stages of excess pore water pressure generation. In addition, the seismic performance of each model is identified for conditions before and after the onset of liquefaction. Chapter 7 presents a series of numerical analyses that aim to compare the seismic responses observed in the shaking table tests with results obtained by using conventional procedures, which are commonly used in the seismic practice. Chapter 8 summarises the findings obtained from the present study and identifies areas for future research.
9
Chapter 2 Literature Review 2.1
Outline of the chapter
This chapter provides background of the research presented in this thesis. In particular, Section 2.3 discusses the main features concerning the undrained behaviour of cohesionless soils prior and after soil liquefaction. Section 2.4 presents state-of-theart in designing pile-supported structures in liquefiable soils. Section 2.5 reviews the main approaches used to model the Dynamic Soil-Structure Interaction (DSSI) and the different methods for constructing p − y curves for DSSI. Finally, Section 2.6 draws the main conclusions.
2.2
Introduction
The dynamic response of pile-supported structures during liquefaction phenomena is strongly affected by the behaviour of soil deposits that support them. Since seismically-induced liquefaction occurs in saturated sandy soils subjected to repetitive loading, this section focuses mainly on the undrained behaviour of cohesionless soils. Before reviewing the main aspects concerning the undrained behaviour of sands, it should be pointed out that, the strength of cohesionless materials is controlled by friction and relies upon the forces transmitted from grain to grain as schematically illustrated in Figure 2.1.
2.3
Undrained behaviour of cohesionless soils
In friction materials failure occurs in the form of relative sliding along internal surfaces, and the failure criterion can be expressed according to the Coulomb’s law
10
2. Literature Review given by Equation (2.1), which has been also graphically illustrated in Figure 2.2. τ = σ 0 tanφ0
(2.1)
Figure 2.1: Schematic representation of forces acting at contacts between grains
= ' tan ' 1
'
'
1
3
tan '
'
Figure 2.2: Coulomb’s failure criterion It has been recognised that the behaviour of cohesionless soils is determined by dilatancy, which according to Reynolds (1885) describe the tendency of soils to change volume while shearing. This tendency is influenced by the degree of packing of particles which, in geotechnical engineering, is commonly expressed in terms of void ratio, e, or relative density, Dr . As schematically illustrated in Figure 2.3, loose and dense sands exhibit different behaviours. Specifically, loosely packed sands exhibit a contractive behaviour during 11
2. Literature Review shearing. Conversely, dense sands tend to expand since the particles are so densely packed that change in volume can occur only with loosening up of the fabric.
shear
shear
dense
loose
compression
volume change
loose
shear dense
dilation
Figure 2.3: Different dilatancy behaviour of sand with different degree of packing Typical behaviours of specimens of both loose and dense sands tested in direct shear apparatus have been depicted in Figure 2.4. It can be observed that, at large strains, both specimens reached an ultimate condition in which shearing occurred at constant volume or constant effective stress ratio.
12
Void ratio
Shear stress
2. Literature Review
dense sand
contractive soils (loose sand)
critical void ratio ultimate strength
loose sand
dilative soils (dense sand)
Shear strain
Shear strain
Figure 2.4: Typical behaviour of specimens of loose and dense sands tested in direct shear apparatus (redrawn after Casagrande 1975) This ultimate condition corresponds to the Critical State defined by Roscoe et al. (1958) as the state in which the ‘soil continues to deform at constant stress and constant void ratio’. The value of void ratio exhibited by the soil at the Critical State is generally referred to as critical void ratio, ecr , after Casagrande (1936). In this thesis, the geotechnical behaviour of soils is described according to the Critical State Soil Mechanics (CSSM) framework (Schofield & Wroth 1968). However, it is also important to point out that several studies (Riemer & Seed 1997, Verdugo & Ishihara 1996, Murthy et al. 2007) have confirmed that the CSSM can be considered equivalent to the Steady State concept as defined by Poulos (1981). According to the Critical State framework, any state of soil can be described in terms of: specific volume, v=(1+e), and two invariant stress parameters, namely, deviator stress, q and effective mean principal stress, p0 . In triaxial condition, i.e. equality between intermediate, σ20 , and minor principal stresses, σ30 , the stress invariant can be expressed as follows: q = σ10 − σ30 , and p0 =σ10 + 2σ30 /3, where σ10 denote the major principal stress. The locus identified by the combinations of q, v and p0 at Critical State is referred to as Critical State Line (CSL), which, in the q − p0 and v − p0 planes, is given by Equation (2.2) and (2.3) respectively. q = Mcr p0
(2.2)
v = Γ − lnp0
(2.3)
where Mcr is a friction parameter that can be expressed by Equation (2.4), Γ is the 13
2. Literature Review specific volume at the reference p0 = 1 kPa and λ is a soil parameter. Mcr =
6sinφ0cr 3 − sinφcr
(2.4)
It has become customary to plot the Critical State Line (CSL) as a double line as represented in Figure 2.5. v
q
C
Lin e t ta M lS a c 1 riti
G
e
Cr
itic a
-
lS ta te
1
p'
1 kPa
(a)
Li ne
ln p'
(b)
Figure 2.5: Critical State Line (CSL). (a) q − p0 plane; (b) semi-log v − p0 plane Before setting out upon the main features concerning the response of cohesionless soils subjected to cyclic loading, it is important to clarify that in the geotechnical engineering terminology (as in this thesis), the term ‘cyclic loading’ will be used to refer to a combination of non-static repetitive loading applied ‘rapidly’ to the soil. In this condition, the behaviour of soil is rate dependent and strongly affected by the drainage patterns. Furthermore, due to the application of ‘fast’ loading, the excess pore water pressures are not able to dissipate therefore the behaviour of the soil can be considered undrained. In loose to medium dense sands, the application of undrained cyclic loading induces a reduction in volume that cannot be followed by an equivalent outflow of water. Hence, the forces between grains will be partially or entirely transferred to the water. Furthermore, for the equilibrium between total load and stress, the reduction in effective stresses must be equivalent to the increment of excess pore water pressure. Ultimately this phenomenon may lead to a significant reduction in friction resistance, i.e. shear strength, and it has been commonly referred to as liquefaction.
14
2. Literature Review
2.3.1
Liquefaction
To the best of author’s knowledge, the term liquefaction was first introduced by Hazen (1920), to describe the collapse of the Calaveras Dam in California, which slipped during its construction in 1918. In the paper presented by Hazen (1920) to the American Society of Civil Engineers (ASCE), which is also reported by Seed (1984), the author explained that the collapse was caused by a sudden increase in pore water pressure, specifically Hazen (1920) wrote: ‘...when a granular material has its pores completely filled with water and is under pressure..., the pressure of the water on the particles tends to hold them apart; and part of the pressure is transmitted through the water. To whatever extent this happens the pressure transmitted by the edges and points of the particles is reduced. As water pressure is increased, the pressure on the edges is reduced and the friction resistance of the material become less. If the pressure of the water in the pores is great enough to carry all the load it will have the effect of holding the particles apart and of producing a condition that is practically equivalent to that of quicksand...The condition of quicksand lasts for only few seconds until the surplus water can find its way out. When this happens the grains again come to solid bearings and stability is restored’. The author continued that: ‘The thought has occurred to the writer, in looking at the material that slid in the Calaveras Dam, that something of this kind may have happened on a large scale - 800,000 cu.yd. of fill flowed for a brief space and then became solid... It may be that after the first movement there was some readjustment of the material in the toe which resulted in producing temporarily this condition of quicksand, and which destroyed for a moment the stability of the material and facilitated the movement that took place... This will not account for the initial movement, but the initial movement of some part of the material might result in the accumulating pressure, first on the point and then on another, successively, as the early points of concentration were liquefied and in that way a condition comparable to quicksand in a large mass may have been produced’. Although the description given by Hazen (1920) referred to a phenomenon occurred in absence of any earthquake shaking, the author clearly identified the main features occurring during soil liquefaction, namely, development of excess pore water pressure and reduction in effective stresses. Over the past years, the term liquefaction has been used to indicate phenomena wherein saturated sand experience a significant softening behaviour as a consequence of generation of excess pore water pressure due to monotonic or cyclic loading applied in undrained condition (i.e. constant volume). This phenomenon can be explained by considering the Principle of effective stress expressed by Equation (2.5), which defines the decomposition of total stress, σo , into 15
2. Literature Review effective stress, σo0 and pore water pressure, u (Terzaghi 1923). σo = σo0 + u
(2.5)
According to the Principle of effective stress, a reduction in effective stress due to pore water pressure development may lead to a significant reduction in shear strength of the soil. The onset of liquefaction occurs when soils subjected to either monotonic or cyclic loading undergo large strains thus tend toward the Critical State (or Steady State). It has become customary to represent the locus of the void ratios at the Critical State (i.e. critical void ratio, ecr ) for different effective minor principal stresses, σ30 . This is generally referred to as Critical Void Ratio (CVR) line (or Steady State Line according to Castro & Poulos 1977). Considering the state diagram illustrated in Figure 2.6, it can be observed that the CVR line also defines the boundary between contractive and dilative behaviours. Specifically, loose sands have void ratios higher then ecr and thus are located above the CSL. Conversely, dense sands have void ratios lower than ecr , therefore in the state diagram they are positioned below the CVR line. The different behaviour exhibited by loose and dense sands is employed to introduce two different phenomena associated with soil liquefaction, namely flow liquefaction and cyclic mobility. Flow liquefaction is a phenomenon that occurs in loose sands with residual strength (i.e. strength at large strains) lower than the strength required to maintain static equilibrium (Kramer & Elgamal 2001). The flow liquefaction occurs when the soil exhibits contractive behaviour under undrained shearing with consequent development of pore water pressure. This is represented in the state diagram in Figure 2.6, by the stress path connecting point C to A. At point A, if the soil is subjected to further shearing, it deforms along the critical state line at constant void ratio and σ30 until it reaches the condition of zero effective stresses corresponding to the onset of liquefaction. The term cyclic mobility was first introduced by Casagrande in 1969, and as reported by Castro & Poulos (1977), it indicated the progressive softening of a saturated sand specimen when subjected to cyclic loading at constant water content. In fact, as already mentioned, the application of cyclic loading to specimens of dense sand causes the generation of excess pore water pressure thus the reduction in effective stresses. This phenomenon has been depicted in the state diagram in Figure 2.6, by the passage from point D to B. Conversely, in the presence of monotonic loading, specimens of dense sands tend to move horizontally towards the CSL as shown by the stress path defined by points D and E. 16
2. Literature Review
Void ratio, e
w flo ction efa
liqu
Q
C
A
cyclic mobility D B
contractive soils (loose sand)
E
monotonic cyclic loading
Critical Void Ratio (CVR) Line dilative soils (dense sand)
Effective minor principal stress,
'
3
Figure 2.6: Undrained behaviour of loose and dense sands depicted in the state diagram (modified from Castro & Poulos 1977) It can be recognised that the development of excess pore water pressure is an important factor influencing both flow liquefaction and cyclic mobility. Over the past years, it has become customary to relate the excess pore water pressure to the 0 . effective overburden stress through the excess pore water pressure ratio, ru =∆u/σvo The condition in which the excess pore water pressure reaches the overburden effective stress (i.e. ru =1) has been referred to as initial liquefaction after Seed & Lee (1966) or simply liquefaction by Ishihara (1993). It should be pointed out that the condition ru =1 corresponds to the state in which the forces at the contact between the grains are practically zero, so as the strength and stiffness of the soil, which may lead to sizeable amount of deformation especially in loose sands. In dense sands, the condition ru =1 is generally only momentarily reached although a considerable softening occurs in the soil. This phenomenon corresponds to the cyclic mobility defined earlier.
2.3.2
Undrained post-liquefaction
Over the past 50 years, soil liquefaction has been extensively studied particularly to determine the liquefaction potential of cohesionless soils. It has been recognised that the resistance of sands to liquefaction is influenced by a number of factors such as initial relative density (Tatsuoka et al. 1986, Seed 1979, Finn 1981, Riemer & Seed 17
2. Literature Review 1997), confining pressure (Murthy et al. 2007, Georgiannou et al. 2008), presence of static shear stress (Lee & Seed 1967, Yoshimi & Oh-Oka 1975, Vaid & Finn 1979, Vaid & Chern 1983, Mohamad & Dobry 1986, Hyodo et al. 1994, Vaid et al. 2001), specimen preparation method (Ladd 1974, Miura & Tuki 1982, Ibrahim & Kagawa 1991) and shaking characteristics such as intensity of the shaking and number of cycles. Despite extensive research in the field of seismic liquefaction, only limited studies focused on the post-liquefaction behaviour of sands under undrained conditions. One of the pioneering work was published by Seed (1979), and concentrated on the post-earthquake stability of dams in liquefiable deposits. Seed (1979) observed that in loose to medium dense saturated sands, development of excess pore water pressure resulting from cyclic loading led to sudden loss of shear strength. However, with further shearing, samples exhibited a significant resistance to deformation and gradually recovered part of their initial strength and stiffness. Later studies carried out by Yoshida et al. (1994) and Kiku & Tsujino (1996), confirmed this strainhardening behaviour, which was to contrast with the usual softening response of soils undergoing large strains. Studies presented by Thomas (1992) and Vaid & Thomas (1995), suggest that the post-liquefaction behaviour of sands subjected to undrained monotonic loading is always dilative even though samples exhibited contractive response before the onset of liquefaction. As a consequence, the hardening behaviour observed at large strains (see Figure 2.7) could be associated with the dilative response of soils subjected to undrained monotonic shearing. In fact, as sands dilated, the excess pore water pressures gradually dissipated which in turn led to an increase in effective stresses. Despite the tendency to dilate, Yasuda et al. (1994) noted that a considerable amount of strength mobilised only beyond a certain value of strain (threshold strain) that was referred to as reference strain at the transformation point.
18
2. Literature Review
typical undrained behaviour of loose sand
Deviator stress, q
undrained post-liquefaction behaviour
E1 1
E2
E1 > E2
1
Axial strain,
a
Figure 2.7: Comparison of pre and post liquefaction behaviours of sand subjected to undrained monotonic loading The amplitude of this threshold strain was found to increase with decreasing relative density, severity of the earthquake and fines content, but it also decreased at higher confining pressures. Over the past years, several models have been proposed to represent the undrained post-liquefaction behaviour. To the author’s knowledge, the first simplified model was described by Thomas (1992) and Vaid & Thomas (1995). This consisted of a stress-strain curve made of three different regions (see Figure 2.8). An initial region characterised by low stiffness and strength that spans from zero up to the axial strain required to mobilise 5 kPa of deviator stress. This region is characterised by very small stiffness and its size decreased with an increase in the relative density. A second region is defined by a parabolic stress-strain pattern, which resulted in a gradual increase in stiffness and strength with strains. A third region is characterised by a linear stress-strain relationship with a slope, i.e. stiffness, function only of the initial relative density for medium-to-dense specimens and dependent also on the confining pressure for loose ones. A different model was described by Yasuda et al. (1995), in which the stress-strain relationship was replaced by two linear stress patterns that modelled the low and higher stiffness responses observed at small and large strains respectively (see Figure 2.8). Sivathayalan & Vaid (2004) investigated the post-liquefied behaviour of in-situ frozen samples of sand. The experimental results confirmed that the undrained post-liquefaction be-
19
2. Literature Review haviour was characterised by dilation and strain-hardening response despite the fact that specimens showed a contractive and strain-softening behaviour during the application of cyclic loading. Based on the experimental results, the authors confirmed that the stress-strain relationship became practically linear at large strains, and its slope was a function of the initial relative density of the samples.
20
Deviator stress
2. Literature Review
Region II Region III
Region I
linear increase parabolic increase
5kPa
essential zero stiffness
axial strain
hig
hs
tiff ne
ss
Shear stress
(Thomas, 1992)
ess low stiffn
shear strain
Shear stress
Yasuda et al. (1995)
max
G2 take-off strain
1kPa
1
to
G1
1.25 to
shear strain
Dash (2010) Figure 2.8: Simplified stress-strain curves for modelling post-liquefaction monotonic undrained behaviour
21
2. Literature Review Dash (2010) proposed a simplified monotonic stress-strain curve to simulate the post-liquefaction behaviour of cohesionless soils (see Figure 2.8). The construction of the stress-strain relationship required four parameters, namely: (i) Take-off strain, γto : shear strain required to mobilise 1kPa of shear stress (ii) Initial shear modulus, G1 : shear modulus at low strains, which according to the definition of Take-off strain can be estimated as 1/γto (in kPa) (iii) Critical state shear modulus G2 : the post-liquefied shear stiffness at large strains, which can be assessed from the preliquefied shear modulus at small strains, Gmax ; (iv) Maximum shear stress, τmax : theoretical maximum possible value of shear stress, which corresponds to the case of absolute vacuum. Differently from previous works, Ashour et al. (2009) introduced a new formulation to predict the undrained post-liquefaction behaviour of sands from their drained response. This model was originally elaborated by Norris et al. (1997) and later modified by Ashour & Norris (1999) and it required as inputs standard soil parameters such as: relative density, effective angle of internal friction, roundness of the grains and drained axial strain at 50 per cent of stress level. Other studies available in the literature focused on different aspects of the postliquefaction response of sands. Shamoto et al. (1997, 1998) introduced a novel approach to evaluate the post-liquefaction shear strain. This was established on the physical basis that the post-liquefaction shear deformation in saturated sand was dictated by two types of strains due to dilatancy, namely, irreversible and reversible dilatancy strains. The shear strain was finally expressed as sum of two shear strain components. Specifically, the first component occurred when the sand had zero effective confining stress. This was a function of the maximum cyclic shear strain experienced by the soil prior to liquefaction. The second strain component developed as a consequence of change in effective stress. This was estimated from the deviatorisotropic stress ratio applied to the specimen. A different research, described by Kokusho et al. (2004), aimed to investigate the effects of particle gradation on the post-liquefied undrained behaviour. It was observed that there was a certain value of threshold strain above which the soil solidified again due to dilatancy response, and this was more pronounced in well-graded soils. A recent study described by Sitharam et al. (2009) highlighted that the post-liquefaction undrained stress-strain response was also influenced by the amplitude of axial strain required for initial liquefaction. From the preceding review, it is evident that over the past few decades, there has been an increasing understanding of the post-liquefaction behaviour of sands. However, the majority of the studies available in the literature are concentrated on the assessment of liquefaction-induced ground settlement and lateral spreading deforma-
22
2. Literature Review tion. As aforementioned, several authors have proposed simplified models for predicting the post-liquefaction behaviour of sands under undrained conditions. These have shown a fairly good agreement especially in modelling the strain-hardening response observed at large strains.
2.4
Current understanding of pile failures during seismic liquefaction
The design of pile foundations in seismically liquefiable areas remains a constant source of attention to the earthquake engineering community. Most design codes employ large factors of safety against both gravity and lateral loads (due to structural inertia and/or lateral spreading), yet the occurrence of pile failures due to liquefaction may suggest that other governing mechanisms are not being adequately considered. The Japanese Highway Code of practice (JRA 1996, 2002) recommends to consider two different loading conditions, namely, (i) kinematic loading exerted by the lateral pressure of the liquefied layer and any non-liquefied crust resting on the top of the liquefied deposit; (ii) inertial force due to the oscillation of the superstructure. The code also suggests designers to check against bending failure due to kinematic and inertia forces separately. Similarly, EC8 (1998a) advises engineers to design piles against bending due to inertia and kinematic forces arising from the deformation of the surrounding soil. In the event of liquefaction, EC8 (1998a) also suggests that ‘the side resistance of soil layers that are susceptible to liquefaction or to substantial strength degradation shall be ignored’. Other provisions, such as the NEHRP code and Indian Code (NEHRP 2000, IS-1893 2002), also focus on the bending strength of the piles. In summary, the codes of practice simply treat piles as laterally loaded beams and assume that the lateral load due to inertia and soil movement causes bending failure. Research into various aspects of bending failure mechanism has been conducted by various researchers (Liu & Dobry 1999, Abdoun 1997, Dobry & Abdoun 1998, Wilson et al. 2000, Ramos et al. 2000, Cubrinovski & Ishihara 2004, Brandenberg et al. 2005, Tokimatsu et al. 2005). In contrast to the bending failure mechanism, investigations carried out by Bhattacharya et al. (2004), Brandenberg et al. (2005), Lin et al. (2007), Kimura & Tokimatsu (2007), Shanker et al. (2007), Bhattacharya et al. (2009), Knappett & Madabhushi (2009), have demonstrated that when soil liquefies and loses much of its stiffness, end-bearing piles act as unsupported long slender columns and may buckle under the action of the axial load arising from the dead load of the superstructure. A 23
2. Literature Review comprehensive critical review of the current theories of pile failures and hypothesis behind the current codes of practice may be found in Bhattacharya & Madabhushi (2008). Figure 2.9 shows the different stages of loading of a pile-supported structure during a seismic liquefaction induced event. Before the earthquake, the axial loads are in equilibrium with the shaft and end-bearing resistance of the piles. As the shaking begins and before the build-up of the pore water pressure, piles are mostly loaded by inertia forces generated by the oscillation of the superstructure, and the lateral load caused by the soil-pile kinematic interplay. At this stage, the bending mechanism is expected to govern the internal stresses within the pile. However, with the onset of liquefaction, i.e. with pore water pressure build up (at full liquefaction the excess pore water pressure reaches the overburden vertical effective stress), the soil loses its strength and stiffness, and the pile acts as an unsupported column over the liquefied depth. Piles that have high slenderness ratios will then be prone to buckling instability, which will also be amplified by imperfections, lateral forces and the dynamics of the earthquake. Before liquefaction
Axial
Before full liquefaction
Inertia
Axial
Inertia
Full liquefaction
Axial
Liquefiable layer
Non-liquefiable layer
Input motion Excess pore water pressure
Figure 2.9: Schematic of loading conditions acting on a typical pile-supported structure subjected to seismic-induced liquefaction. In routine practice, the seismic design of piles in liquefiable soils is often carried out by considering all external loads (i.e. lateral and axial) applied pseudo-statically to the structure, see for example JRA (2002). Consideration of the dynamic char24
2. Literature Review acteristics of the structure is used only for the estimation of the seismic input. In seismic codes based on response spectrum analysis, the values of fundamental natural frequency and equivalent viscous damping ratio represent critical input parameters for evaluating the amplitude of the spectral acceleration and also the assessment of the design base shear force. The fundamental vibration period of a building is most often estimated using empirical formulae, which only considers the dimensions, type and material of the superstructure, whereas the foundation is considered to be rigid. For example, EC8 (1998b) recommends Equation (2.6) to assess the fundamental period, T, of the superstructure. T = Ct H 3/4
(2.6)
Where T is in seconds, H is the height of the building in m, which must be measured from the foundation or from the top of a rigid basement; Ct is equal to 0.085 for moment resistant space steel frames, 0.075 for moment resistant space concrete frames and for eccentrically braced steel frames, and 0.050 for all other structures. Equation (2.6) is quite similar to the well-known formula T = 0.1n, where n is the number of stories of the building. It may be noted that most codes of practice estimate the fundamental period of vibration considering only the characteristics of superstructure, whereas the effects due to the Soil-Structure Interaction (SSI) (or in other words the foundations flexibility) are generally neglected. Although such an assumption is often conservative due to the beneficial effects of the SSI, i.e. deamplification of spectral accelerations due to increase of damping and lengthening of the period, several studies (Goel & Chopra 1998, Mylonakis & Gazetas 2000, Khalil et al. 2007, Crowley & Pinho 2010) demonstrated that the effects due to Dynamic Soil Structure Interaction (DSSI), especially in the presence of liquefaction, can be un-conservative and may lead to higher spectral accelerations and displacements.
2.5
Dynamic Soil-Structure Interaction
Over the past years, different approaches have been proposed to study the Dynamic Soil-Structure Interaction (DSSI) of pile supported structures. However, depending on the model used to represent the soil, these approaches can be classified in two main categories: (i) continuum approach, in which the soil is treated as a continuum (Banerjee & Davies 1978, Randolph 1981, Sen et al. 1985, Salgado 2009); (ii) Winkler approach, in which the soil-pile interaction is modelled by using a set of discrete springs distributed along the pile length. It should be pointed out that, despite the complexity of the DSSI phenomena, discretised methods have been extensively 25
2. Literature Review used by both practicing engineers and researchers due to the minimal computational effort needed for the analysis and the reliable results that they provide. Most of the discretised methods currently in use are based on the Beam on Elastic Foundation approach (Hetenyi 1946), which stands on the hypothesis that the reaction forces of the foundation are proportional at every point to the deflection of the beam at that point and is independent of pressures or deflection produced elsewhere in the foundation. According to this method, the soil-structure interaction can be conveniently modelled by independent springs located at discrete locations along the foundation as shown in Figure 2.10. The pile foundation is generally modelled by means of consecutive beam-column elements. The suggestion of modelling the soil structure interaction by means of discrete springs was introduced first by Winkler (1867), and this was established on the assumption that the supporting medium was elastic, thus the soil resistance, p, with units of f orce/displacement2 , at any point along the pile was directly proportional to the pile deflection at that point, i.e.: p = ks y
(2.7)
The constant of proportionality has been generally referred to as coefficient of subgrade reaction, ks , with units of F orce/Length3 . However, many authors refer to the modulus of subgrade reaction, Ks , which takes into account the diameter of the pile, Ks = ks D and is expressed in units of F orce/Length2 . To take into account the variation of soil stiffness with depth, the value of ks can be conveniently varied along the length of the pile as schematically represented in Figure 2.10. The differential equation governing the response of a vertical pile loaded by a static axial force N and a static lateral load Heq can be expressed as follows: d2 y d4 y + N − ks y = Heq (2.8) dx4 dx2 where EI is the flexural rigidity of the pile and x denotes the position along the vertical pile axis. EI
26
2. Literature Review
N Heq
linear elastic p-y curves
y
ks
non-linear p-y curves
p
p 1
ks
y
y
x Figure 2.10: Beam on elastic foundation approach (Winkler 1867) Equation (2.8) can be solved by using finite difference techniques or finite element formulations, although closed form solutions are available in the literature for numerous boundary and loading conditions (Hetenyi 1946). The solutions of Equation (2.8) provide the displacement profile along the pile length y(x), whereas its differentiation allows the estimation of shear, V (x) and bending moment diagrams M (x), as expressed by Equations (2.9) and (2.10) respectively. V (x) = EI
d3 y dx3
(2.9)
d2 y (2.10) dx2 The linear relationship between p and y (expressed by Equation (2.7)) provides simple and practically available solutions for Equation (2.8), however, the main limitation consists in the inability to account for the non-linearity of soils undergoing large strains. The model is improved by allowing the use of non-linear loaddisplacement relationships, which are commonly referred to as p − y curves. These will be discussed in details in the following sections. M (x) = EI
27
2. Literature Review
2.5.1
Load-Deflection p − y curves for DSSI modelling in non-liquefiable soils
Over the past 40 years, p−y curves have been extensively used in beam on nonlinear Winkler foundation (BNWF) analyses, especially in the offshore industry. Specifically, Institutions such as the American Petroleum Institute and Det Norske Veritas have been providing guidelines for the construction of simplified non-linear p − y curves for different soil conditions. These procedures were originally developed from a limited number of tests that were carried out on full-scale small diameter steel piles subjected to slow-cyclic loading (Matlock 1970, Reese et al. 1974). Therefore, the reliability of these p − y curves has been long questioned. In particular one of the main limitations consisted of the selection of an appropriate load-displacement relationship for piles having different rigidities and subjected to different loading condition. In fact, p − y curves were initially developed for static and quasi-static (i.e. low frequency) loading conditions, therefore their application to cases involving cyclic loading such as the ones induced by earthquakes, wind and waves, has always been a matter of concern. However, despite these limitations, in absence of more reliable in-situ tests, the p − y curves recommended by API represent a convenient tool for the analysis of dynamic soil-structure interaction problems. The following sections illustrate the guidelines for the construction of p − y curves for both sand and soft clay soils. p − y curves for sand The Load-Deflection curves for sandy soils recommended by API (2000) were originated from a report written by O’Neill & Murchison (1983). The p − y curve is expressed by a hyperbolic function given by Equation (2.11), which has been plotted in Figure 2.11. ks H p = Apu tanh Apu
28
!
y
(2.11)
2. Literature Review
p pu
y Figure 2.11: p − y for sand recommended by API 2000 where: • A is a coefficient to account for static or cyclic loading. In particular for static loading A is given by 3 − 0.8H/D, however this must be always larger or equal to 0.9. For cyclic loading the code considers the potential of stiffness degradation, thus suggests A = 0.9. • ks denotes the initial coefficient of subgrade reaction, which can be estimated from Figure 2.12 as a function of the angle of internal friction, φ. • pu denotes the ultimate lateral bearing capacity for sand. The code provides two equations for the assessment of pu , specifically, Equation (2.12) for shallow depth pus , and Equation (2.13) for deep depths pud .
p = (C1 H + C2 ) γ 0 H
(2.12)
p = C3 Dγ 0 H
(2.13)
29
2. Literature Review Angle of Internal Friction, 28 300
Initial modulus of subgrade reaction, k [lb/in.3]
29 Very Loose
30
36 Medium Dense
Loose
' [deg] 40
45 Very Dense
Dense
250
Sand above the water table
200
150
Sand below the water table
100
50
0
0
20
40
60
80
100
Relative density, Dr [%]
Figure 2.12: Initial coefficient of subgrade reaction versus relative density recommended by API 2000 where C1 , C2 and C3 are coefficients determined from Figure 2.13 as a function of the angle of internal friction of the sand expressed in degrees. H is depth in metres, γ 0 is the effective soil weight, and D the average pile diameter (in metres) from the surface to depth.
30
2. Literature Review 100 90 4
80 70
3
60 C2
50
2
40 C1
30
C3
Value of Coefficients C3
Values of Coefficients C1 and C2
5
20
1
10 0 20
25
30
Angle of Internal Friction,
35
40
0
' [deg]
Figure 2.13: Coefficients C1 , C2 and C3 versus angle of internal friction recommended by API 2000 The code does not define the range of depths for which the equations should be applied, however it suggests that, for a given depth, the equation giving the smallest value of pu should be used as the ultimate bearing capacity. p − y curves for soft clay For soft clay deposits, the construction of p − y curves is given by a different set of equations that have been derived from the work carried out by (Matlock 1970). The ultimate resistance, pu can be estimated as: cX (2.14) D where X denotes the depth below the soil surface expressed in mm. XR indicates the depth, in mm, below the soil surface to the bottom of reduced resistance zone. This can be estimated by Equation (2.15) in the presence of clay deposit, which is characterised by a constant strength with depth. Conversely if the strength varies with depth the equations must be plotted simultaneously and the point of first intersection should be taken as XR . p = 3c + γX + J
XR =
6D J + γD c
31
(2.15)
2. Literature Review However, for depth X > XR , the ultimate resistance should be estimated by Equation (2.16): pu = 9cu
(2.16)
where: cu is the undrained shear strength for undisturbed clay sample expressed in kPa, J is a constant that ranges from 0.25 to 0.5, with the upper bound value appropriate for Gulf of Mexico clays. Finally, the non-dimensional p − y curves for piles in soft clay loaded statically and cyclically are given in Table 2.1 and Table 2.2 respectively. Table 2.1: Non-dimensional static p − y curves for soft clays from API (2000) p/pu y/yc 0.0 0.23 0.33 0.50 0.72 1.00 1.00
0.0 0.1 0.3 1.0 3.0 8.0 ∞
Table 2.2: Non-dimensional cyclic p − y curves for soft clays from API (2000) p/pu y/yc p/pu y/yc 0.0 0.23 0.33 0.50 0.72 0.72 -
0.0 0.1 0.3 1.0 3.0 ∞ -
0.0 0.23 0.33 0.50 0.72 0.72X/XR 0.72
0.0 0.1 0.3 1.0 3.0 15 X/XR
The quantity yc is given by Equation (2.17), whereas c is is the axial strain measured at one-half of the maximum deviator stress measured during undrained compression tests. yc = 2.5c D[mm] 32
(2.17)
2. Literature Review Typical p − y curve for soft clay in both static and cyclic loading conditions are depicted in Figure 2.14 and Figure 2.15 respectively.
p / pu 1.0 0.8 0.6 0.4 0.2 0
2
0
4
6
8
10
12
y / yc
14
Figure 2.14: Static p − y curve for soft clay recommended by API 2000
p / pu 1.0 0.9 0.8
depth X>XR
0.7
shallow
0.6
depth X
0.5
0.72 X/XR
0.1%).
100
4. Soil element testing
Post-liquefied shear modulus, G2 [kPa]
16000
Redhill 110 sand 14000
Toyoura sand
12000 10000
G2=182 Dr - 2880
8000 6000 4000 2000 0
0
10
20
30
40
50
60
70
80
90
100
Relative density, Dr [%] (a)
Normalised shear modulus, G2 /Gmax
0.2
Redhill 110 sand
0.18
Toyoura sand
0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
0
10
20
30
40
50
60
70
80
90
100
Relative density, Dr [%] (b)
Figure 4.26: (a) Effects of relative density on post-liquefied shear modulus at large strains G2 ; (b) G2 /Gmax versus the relative density Finally, two undrained monotonic tests were carried out in extension. Based on the results plotted in Figures 4.27a and 4.27b, it could be observed that, the two samples exhibited dilative and strain-stiffening responses, similarly to those obtained from the compression monotonic tests. It was found that the extensional loading 101
4. Soil element testing had apparently a limited effect on the amplitudes of γto (and consequently of G1 ). In particular, γto and G1 were comparable with those computed from the monotonic compression tests. Conversely, the post-liquefaction stiffnesses at large strains (i.e. G2 ) were found somewhat lower than the ones measured in monotonic compression on specimens prepared at same relative densities. This result was consistent with data presented by Vaid & Thomas (1995).
102
4. Soil element testing
Axial strain, a [%] -8
-7
-6
-5
-3
-4
0
0
Deviator stress, q [kPa]
to
-1
-2
-20
=7.2%
G1 =13 kPa
-40
Redhill 110 sand (RH-11) ' c =100 kPa Dr =38%
G2 =3000 kPa
-60 -80 -100
1 0.8 0.6 r
u
0.4 0.2 -8
-7
-6
-5
-3
-4
-1
-2
0
0
Axial strain, a [%]
(a) Axial strain, a [%] -12
-10
-6
-8
-2
-4
00 -5
=11.85% kPa
to G1 =8
-10 -15
Toyoura sand (TY-4)
'
c =100 kPa Dr =32%
G2 =622 kPa
-20 -25 -30
Deviator stress, q [kPa]
-14
1 0.8 0.6
ru
0.4 0.2
-14
-12
-10
-6
-8
-4
-2
0
0
Axial strain, a [%]
(b)
Figure 4.27: Post-liquefaction undrained monotonic response in extension. (a) Redhill 110 sand (RH-11); (b) Toyoura sand (TY-4)
103
4. Soil element testing
4.9
Conclusions
The cyclic and post-liquefaction undrained monotonic behaviour of two silica sands, namely Redhill 110 and Toyoura sand, were examined by means of multi-stage triaxial tests. The samples were prepared at different initial relative densities and isotropically consolidated at same confining effective stress, i.e. 100 kPa. The multi-stage loading conditions consisted of cyclic loading ceased with the onset of liquefaction, followed by undrained monotonic loading, which aimed to investigate the post-liquefaction behaviour. Based on the results presented in this chapter the following conclusions can be drawn:
4.9.1
Undrained Cyclic Behaviour
Results obtained from undrained cyclic tests showed that the application of cyclic loading caused the effective stress paths (q − p0 plot) to gradually move towards the state of zero effective mean principal stress. For dense specimens this condition was only momentarily reached (see Figures 4.13 and 4.17), yet a certain degree of softening took place in the samples leading to a sizeable amount of axial strain (Figures 4.14a and 4.18a). The softening behaviour observed in dense sands has been commonly referred to as cyclic mobility, therefore to contemplate both liquefaction and cyclic mobility phenomena, the resistance to liquefaction was defined in terms of cyclic stress ratio, CSR, required to develop 5% in double-amplitude axial strain in 20 cycles. The results presented in Figure 4.19 and 4.20 clearly demonstrated that the resistance to liquefaction of the two silica sands was comparable for similar testing conditions. It was found that the resistance to liquefaction increased with increasing relative densities. It should be noted that the results presented for Redhill 110 sand were unique as the cyclic undrained behaviour of this sand has been poorly investigated, thus limited data are available in the current literature.
4.9.2
Post-liquefaction undrained monotonic behaviour
The stress-strain responses obtained from the undrained monotonic tests showed that the post-liquefaction behaviour of the two sands was always dilative regardless of the initial relative density of the sample. Furthermore, the stress-strain curves plotted in Figures 4.22 - 4.23 indicated that samples initially deformed at nearly zero stiffness, but, with further straining, they gradually mobilised strength and stiffness which was accompanied by a progressive dissipation of excess pore water pressure. It was also found that, at large strain levels, the stress-strain responses became practically linear. 104
4. Soil element testing The post-liquefaction behaviour could be thoroughly described by means of three different parameters following Dash (2010). These consisted of: (a) take-off shear strain, γto , i.e. shear strain required to mobilise 1 kPa of shear stress; (b) initial secant shear modulus, G1 , defined as 1/γto ; (c) post-liquefaction shear modulus at large strains γ γto , G2 . It was found that these parameters were strongly influenced by the initial relative densities of the sample. Specifically, γto decreased with increasing relative density, whereas, both shear moduli increased with increasing Dr . Finally, the shear modulus at large strains was compared with the maximum shear modulus Gmax that samples would have exhibited at very low strains in absence of liquefaction. The comparison suggested that G2 /Gmax ranged from 2 to 20% depending on the relative density of the sample. In particular, dense samples exhibited higher G2 /Gmax ratio. In addition, these findings suggested that, the value of G2 was comparable with values of secant shear modulus exhibited by soils at large strains, i.e. γ > 0.1%. Finally two tests were carried out in extension. The results demonstrated that the direction of the loading had little effect on the post-liquefaction behaviour and on the amplitudes of γto and G1 . Conversely, the post-liquefaction stiffness at large strains (i.e. G2 ) were found somewhat lower than the ones measured in monotonic compression on specimens prepared at same relative densities, which was in agreement with the results presented by Vaid & Thomas (1995).
105
Chapter 5 Geotechnical model container 5.1
Outline of the chapter
The chapter is structured in three main parts. The first part of the chapter discusses the main requirements for an ideal geotechnical model container. The different types of soil containers commonly used in earthquake geotechnical physical modelling are also presented and examined. In the second part, the chapter describes a series of 1-g experimental tests which aimed to investigate the effects induced by different boundary arrangements on the dynamic response of the soil deposit enclosed in the container. Finally, the results obtained from the experimental investigation are used for the development of a new geotechnical model container, which has been subsequently employed for the shaking table test program described in Chapter 6.
5.2
Introduction
Geotechnical physical modelling is an established method to investigate seismic soilstructure interaction problems and seismic response of soil deposits. Whether the tests are carried out using shaking tables at normal gravity or geotechnical centrifuges, the soil stratum needs to be confined in a container with relatively small dimensions. A significant challenge encountered when performing geotechnical physical modelling consists of minimising the boundaries effects created by the model confinement, therefore to simulate free-field seismic conditions. In this study, the tests were carried out at single gravity on a shaking table. In particular the shaking table was required for the application of the horizontal shaking to the system schematically illustrated in Figure 5.1. In addition, the assessment of the dynamic response of the soil-container system required the application of a ran106
5. Geotechnical model container dom signal characterised by a frequency bandwidth well above the frequency range of the system. The latter ranged between 40 and 70 Hz. As a consequence, a white noise signal, with bandwidth frequency from 0.5 to 100Hz, needed to be applied by means 8 servo hydraulic actuators, which composed the earthquake simulator (or shaking table). In geotechnical physical modelling, shaking tables are of value because the seismic wave propagation in the soil can be realistically reproduced since the ground motion is applied directly to the base of the soil container, which can be assumed as bedrock. Other advantages of single gravity tests in comparison to centrifuge testing are related to the larger space available for the instrumentation, better control of the experimental apparatus, direct observation of the tests, and larger dimensions of both soil container and models. In particular, the larger sizes of the soil container have the benefit of reducing the boundary effects since the model can be placed at a greater distance from the artificial boundaries. In addition, the larger dimensions of the models minimise the so-called ‘particle size effects’. The latter are particularly important in the experimental investigation described in Chapter 6, since they may affect the soil-structure interaction. It is recognised that the ‘particle size effects’ can be minimised by increasing the ratio between the pile diameter and average particle diameter expressed by D50 . In fact, considering the lowest pile diameter (refer to Table 6.2 in Chapter 6) and average particle diameter of Redhill 110 sand, D50 (listed in Table 4.1 in Chapter 4), it can be concluded that the ‘particle size effects’ can be considered negligible since the ratio given by Equation (5.1) is well above 100. 25.4mm D = = 181.43 D50 0.14mm
(5.1)
The vast majority of research activities in earthquake engineering are based on the simulation of an idealised infinite lateral extent soil stratum that overlays the bedrock, which is shaken at its base. It is commonly assumed that the input motion is one-dimensional and its energy is transmitted in the form of pure shear waves propagating vertically within the soil medium (Zeng & Schofield 1996). However, in the model test, the deformation of the soil medium is restricted by the artificial boundaries. Therefore, the actual mode shape may be significantly different from the one exhibited by the real prototype. Moreover, during the shaking, the soil near the boundaries may undergo compression and extension deformations causing the generation and reflection of body waves from the artificial boundaries of the container. In conclusion, the design of a model container for geotechnical physical modelling 107
5. Geotechnical model container should be carried out in such a way to minimise the boundary effects, thus to replicate as close as possible the prototype conditions.
5.3
Requirements for geotechnical model container
The main requirements for a model container for earthquake geotechnical physical modelling can be summarised as follows: • Stress similarity • Strain similarity • Appropriate propagation of shaking to the soil deposit • Minimisation of reflection and generation of body waves from the artificial boundaries
5.3.1
Stress similarity
During the shaking the soil layer generates an inertia force that acts in the direction opposite to that generated by the shaking. Considering the situation depicted in Figure 5.1, the inertia force can be calculated as Fsoil = kx W , where W stands for the mass of the soil (expressed in the units of kg) and kx was already introduced in Chapter 4 and denotes the coefficient of horizontal acceleration. As can be observed from the figure, the inertia force generates a clockwise overturning moment which, in order to satisfy the rotational equilibrium, must be counterbalanced by a set of shear stresses acting on the vertical planes near the end-walls. However, the shear stresses can be generated only if there is adequate friction at the interface between soil and artificial boundaries, which can be developed, for example, by applying a coarse-grained material on the inner surface of the end-walls.
108
5. Geotechnical model container xy soil deposit
Fsoil = k x W
x0
end-wall
end-wall
xy
ah = k x g Figure 5.1: Schematic of soil mass subjected to horizontal shaking and representations of shear and normal stresses generated during shaking
5.3.2
Strain similarity
In the idealised soil deposit depicted in Figure 5.1, the dynamic state of stress is given by the static free-field horizontal stress, σxo and the shear stress, τxz . It is noted that the latter are introduced by the horizontal shaking (see Figure 5.2). Assuming a linear stress-strain relationship, the mode shape of the soil column having a depth Hs is given by the parabolic equation expressed as follows: γ (Hs2 − z 2 ) (5.2) 2G The mode shape function expressed by Equation (5.2), corresponds to the socalled elastic shear beam idealisation. This assumes that the soil column undergoes a simple shear deformation with the rotation of the vertical planes while the horizontal planes remain horizontal. Based on these observations, the strain similarity can be considered satisfied when the soil layer (confined in the geotechnical container) exhibits a constant horizontal displacement at a given depth. u (z) = kx
109
5. Geotechnical model container x z0
soil properties
xy
, K0 , G
x0
Hs
z S-waves
one-dimensional shaking
ah = k x
g
Figure 5.2: Shear-beam idealisation of infinite lateral extent stratum overlying a bedrock subjected to one-dimensional shaking
5.3.3
Propagation of shaking to the soil deposit
In geotechnical physical modelling, the ground motion is often generated by means of shaking tables. However, in order to allow the propagation of the input shaking from the table to upper layers of the soil deposit, it is important that shear stresses are generated in the horizontal planes close to the interface between the soil and the base of the container. Therefore, to satisfy this requirement, the base of the container should be treated with a coarse-grained material which allows the generation of adequate friction. In practice this is generally achieved by gluing coarse sand particles on the base of the container.
5.3.4
Reflection and generation of body waves from the artificial boundaries
Over the past decade, researchers have developed different types of model container to minimise reflection and generation of body waves from the artificial boundaries. One example is represented by flexible soil containers. Assuming that the soil layer and the adjacent end-walls behave as an assembly of equivalent shear beams, the container is designed to mimic the shear beam response. This can be achieved by matching the shear stiffness between the model container and the soil it includes (Dar 1993, Zeng & Schofield 1996, Teymur & Madabhushi 2003, Bhattacharya et al. 2004, Elgamal et al. 2005, Pitilakis et al. 2008). As shown in Figure 5.3, this type of container is commonly made by aluminium rings spaced by soft rubber layers which 110
5. Geotechnical model container provide the desired lateral stiffness.
Figure 5.3: Example of flexible model container used on the shaking table at the University of Bristol However, due to the high non-linearity of the soil, particularly at large strains, the matching between the soil and container stiffness is possible only for a predefined range of strains, and it is generally not suitable for soil subjected to large deformations, such as those measured during soil liquefaction. A new type of model container with flexible boundaries was first introduced by Whitman & Lambe (1986) to study liquefaction phenomena. This new container concept has been subsequently used by many research teams (Hushmand et al. 1988, Law et al. 1991, Elgamal et al. 1996, Pamuk et al. 2007, Paolucci et al. 2008, Chen et al. 2013). The design principle of the flexible laminar box consists of minimising the lateral stiffness of the container to match the one of the liquefied soil column. This can be achieved by using a stack of aluminium rings supported individually with bearings, which permit a relative movement between the rings with minimal frictions. An example of laminar container used at the University of Cambridge is shown in Figure 5.4.
111
5. Geotechnical model container
Figure 5.4: Laminar container used in the centrifuge available at the University of Cambridge Several studies have confirmed that laminar containers are compatible with the large soil deformation expected during the simulation of earthquake-induced liquefaction. However, the laminar box may not replicate the actual boundary conditions when the soil column is not fully liquefied or is subjected to low strain levels. The model container with rigid ends has been used by several research groups in both centrifuge (Whitman & Lambe 1986, Adalier & Elgamal 2002, Ng et al. 2004, Uchita et al. 2005) and 1-g shaking table tests (Taguchi et al. 1992, Fishman et al. 1995, Lee & Santamarina 2007). Numerical studies conducted by Whitman & Lambe (1986) and Fishman et al. (1995) have demonstrated that the effects caused by the rigid boundaries are significant up to a distance of 1.5-2.0 times the depth of the soil stratum. To increase the volume of soil subjected to the free-field condition, soft material can be placed on the inner sides of the model container, which in turn diminishes the reflection of body waves from the boundaries and also the P-wave generation. Duxseal material (a putty-like, pipe sealant rubber mixture compound) has been extensively used in the past decade for centrifuge modelling (Coe et al. 1985, Cheney et al. 1990, Cilingir & Madabhushi 2011, Pak et al. 2011, Soudkhah & Pak 2012) due to its high damping and relatively high stiffness required for high stress level attained during the spin-up process. Cilingir & Madabhushi (2011) reported that Duxseal can absorb up to 65% of incident P-waves. In experimental modelling conducted on a shaking table at normal gravity, the relatively low stress at which the model is subjected, makes Duxseal material too stiff and therefore it is generally replaced by softer material such as conventional foam (Ha et al. 2011).
112
5. Geotechnical model container In the recent years, due to the relatively simple design and low cost of the material, the use of absorbing boundary for geotechnical containers has become an alternative solution for minimising generation and reflection of body waves from the artificial boundaries. Despite this, limited systematic experimental studies have been carried out to investigate the effects induced by the absorbing material on the dynamic response of the soil deposit.
5.4
Basic concept of wave propagation
In an infinite elastic medium two types of body waves may propagate, compression (P-waves) and shear waves (S-waves). Shear waves can be decomposed into two normal polarization components, i.e. SV-wave, which are polarized in the vertical planes and SH-wave, which are polarized in the horizontal planes. The wave equation for the one-dimensional case that describes the propagation of body waves within an elastic isotropic medium is given by (Kolsky 1963): ∂ ∂ds ∂ 2 ds (λl + 2G) ρ (x) 2 = ∂t ∂x ∂x "
#
(5.3)
where ds = ds (x, t) is the longitudinal displacement in the x-direction due to compression waves or transverse displacement perpendicular to the x-direction due to shear waves. λl (x) and G (x) are the Lam´e ’s constants, G is the shear modulus of the medium, which, for an isotropic material, may be related to the Young’s modulus, E, and Poisson’s ratio, ν: λl = E
(1 + ν) (1 + ν) (1 − 2ν)
G=
E 2 (1 + ν)
(5.4)
(5.5)
The resistance offered by a general medium to a given particle motion can be expressed in terms of its characteristic impedance Z = ρV , where ρ is the mass density and V is the velocity of propagation (Kolsky 1963). In this study, the characteristic impedance has been used to characterise the foams employed as absorbing material and identify the different boundary arrangements used in tests as it will be illustrated in the following sections. The values of the wave propagation velocities for the compressional, Vp and shear waves, Vs can be generally computed as: Vp =
λl + 2G ρ 113
!0.5
(5.6)
5. Geotechnical model container
G ρ
Vs =
!0.5
(5.7)
Furthermore the ratio Vp /Vs can be expressed in terms of the Poisson’s ratio, ν, of the material (i.e. soil or foam). "
Vp 2 (1 − ν) = Vs (1 − 2ν)
#0.5
=
λl + 2G G
!0.5
(5.8)
However, it should be pointed out that Equations (5.6), (5.7) and (5.8) are valid only for an elastic isotropic medium. Porous or cellular solids would be better represented as poroelastic materials using Biot-type theories (Biot 1956a,b). However, in the following sections, Equation (5.7) was employed to estimate the shear velocities of both soil deposit and absorbing materials due to its simplicity. It must be also pointed out that expressions like Equations (5.6) and (5.7) have been used in main literature to provide a comparative estimate of the wave group velocities belonging to different classes of cellular solids (Gibson & Ashby 1999). In a geotechnical model container subjected to one-dimensional motion, when a body wave encounters the interface between media having different impedances (i.e. interface soil-wall), the wave energy is partially reflected and partially transmitted through the boundary. Wave mode conversion therefore occurs, whereby P-waves are converted in S-waves and vice-versa. However, in the case of a rigid box with absorbing boundaries (see Figure 5.5), as the P-wave propagates from the soil into the foam layer, the velocity of propagation slows down due to the low impedance of the softer material (Kolsky 1963). At the interface the frequency of the propagating wave (f = V /λw , where λw is the wavelength) must remain constant. Therefore, when the wave propagates from the soil medium into the foam, the wavelength must decrease. This reduction in wavelength can be associated with energy dissipation (Kolsky 1963). A significant amount of energy can be also absorbed by the hysteretic damping provided by the foam. The damping of a material undergoing harmonic loading may be taken into account using the concept of the complex elastic modulus, E ∗ , which can be related to the wave velocity as follows: s ∗
V =
E∗ = ρ
s
E (1 + jζ) ρ
(5.9)
where E and ζ are real numbers representing the Young’s modulus and the damping ratio of the absorbing material.
114
5. Geotechnical model container foam
soil medium
container
V foam
Vsoil
foam
soil
V soil
=
soil
V foam foam
Figure 5.5: Schematic of wave propagation within a soil container having absorbing boundaries
5.5
Experimental investigation
The tests were conducted using the shaking table available at the Bristol Laboratory for Advanced Dynamics Engineering (BLADE) at the University of Bristol (UK).
5.5.1
Earthquake simulator
The earthquake simulator, which is normally referred to as shaking table, consists of a 3 × 3m cast aluminium platform weighing 3.8 tonnes which is placed inside a reinforced concrete seismic block having a mass of 300 tonnes (Crewe 2007). The aluminium plate is attached to the block by means of 8 servo hydraulic actuators that also provide full control of motion in all six-degrees of freedom. Each actuator has a dynamic capacity of 70 kN and maximum stroke of 300 mm (Crewe 2007), permitting to apply a maximum acceleration 1.6 and 1.2 g in the horizontal and vertical direction respectively (considering a payload of 10 tonnes) and an operational frequency in the range between 0 and 100 Hz. The actuators are powered by 6 shared variable volume hydraulic pumps that can provide up to 900 litres/min at a working pressure of 205 bar (Crewe 2007). A summary of the specification of the earthquake simulator is provided in Table 5.1. The dynamic characteristics of the earthquake simulator were reported by Crewe (2007). It was noted that the dynamic response of the shaking table could be approximated by considering a single degree of freedom (SDOF) system with the following resonance frequencies: 16.3 Hz and 14.5 Hz (horizontal directions) and 17.8 Hz in the vertical direction. However, these values were computed with no load except the aluminium plate itself which has a weight of 3.8 tonnes and a resonance frequency well in excess of 100 Hz. 115
5. Geotechnical model container Therefore, the presence of the specimen, in this thesis represented by the geotechnical container and geotechnical container plus models (see Chapter 6), the values of resonance frequency mentioned before will change. Table 5.1: Earthquake simulator specifications (Crewe 2007) Characteristic Value Size 3 m by 3 m Axes 6 Construction 4 pieces cast aluminium Mass 3.8 tonnes Maximum payload 15 tonnes Maximum payload height 15 m Maximum height of payload centre of gravity 5 m (subject to mass specimen) Vertical actuator 4 at 70 kN Vertical acceleration (no payload) 5.6 g Vertical acceleration (10 tonnes payload) 1.2 g Vertical displacement ± 150 mm Yaw rotation ± 3.6 Vertical velocity 1.2 m/s Yaw velocity 1.5 rad/s Longitudinal and lateral actuators 4 at 70 kN Horizontal acceleration (no payload) 3.7 g Horizontal acceleration (10 tonnes payload) 1.6 g Horizontal displacement ± 150 mm Pitch/roll rotation ± 5.2 Horizontal velocity 1.2 m/s Pitch/roll velocity 1.5 rad/s Operational frequency range 0-100 Hz Hydraulic supply 900 litres/min Supply pressure 205 bar (working), 230 bar (max)
Figure 5.6 depicts a photograph of the shaking table and the small geotechnical model container for the preliminary experimental investigation.
116
5. Geotechnical model container
Figure 5.6: Photograph of the shaking table and small geotechnical model container used for the experimental investigation Geotechnical model container The geotechnical model container used in this preliminary experimental investigation consisted of a rigid box with internal dimensions of 450 mm long, 200 mm wide and 400 mm high. It is noted that, since the experimental investigation consisted of several tests that required a considerable amount of preparation time and expense of the absorbing material, the dimensions of the soil container were minimised. The container was formed by assembling 5 sheets of PTFE (Poly-Tetra-FluoroEthylene) having a thickness of 25 mm, which were connected together by threadlocked bolts. To minimise the generation and reflection of the body waves from the rigid walls, panels of foam were placed on the inner sides of the end-walls, i.e. sides perpendicular to the direction of the shaking (see Figure 5.7).
117
5. Geotechnical model container
Shaking table
model container
Shaki ng
direct ion
Figure 5.7: Geotechnical model container used in the tests
5.5.2
Soil material
The soil used in the tests was a relatively uniform dry layer of Redhill 110 sand. Homogeneity of the soil deposit was achieved by using the dry pluviation technique with a constant height of fall of 20 cm from the soil surface. The main properties of Redhill 110 were previously presented in Chapter 4.
5.5.3
Absorbing material
The absorbing material comprised of commercially available conventional foams that was supplied in 1 m3 blocks by SM Upholstery Ltd. (Cardiff, UK). To obtain more general results the tests were conducted using three types of foams having different mechanical properties: density, Poisson’s ratio, Young’s modulus and damping ratios (see Table 5.2 for actual values). For each tests, two flat pads of foam, with dimensions 400 × 200 × 30 mm, were cut from the initial blocks, and subsequently placed on the inner sides of the end-walls. The mechanical characterization of the foams was obtained from a series of tests performed using a 1 kN Instron 3343 K 2887 testing machine (see Figure 5.8), with position accuracy of 0.5% and load accuracy of 0.5% (±0.1 N), equipped with an Instron load cell (model 2519-105). The machine was connected to a PC running Bluehill lite software (Version 2.8) set to acquire force and displacement during loading. The stiffness of each foam sample was determined from results of compression tests, in which the Young’s modulus was calculated as the slope of the linear region of the stress-strain curve. Typical results obtained from the compression tests are illustrated in Figure 5.9. The Poisson’s
118
5. Geotechnical model container ratio was calculated according to the classical definition: ν=−
εtran εlong
(5.10)
where εlong and εtran are the longitudinal and transverse strain of the samples, which were evaluated as follows: εlong =
∆l l0
εtran =
∆d d0
(5.11)
where ∆l is the longitudinal deformation, ∆d is the change in diameter, and l0 and d0 the starting specimen length and diameter respectively. ∆l and ∆d were obtained from images acquired by an independent Q-400 Dantec optical measuring instrument during the deformation of the samples. To improve the measuring accuracy, a cold light illumination system (HILIS) was employed to provide a homogeneous illumination of the sample. The images were post-processed in MATLAB environment using a specifically designed routine to identify, through edge detection methods, the longitudinal and transverse deformations of the samples. Instron 3343 K2887
foam sample
Q-400 Dantec (optical measuring instrument)
Figure 5.8: kN Instron 3343 K 2887 testing machine (model 3343) used for the mechanical characterization of the absorbing material
119
5. Geotechnical model container 12
10
Stress [kPa]
8
6
Ef-2
Ef-3
FOAM 2
FOAM 3
FOAM 1
Ef-1
4
2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Strain [mm/mm]
Figure 5.9: Typical stress-strain behaviour obtained from compression tests Furthermore, to estimate the damping of the different foams used in this study, a series of cyclic compression tests were performed and the main results are listed in Table 5.2. The procedure employed for the assessment of the damping is described by Lakes (2004) and takes into account the area within the hysteresis cycles. For small displacement, i.e. within 25%, the area is representative of the behaviour of a linearly viscoelastic material and is elliptic in shape (Bianchi et al. 2008). The absorption properties of the foams were identified by their acoustic impedance, which for the foam can be expressed as: Zf oam = ρf oam Vpf oam
(5.12)
where ρf oam is the density of the foam and Vp−f oam is the compressional wave velocity within the foam, which can be calculated from the Young’s modulus and Poisson’s ratio, using Equations (5.4) and (5.6).
5.5.4
Testing program and instrumentation set-up
The experimental program consisted of eight tests carried out on four different boundary arrangements, namely, no foam, foam 1, foam 2 and foam 3. Each configuration was subjected to broadband random white noise having 0.5-100 Hz bandwidth frequency. Moreover, to investigate the nonlinearity of the phenomenon, each configuration was subjected to two different levels of acceleration, i.e. 0.1 and 0.5 g. 120
5. Geotechnical model container
Table 5.2: Mechanical properties of the absorbing material Foam ID ρf oam [kg/m3 ] Ef oam [kPa] νf oam ζf oam [%] Zf oam [N s/m3 ] Foam 1 Foam 2 Foam 3
22 24 28
22 39 34
0.33 0.36 0.31
22 16 12
847 1254 1149
The acceleration measurements were recorded by 7 accelerometers, which consisted of piezoelectric sensors, model 333M07 manufactured by PCB Piezotronics INC. The accelerometer had a frequency range between 0.5 and 3000 Hz, and other specifications have been listed in Table 5.3. A schematic of the instrumentation layout is given in Figure 5.10. Table 5.3: Specification of piezoelectric accelerometers Property Value Model Weight Width Height Sensing element material Housing material Frequency range Voltage sensitivity Operating temperature range
121
300M07 6.7 gm 11.1 mm 20.8 mm Ceramic Titanium 0.5 - 3000 Hz (+7%, -5%) 100 mV/g -18 to 66 ◦ C
5. Geotechnical model container
98mm 98mm
195mm
50mm ACC-6
ACC-5
ACC-4
ACC-3
ACC-2
350mm
400mm
ACC-7
100mm
200mm ACC-1
450mm SHAKING DIRECTION
Figure 5.10: Schematic of the instrumentation layout Data was recorded in the time domain at a fixed sampling frequency of 1000 Hz, and subsequently digitalised using DSPACE as data acquisition system. The accelerometers were connected to DSPACE by a controller board that was fed into a PCI slot of the PC and which was controlled using ControlDesk and Simulink. Table 5.4 gives a summary of the tests carried out in this study, and the conditions of soil, which are expressed in terms of: soil density, ρs , relative density, Dr , resonance frequency, fs and shear wave velocity Vs . The resonance frequency of the soil was evaluated from the peak of the transmissibility in the frequency domain calculated using Fast Fourier Transforms (FFT). The modulus of the transmissibility between two signals is complex valued function over a frequency range and it may be expressed analytically as: |H (f ) |2 =
Sxy (f ) Sx (f )
(5.13)
where Sxy is the Cross Power Spectral Density of the input and output and Sx is the Power Spectral density of the input (Clough & Penzien 1993, Thorby 2008). In this study, the input and the output consisted of the acceleration time histories recorded on the shaking table and within the soil respectively. From the transmissibility plots, the assessment of the resonance frequency of the soil medium was obtained using the Peak-Picking Method (Bendat & Piersol 1980), which identifies the resonance frequency with the peak value of the FFT. Considering that the soil layer was subjected to one-dimensional excitation (i.e. shaking), the resonance 122
5. Geotechnical model container frequency assessed during the tests can be related to the shear mode of the soil stratum and its shear wave velocity Vs by using the equation suggested by (Dobry et al. 1976): fs =
Vs 4Hs
(5.14)
where Hs is the depth of the soil layer. In Table 5.4 the different boundary conditions are identified in terms of ratio between the impedances of the soil and foam. The impedance of the soil deposit, Zs , was calculated using an equation similar to that given in (5.12)considering instead the density and compressional wave velocity relative to the soil. The compressional wave velocity of the soil, Vp−s , was estimated from Vs and Poisson’s ratio which was assumed to be equal to 0.25, by using Equation (5.8).
Test ID T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8
5.6
Table 5.4: Summary of the tests carried out in this study Foam ID ρsoil [kg/m3 ] Dr fs [Hz] Vs [m/s] Zsoil /Zf oam
ag
no foam no foam foam 1 foam 1 foam 2 foam 2 foam 3 foam 3
0.1 0.5 0.1 0.5 0.1 0.5 0.1 0.5
1464 1464 1422 1422 1419 1419 1426 1426
53 53 40 40 39 39 41 41
65 43 60 32 61 33 61 40
91 60 84 44 85 46 85 56
no foam no foam 244 130 167 91 184 120
Experimental results
The test results have been presented by comparing the transmissibilities corresponding to different boundary arrangements, namely: no foam, foam 1, foam 2 and foam 3. Figure 5.11 shows the results calculated considering accelerometer ACC-2 as output and ACC-1 as input.
123
5. Geotechnical model container
5
No foam Foam 1 Foam 2 Foam 3
frequency range of soil deposit
Transmissibility ACC-2/ACC-1
4.5 ACC-2
4
ACC-1
3.5 3 2.5 2 1.5 1
10
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Figure 5.11: Comparison of the transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC-2 (output) and ACC-1 (input) As expected the maximum level of energy (which is proportional to the area underneath the transmissibility curve) corresponded to the response obtained from the container with rigid walls only. The results computed from the systems with absorbing boundaries showed a significant reduction in both magnitude and frequency content of the FFT, which suggested that a certain degree of energy was dissipated by the boundaries. Furthermore, it should be pointed out that the drop in transmissibility occurred within the frequency range right close to the resonance frequencies of the soil deposits, which ranged between 60-65 Hz when the input acceleration was of the order of 0.1 g (see Table 5.4). This feature provided evidence that the shaking systems with foams were characterised by a considerably lower amount of energy directly associated with lower generation and reflection of body waves from the artificial boundaries. From a theoretical point of view, the energy associated with the shear mode of a semi-infinite medium subjected to one-dimensional shaking must be constant on the horizontal planes of the soil layer (Zeng & Schofield 1996). However, in a model container, the presence of artificial boundaries could alter the horizontal energy distribution. Specifically, volumes of soil closer to the walls could be characterised by higher magnitudes and broader frequency contents due to generation and reflection of body waves from the edges. To investigate this phenomenon, the responses were 124
5. Geotechnical model container evaluated considering, as output, the signal recorded by accelerometer ACC-3, which was located near the end-wall. The results are illustrated in Figure 5.12. It can be observed that the magnitude and frequency content of the transmissibilities relative to the rigid container did not vary significantly in comparison with the response estimated from the accelerometer ACC-2 (shown in Figure 5.11). Moreover, the beneficial effects introduced by the foams (drop in transmissibilities) were evident at frequencies close to the ones associated with the shear mode of the soil deposit. Conversely, the magnitudes measured in the range between 30-55 Hz were higher than the ones computed from the rigid container. This discrepancy suggests that the effects due to the generation of P-waves and reflection of body waves from the boundaries affects the response of the system in the frequency content between 30 and 55 Hz, which is lower than the frequency associated with the fundamental mode of the soil deposit. 5 4.5
Transmissibility ACC-3/ACC-1
No foam Foam 1 Foam 2 Foam 3
frequency range of soil deposit
4
ACC-3 ACC-1
3.5 3 2.5 2 1.5 1
10
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Figure 5.12: Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC-3 (output) and ACC1(input) Figure 5.13 shows the results calculated from the signals recorded by accelerometer ACC-4 located on the external side of the end-wall. The transmissibility computed for the model having rigid walls was characterised by a higher magnitude and broader frequency content, which replicated the similar soil responses extrapolated by ACC-2 (Figure 5.11). In agreement with previous results, the transmissibilities estimated by the ACC-1 accelerometer clearly demonstrated that absorbing bound125
5. Geotechnical model container aries reduced significantly the energy associated with the fundamental mode of the soil deposit. 3
Transmissibility ACC-4/ACC-1
2.6
No foam Foam 1 Foam 2 Foam 3
frequency range of soil deposit
2.8 ACC-4
2.4 ACC-1
2.2 2 1.8 1.6 1.4 1.2 1
10
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Figure 5.13: Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC-4 (output) and ACC1(input) To investigate the effects of foams at shallower depths, the transmissibilities were computed considering as output the signals measured by accelerometers ACC-5 and ACC-6, which were both located at 50 mm below the ground surface but at different distances from the boundaries. The results obtained from accelerometer ACC-5 are plotted in Figure 5.14. The trends of the transmissibilities confirmed the significant reduction in both magnitude and frequency contents due to the absorbing boundaries. A similar behaviour was also observed from data recorded by accelerometers ACC-6.
126
5. Geotechnical model container
9
No foam Foam 1 Foam 2 Foam 3
frequency range of soil deposit
Transmissibility ACC-5/ACC-1
8
ACC-5
7 ACC-1
6 5 4 3 2 1
10
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Figure 5.14: Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC-5 (output) and ACC1(input) Figure 5.15 shows the transmissibilities computed from signals recorded by ACC7, which was located on the external side of the end-wall. The overall trends of the transmissibilities confirmed that models with foams had significantly lower magnitude especially within the resonance frequencies of the soil deposits, and also narrower frequency contents than those computed from the container with rigid boundaries which indicated that generation and reflection of body waves from the walls were reduced.
127
5. Geotechnical model container
4
No foam Foam 1 Foam 2 Foam 3
Transmissibility ACC-7/ACC-1
frequency range of soil deposit
3.5
ACC-7
3
ACC-1
2.5
2
1.5
1
10
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Figure 5.15: Comparison of transmissibilities relative to different boundary arrangements, estimated from signals recorded by accelerometers ACC-7 (output) and ACC1(input) To examine the non-linearity of the wave propagation and energy absorption phenomenon, each boundary arrangement was subjected to a higher acceleration level of about 0.5 g. The transmissibilities calculated considering as output accelerometers ACC-2 and ACC-5 are presented in Figures 5.16 and 5.17. It was found that at higher acceleration level the drop in magnitudes was even more important at higher frequency range.
128
5. Geotechnical model container
2
Transmissibility ACC-2/ACC-1
1.9
frequency range of soil deposit ACC-2
1.8 ACC-1
1.7 1.6 1.5 1.4 1.3
No foam Foam 1 Foam 2 Foam 3
1.2 1.1 1
10
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Figure 5.16: Comparison of transmissibilities relative to different boundary arrangements subjected to 0.5g acceleration, and estimated from signals recorded by accelerometers ACC-2 (output) and ACC-1(input)
3
Transmissibility ACC-5/ACC-1
2.8 2.6
frequency range of soil deposit
No foam Foam 1 Foam 2 Foam 3
ACC-5
ACC-1
2.4 2.2 2
1.8 1.6 1.4 1.2 1
10
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Figure 5.17: Comparison of transmissibilities relative to different boundary arrangements subjected to 0.5g acceleration, and estimated from signals recorded by accelerometers ACC-5 (output) and ACC-1(input) Finally, the actual amount of energy dissipated by the absorbing boundaries was 129
5. Geotechnical model container quantified from the energy densities ES of the output signals, calculated as frequency integrals of the Power Spectral Density of the time acceleration histories. The reduction in energy was then estimated from the ratio between the ES computed from the container with rigid walls and from the one related to the container with absorbing boundaries. The results are shown in Table 5.5. The amount of reduced energy has been indicated by the abbreviation RE, followed by the ID of the accelerometer used for the assessment of the PSD. Table 5.5: Reduction in energy, RE, computed at two depth and for two different levels of acceleration ag Test ID Foam type RE (Acc-2) RE (Acc-5) Zf oam [Ns/m3 ] 0.1 g
2 3 4
Foam 1 Foam 2 Foam 3
86% 66% 41%
85% 61% 69%
847 1254 1149
0.5 g
5 6 7
Foam 1 Foam 2 Foam 3
92% 61% 41%
89% 51% 61%
847 1254 1149
The results listed in Table 5.5 suggest that the energy reduction estimated within the systems with absorbing material ranged from a minimum of 41% to a maximum of 92%. The reduction was mainly a function of the type of foam used, defined by the acoustic impedance Zf oam estimated by Equation (5.12). It is worth noticing that most of the energy reduction occurred in the frequency bandwidth close to the resonance of the soil deposit. Foams with lower impedances absorbed more energy than the ones with higher impedances (see Table 5.5 for more details). Foam 1 was however characterised by higher damping (22%) than foams 2 and 3 (16 and 12% respectively, see Table 5.2 for more details). Furthermore, the experimental results suggested that the effects on the energy reduction of soil depths and the acceleration levels were practically negligible. However, further studies are required to confirm these observations.
5.7
Development of new geotechnical model container
The geotechnical model container (see Figure 5.21) employed for the shaking table test program (Chapter 6) is constructed from 18 ’channel’ sections (100 mm × 50 mm). Each section are cut into pieces 2.4 m long (see Figure 5.18) that are bolted 130
5. Geotechnical model container together through stainless M20 hexagon head bolts. As shown in Figure 5.19 the channels are ultimately bolted to a steel plate having a thickness of 10 mm and plan dimensions of 2.6 m × 2.6 m. The final dimensions (external) of the geotechnical container are 2.4 m × 1.2 m × 2.4 m. The container is made water proof by coating its internal sides with a rubber matting 1 mm thick (see Figure 5.20). It is noted that the dimensions of the soil container are determined based on three important considerations. Firstly, the container needed to be as large as it can be, so to replicate the stress levels existing in real soil deposits. This aspect is particularly important, since the soil behaviour is strongly dependent on the stress level, which is mainly a function of the soil depth. As a consequence, an important requirement is to maximise the height of the soil container. On the other hand, the maximum dimensions of the container are limited by: (a) the maximum payload that may be applied to the shaking table, that is 15 tonnes (see Table 5.1); (b) the reliability of the control of the shaking table, which reduces as the mass of the specimen increases.
Figure 5.18: Steel ’Channel’ sections employed for the construction of container
131
5. Geotechnical model container
Figure 5.19: Close-up of connections between ’channel’ sections and bottom steel plate
Figure 5.20: Rubber matting
132
5. Geotechnical model container
2.4
foam
1.20m 2 . 4 0 m
n shaking directio
2.40m
container
Figure 5.21: Geotechnical model container used in the shaking table program
5.8
Conclusion
A series of shaking table tests were carried out to quantify the dynamic performance of the absorbing material and the amount of energy absorbed by the boundaries. The absorbing material consisted of panels made from conventional foam placed on the inner sides of the artificial walls of the soil container. Tests were conducted using three types of foams with different mechanical properties, see Table 5.4 for more details. Based on the experimental results, which were presented by comparing the transmissibilities corresponding to different boundaries arrangements, namely no foam, foam 1, foam 2 and foam 3, the following conclusions can be drawn:
133
5. Geotechnical model container • The test results demonstrated that the systems with absorbing boundaries showed a significant drop in transmissibility magnitudes particularly in the frequency range close to the fundamental frequencies of the soil deposits. This response demonstrated that the systems with foams were characterised by a considerably lower amount of energy which can be directly associated with minor generation (and reflection) of body waves from the artificial boundaries. • To examine the nonlinearity of the energy absorption phenomenon, each system was subjected to a higher acceleration level (see Table 5.4 for more details). The results showed that at higher acceleration level the energy dissipation was higher. • The actual amount of energy dissipated by the absorbing boundaries was quantified through frequency integral of the Power Spectral Density of the output signals. The results showed that the reduction in energy ranged from a minimum of 41% to a maximum of 92%, depending principally on the foam used in the test, whereas the effects of the acceleration level and depth at which the energy was computed were practically negligible. • Based on the results presented in this chapter, it can be concluded that, the use of geotechnical model containers with absorbing boundaries present some advantages especially in terms of minimising generation and reflection of body waves from artificial boundaries. As a consequence, this type of boundary arrangement was used for the development of the geotechnical model container employed in the shaking table test reported in Chapter 6.
134
Chapter 6 Experimental investigation (shaking table tests) 6.1
Outline of the chapter
The purpose of this chapter is twofold. Firstly, the chapter describes the experimental apparatus and the main properties of the models used in the shaking table test program. After a brief description of the sand pluviation procedure used for the preparation of the soil deposit, full details regarding the instrumentation and data acquisition system employed for the collection of data are provided. In addition, details regarding the signal conditioning techniques used to improve the quality of data are discussed. The second part of the chapter describes the test program undertaken in this experimental investigation. This consisted of two stages herein referred to as first stage and second stage. In the first stage dynamic properties of the models were assessed using the so called free-decay responses, which were generated through an impact hammer. In the second stage the models were subjected to random input motion characterised by a broad frequency range. Before presenting the experimental results, the chapter provides a comprehensive overview of the system identification techniques employed in the two stages for the post-processing of the raw data.
6.2
Introduction
The experimental investigation presented in this chapter was conducted on the 3×3 m shaking table facility of the Bristol Laboratory for Advanced Dynamics Engineering (BLADE) at the University of Bristol (UK). The tests were carried out at normal gravity on small scale models representing typical pile-supported structures. Specif135
6. Experimental investigation (shaking table tests) ically two single piles and two (2×2) piles groups were considered as prototypes. The results were analysed in order to obtain a valuable insight into the variation of the dynamic properties of the models, namely resonance frequencies and damping ratios, which varied as a consequence of seismic-induced liquefaction of the soil deposit. Furthermore, bending moment profiles were estimated from strain data which were recorded by means of strain gauges positioned at different elevations along the piles. Finally, to better understand the effects induced by soil liquefaction on the seismic behaviour of the models, response spectra were evaluated from acceleration time histories recorded directly on the table and in the soil deposit. The latter were used to simulate the response spectra of both bedrock and free-field.
6.3 6.3.1
Experimental apparatus Earthquake simulator
The main characteristics of the earthquake simulator, i.e. shaking table, have already been presented in detail in Chapter 5.
6.3.2
Geotechnical soil container
The geotechnical soil container used in this experimental investigation consisted of a rigid box with absorbing boundaries. The soil container was secured to the shaking table by bolting the bottom plate of the container to the aluminium platform by using a set of steel wedges as can be seen from the photograph shown in Figure 6.1. As already discussed in Chapter 5, the main limitations of using rigid containers were represented by the generation and reflection of P-waves from the end walls. In a typical soil layer, which may be idealised as semi-infinite extended deposit, the energy associated with the wave propagation diminishes gradually with distance. This dissipation may be related to the combined presence of hysteretic and radiation damping as well as the fact that energy is spreading to a larger volume of soil, the so-called geometric attenuation.
136
6. Experimental investigation (shaking table tests)
model container
shaking direction
shaking table Figure 6.1: Geotechnical model container mounted on the shaking table Clearly, the finite dimensions of a soil container did not allow this dissipation, and P-waves could be generated from its artificial boundaries. To minimise the reflection of P-waves from the end-walls as well as to aid the dissipation of energy, sheets of absorbing materials were placed on both end-walls of the container. The selection of the soft materials used as remediation of the wave reflection has been extensively investigated in Chapter 5.
6.3.3
Models of Pile-supported structures
The tests were carried out on four physical models, which consisted of two single piles and two (2×2) piles groups. Model SP1 and SP2 corresponded to the single pile models with outer diameter of 25.4 mm and 41.27 mm respectively. Model GP1 and GP2 corresponded to the pile groups, which were composed of four piles having outer diameter of 25.4 mm and 41.27 mm respectively. The pile spacing ratio (i.e. ratio between centre-to-centre distance and outer diameter) was 3 for both pile group configurations GP1 and GP2. This value was chosen according to the current practice, which adopts a spacing of 3 to 4 diameters (Fleming et al. 2008).
137
6. Experimental investigation (shaking table tests)
GP1
SP2
SP1
GP2
Figure 6.2: Pile-supported structure models Aluminium alloy (type L114-T4 6082-T4) was chosen as the material for all piles (see Table 6.1 for mechanical properties). The aluminium tubes (with thickness of 0.711 mm) were cut into pieces of 2 m long, which corresponded also to the total height of the four models. Furthermore, all models were equipped with a rigid pile cap fabricated from steel plates (see Figure 6.2). The dimensions and mechanical properties of the models are listed in Table 6.2. Table 6.1: Mechanical properties of Aluminium alloy L114-T4 6082-T4 Alloy name Density Young’s modulus Proof stress Tensile strength L114-T4 6082 T4
2.70 M g/m3
70 GPa
100 MPa
260 MPa
Table 6.2: Dimensions and mechanical properties of the physical models Model ID D [mm] EI [N m2 ] Pile-cap dimens. [mm] Pile-cap mass [kg] SP1 SP2 GP1 GP2∗
25.4 41.275 25.4 41.275
294 1305 294 1305
100 150 260 260
× × × ×
100 150 260 260
× × × ×
25.4 25.4 25.4 25.4
1.9 8.44 13.08 22.72
Note: ∗ Two plates were used for the pile-cap
Before placing the four models into the soil container, a 100 mm thick wood base (see photograph in Figure 6.3) was lowered by the crane and placed into the 138
6. Experimental investigation (shaking table tests) container. The wood base accommodated four steel plates which facilitated the connection of the aluminium tubes to the bottom plate so as to guarantee a rigid bottom boundary conditions for all models.
steel base (SP1)
steel base (GP1)
wood base
Figure 6.3: Steel plates bolted on the wood base
SP1 model
bottom base
Figure 6.4: Installation of SP1 model into steel plates attached to the bottom wood base Before the dry pluviation, each model was lowered by a crane into the rigid box and glued to the steel plates mounted on the wood plate. In order to minimise the interaction between the foundations, the models were installed at a distance of about 15 pile-diameters apart.
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6. Experimental investigation (shaking table tests)
6.3.4
Soil properties
The sand deposit consisted of a relatively uniform layer of Redhill 110 sand. The main properties of the sand, along with its resistance to liquefaction and postliquefaction undrained monotonic behaviour were assessed from a series of multistage cyclic triaxial tests which have been presented in Chapter 4. Dry sand was deposited into the soil container by means of dry pluviation (see Figure 6.5). This was carried out by using a drum filled with about 300 kg of dry Redhill 110 sand. A steel funnel having an outlet of 50 mm in diameter was mounted to one end of the drum. The choice of the diameter of the outlet was determined in order to obtain the loosest condition achievable with the current apparatus. The pluviation was facilitated by the use of a flexible tube made of rubber, with 1 m in total length and 50 mm in diameter (see Figure 6.5a). Homogeneity in soil density was achieved using a constant height of fall, i.e. 1.5 m. The pluviation was completed when the soil layer reached a total height of 1.8 m, which corresponded to a total volume of 4.158 m3 (i.e. 1.8 m × 1.4 m × 1.65 m) and a total weight of sand poured into the container of 4496 kg. Based on these values, a relative density of 14% was estimated based on the expressions given by Equations (6.1) and (6.2). e=
Dr =
Gs γwater − 1 γdry
emax − e × 100 emax − emin
(6.1)
(6.2)
Where e is the void ratio Gs denotes the specific gravity of the sand (see Chapter 4), γdry and γwater are the unit weights of dry sand and water respectively, Dr is the relative density expressed in percentage.
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6. Experimental investigation (shaking table tests)
drum
flexible tube drum funnel
container flexible tube
shaking table (a)
(b)
Figure 6.5: (a) Dry pluviation apparatus; (b) Pluviation of dry sand into the soil container The saturation of the soil layer was carried out from the top to bottom. Although this method of saturation posed several disadvantages, its choice was driven by its simplicity and physical restrictions due by the presence of very sensitive (especially to water) devices such as hydraulic actuators, servo-valves etc. Nevertheless, the complete and homogenous saturation of the soil layer was confirmed by the measurements recorded by the pore water pressure transducers embedded at several locations within the sand. At full saturation, the relative density of the soil increased from 14% to 34% due to a soil settlement of about 10 cm (average value).
6.4
Instrumentations
All physical quantities measured during the tests, namely strains, accelerations and pressures were converted into electrical signals by means of transducers. A schematic of the instrumentation layout used in this study is shown in Figure 6.6. Specifically, in order to monitor the dynamic response of the four structures, each pile cap was instrumented with a SETRA accelerometer. The input motion applied through the shaking table was also recorded by a SETRA accelerometer mounted on the table, whereas the ground response was measured by two MEMS accelerometer positioned at a depth of 600 mm and 1000 mm from the soil surface. Pore water pressure transducers (PPTs) were placed at four depths for measuring the pore 141
6. Experimental investigation (shaking table tests) water pressures build up during shaking (see Figure 6.6 for more details). Finally, in order to estimate the bending moments generated in the piles during the application of the shaking, one aluminium tube in each model was instrumented with pairs of strain gauges placed at 4 different levels along the length. More details regarding all instrumentations used in this study are provided in the following sections.
142
PPT
GP1 GP2
SP1
ABSORBING BOUNDARY
ABSORBING BOUNDARY
1200 mm
AA
SP2
200 mm
BB
200 mm
BB
Pore Water Pressure Trasducers (PPT) SETRA accelerometer MEMS accelerometer Strain gauges
AA
2400 mm 200 mm
ABSORBING BOUNDARY
2400 mm 1800 mm
ABSORBING BOUNDARY
PPT1
2400 mm
Figure 6.6: Plan view and cross section of physical models and instrumentation layout
1300mm 850mm 550mm 250mm
PPT2
PPT1
1800mm
PPT2
1600mm
PPT3
PPT1
PPT3
1300mm
PPT4
1000mm
600mm
1800mm
1300mm 850mm 550mm 250mm
1600mm
1300mm
-550mm
PPT2
SP2
PPT3
GP1
200 mm
PPT4
PPT1
PPT2
1000mm
2400 mm
PPT3
PPT4
600mm
ABSORBING BOUNDARY
GP2
PPT4
143 2400 mm 1800 mm
SP1
BB--BB
500 mm
ABSORBING BOUNDARY
AA--AA 500 mm
6. Experimental investigation (shaking table tests)
500 mm
6. Experimental investigation (shaking table tests)
6.4.1
Accelerometers
As mentioned in the previous section, two different types of accelerometer were used in this study. These consisted of SETRA and Micro Electro Mechanicals Systems (MEMS) based accelerometers. It is noted that MEMS accelerometers were built specifically for this experimental investigation as the available SETRA accelerometers were not water proof thus could not be embedded in the saturated sand. SETRA accelerometer SETRA consisted of ±8 g servo accelerometers, type 141A manufactured by Setra. The accelerometers had a high output capacitance type with inbuilt pre-amplifiers which operate over a frequency range of 0 to 3000 Hz. The accelerometers presented a flat response in the range between 0 and 300 Hz and a resonance frequency of about 600 Hz, which were well above the frequency range of interest for these tests. Figure 6.7 shows the SETRA accelerometers employed in this study. shaking direction SETRA
SETRA accelerometer
accelerometer
Pile cap
(a)
shaking table
(b)
Figure 6.7: SETRA accelerometers: (a) SETRA mounted on the pile cap of model SP1; (b) SETRA accelerometers mounted on the shaking table for monitoring input motion MEMS accelerometers A new set of Micro Electro Mechanical System (MEMS) based accelerometers were developed as a part of this experimental investigation. A typical MEMS accelerometer consisted of chip (type ADXL 203 ) having dimensions 4 mm × 4 mm × 1.45 mm mounted on a breakout board (type SEN 09269 ) with dimensions 18 mm × 18 mm × 1.63 mm and weight of 1.18 g (see Figure 6.8 ). The chip had a capacitor of 0.1µ which gave a frequency bandwidth up to 50 Hz.
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6. Experimental investigation (shaking table tests)
18 mm 18 mm
Breakout board ADXL335 chip
Figure 6.8: Close-up of ADXL chip mounted on the breakout board It can be seen from Figure 6.8 that the breakout board had 6 connecting cables. Three, named X, Y, Z represented the acceleration data output in three different directions. ‘ST’ was the common grounding to all three axes. Finally ‘VCC’ and ‘ST’ denoted the cables for the power supply and ground respectively. A power supply of 3V was provided through a RDP 611 signal conditioning amplifier, which gave an output analog voltage of 300 mV/g. Each breakout board was placed into a PTFE (Poly Tetra Fluoro Ethylene) casing which was then filled by hardening epoxy resin (see Figure 6.9. The final size of the MEMS accelerometers was 40 mm × 40 mm × 17 mm with a total weight of 50 g. However, it should be pointed out that the dimension of the casing were determined so to obtain a neutrally buoyant accelerometer under liquefied condition which could remain in a stable position during liquefaction.
145
6. Experimental investigation (shaking table tests) hardening epoxy resin
40mm
Breakout board PTFE casing 40mm
Figure 6.9: Construction of new casing for MEMS accelerometer
6.4.2
Strain Gauges
C2A-06-125-lW-350 strain gauges manufactured by Micro-Measurements Group were employed to record strains in the aluminium tubes (see Table 6.3 for more specifications) Table 6.3: Characteristics of C2A-06-125-lW-35 0 strain gauges Characteristic Value Grid resistance in Ohms TC of Gauge factor %100 ◦ C Gauge factor at 24◦ C Transverse sensitivity
350.0 ± o.6% +1.3 ± 0.2 +2.115 ±0.5% +0.3 ± 0.2 %
Specifically, one aluminium tube of each model was instrumented with four pairs of strain gauges mounted on the opposite faces of the pile. M-Bond 200 adhesive was used to attach the gauges to the external surface of the tubes and the wires were passed internally to the tubes through holes with diameters of about 2 mm (see Figure 6.10). To ensure adequate protection, each strain gauge was covered by M-Coat, a polyurethane protective coating. Finally, the excitation voltage was provided by a RDP 600 Multi-Channel Signal Conditioning while completion of the Wheatstone bridge circuit was provided by RDP 628-type strain gauge amplifier modules wire into the RDP 600 rack (see Figure 6.11) 146
6. Experimental investigation (shaking table tests)
aluminium tube strain gauge
Figure 6.10: Example of C2A-06-125-lW-350 strain gauge mounted on the aluminium tube
Figure 6.11: RDP 628-type strain gauge amplifier modules mounted on the RDP 600 rack
6.4.3
Pore-water pressure transducers
PDCR 811 Druck pressure sensors were used to monitor the excess pore water pressure generated during shaking. A power supply of 10 V and 5 mA (nominal) was provided through a RDP 611 signal conditioning amplifier, this gave an output analog voltage of 10 Volts per 50 kPa. The pressure was measured by means of a flexible silicon diaphragm placed in front of the PPT. Moreover, in order to protect the diaphragm from the soil grains, a sintered metal filter was mounted in the front of each transducer. During the pluviation of the sand, 5 PPT transducers were 147
6. Experimental investigation (shaking table tests) embedded within the soil (see Figure 6.12) at different elevations as schematically illustrated in Figure 6.6.
Figure 6.12: Positioning of PPT during dry pluviation
6.4.4
Instrumented impact hammer
An instrumented impact hammer model 086C01 manufactured by PCB Piezotronics was used to excite the models in the free vibration tests (see Figure 6.13a). This also recorded the amplitude and frequency content of the excitation imparted to the models. The instrumented hammer consisted of a head body containing a quartz force sensor and a handle with rubber grips. A constant excitation voltage of 30VDC at a constant current excitation of 20 mA was provided through a Kistler (model 5134A) power supply/coupler which was also used for the amplification of the signal. A photograph of the Kistler is given in Figure 6.13b. More information is listed in Table 6.4. Table 6.4: Characteristics of Instrumented impact hammer (model 086C01, PCB) Characteristic Value Sensitivity Measurement range Resonant frequency Hammer mass Head diameter Tip diameter Hammer length
148
11.2 mV/N ± 400 N pk ≥ 15 Hz 100 gm 1.57 cm 0.63 cm 21.6 cm
6. Experimental investigation (shaking table tests)
(a)
(b)
Figure 6.13: : (a) Instrumented impact hammer model 086C01; (b)Kistler (model 5134A) power supply/coupler
6.4.5
Signal Conditioning and Data acquisition system
Signal conditioning procedures, namely amplification and filtering, were employed to improve the quality of the acquired data. Specifically, all the channels were passed through a low pass Butterworth filter set to 80 Hz. The data acquisition system consisted of 4 Microstar Laboratories MSXB028 analog-digital converter (ADC) cards, which provided with a total of 64 channels. Channels were simultaneously sampled at a target frequency of 200 Hz so to have zero phase lag. However, an actual frequency of 200.64 Hz was ultimately attained during the test. Furthermore, the acquisition was always initiated a few seconds prior the start of the actual test. The duration of the acquisition as well as the sampling frequency were controlled by a software called SIMACQ cer2.09 (written in HP-VEE version 4.01 ). The output data were all converted into text files. This facilitated the post-processing analysis which was carried out with the software program Matlab.
6.4.6
Testing programme
The experimental investigation was conducted in two stages hereafter referred to as first stage and second stage.
149
6. Experimental investigation (shaking table tests)
First stage In the first stage, the natural frequency and damping of the four physical models were assessed for three conditions. These were: • Free standing, i.e. before the dry pluviation of sand into the soil container; • After the dry pluviation of sand, i.e. piles embedded in dry soil at a relative density of 14%; • After full saturation of soil deposit. At this stage the soil layer was characterised by a relative density of 34%. The modal parameters were subsequently estimated from free vibration tests, in which an instrumented hammer tapped the pile cap of each model and generated its free decay response (see Figure 6.14). The modal parameters were then evaluated from the free decay responses recorded by the accelerometers positioned on the pilecaps. More details regarding the system identification techniques employed for the assessment of the resonance frequency and damping ratio are given in the following sections.
Figure 6.14: Impact test carried out on model GP1 before saturation of soil deposit
Second stage The purpose of the second stage was twofold. First, the tests were performed to evaluate the dynamic properties of the four physical models during the application of the horizontal shaking. Secondly, with the onset of liquefaction, the experimental 150
6. Experimental investigation (shaking table tests) results were used to investigate the effects induced by liquefaction on the dynamic properties of the models, bending moment profiles and response spectra. The selection of the input ground motion used in the second stage is discussed in details in the following section. The input ground motion consisted of a broad random white noise having a bandwidth frequency ranging from about 0 up to 100 Hz, which also corresponded with the operating frequency range of the shaking table (see Chapter 5 for more details). The input signal was produced through a signal generator built in a digital spectrum analyser (type Advantest series R9211 ) and was applied along the longside of the geotechnical model container. Since the shaking table was capable of operating in all six degrees of freedom simultaneously, the unidirectional motion was achieved by setting at zero five of the six degrees of freedom. It should be noted that the actual motion applied by the table is generally affected by parasitic movements due to distribution of mass on the table (Wood et al. 2002). These motions generally include vertical and lateral motions, yawing and pitching. As a consequence of this, the authentic input motion applied by the earthquake simulator was measured also by means of SETRA accelerometers mounted on the aluminium plate of the shaking table (see Figure 6.6). During the shaking table tests, the models were subjected to three levels of acceleration, namely 0.02 g, 0.04 g and 0.15 g, which aimed to study the dynamic behaviour of the models in three different phases (see also Figure 6.15). Each phase was identified by using the average value of the excess pore water pressure ratio ru (defined as the ratio 0 between the excess pore water pressure ∆u, and the effective overburden stress σvo ) developed by the shaking. The values of excess pore water pressure ratio illustrated in the figure were estimated from the 4 pore water pressure transducers embedded in the soil layer (see Figure 6.6 for more details regarding the instrumentation layout). The three phases are summarised here as follows: • Phase 1: before liquefaction, i.e. ru
