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Effects of void redistribution on liquefaction-induced ground deformations in earthquakes : a numerical… Seid-Karbasi, Mahmood 2009

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EFFECTS OF VOID REDISTRIBUTION ON LIQUEFACTION-INDUCED GROUND DEFORMATIONS IN EARTHQUAKES: A NUMERICAL INVESTIGATION  by MARMOOD SEID-KARBASI M. Sc., Iran University of Science & Technology, Tehran B. Sc., Iran University of Science & Technology, Tehran  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) March 2009 © Mahmood Seid-Karbasi, 2009  ii  ABSTRACT  Liquefaction-induced ground failure continues to be a major component of earthquakerelated damages in many parts of the world. Experience from past earthquakes indicates lateral spreads and flow slides have been widespread in saturated granular soils in coastal and river areas. Movements may exceed several meters even in very gentle slopes. More interestingly, failures have occurred not only during, but also after earthquake shaking. The mechanism involved in large lateral displacements is still poorly understood. Sand deposits often comprise of low permeability sub-layers e.g., silt seams. Such layers form a hydraulic barrier to upward flow of water associated with earthquake-induced pore pressures. This impedance of flow path results in an increase of soil skeleton volume (or void ratio) beneath the barrier. The void redistribution mechanism as the focus of this study explains why residual strengths from failed case histories are generally much lower than that of laboratory data based on undrained condition. A numerical stress-flow coupled procedure based on an effective stress approach has been utilized to investigate void redistribution effects on the seismic behavior of gentle sandy slopes. This study showed that an expansion zone develops at the base of barrier layers in stratified deposits subjected to cyclic loading that can greatly reduce shear strength and results in large deformations. This mechanism can lead to a steady state condition within a thin zone beneath the barrier causing flow slide when a threshold expansion occurs in that zone. It was found that contraction and expansion, respectively at lower parts and upper parts of a liquefiable slope with a barrier layer is a characteristic feature of seismic behavior of such deposits. A key factor is the pattern of deformations localized at the barrier base, and magnitude that takes place with some delay. In this thesis, a framework for understanding the mechanism of large deformations, and a practical approach for numerical modeling of flow slides are presented. The study was extended to investigate factors affecting the seismic response of slopes, including: layer thickness, barrier depth and thickness, ground inclination, permeability contrast, base motion characteristics and soil consistency.  iii Another finding of this study was that a partial saturation condition results in delay in excess pore pressure rise, and this factor may be responsible for the controversial behavior of the Wildlife Liquefaction Array, California (USA) during the 1987 Superstition earthquake. It was demonstrated that seismic drains are a promising measure to mitigate the possible devastating effects of barrier layers.  iv  TABLE OF CONTENTS  ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS ACKNOWLEDGEMENTS DEDICATION  ii iv viii ix xxi xxv xxvii  CHAPTER 1: INTRODUCTION 1 Background 1.1 Post-Liquefaction Strength and Void Redistribution 1.2 Objectives and Scope of Work 1.3 Organization of the Thesis  1 1 4 9 10  CHAPTER 2: CHARACTERISTIC BEHAVIOR OF SANDS AND LIQUEFACTION 2 Introduction Characteristic Behavior of Sands 2.1 2.1.1 Monotonic Loading Condition 2.1.2 Stress Path, Anisotropy, and Fabric 2.1.3 Cyclic Loading Condition 2.2 Impact of Partially-Drained Condition on Sand Behavior 2.3 Post-Liquefaction Response and Flow Slide 2.4 Flow Properties 2.5 Partial Saturation 2.6 Summary and Concluding Remarks  12 12 13 13 21 23 32 39 41 42 43  CHAPTER 3: LIQUEFACTION INDUCED-GROUND FAILURES 3.1 Introduction 3.2 Physical Model Studies on Void-Redistribution 3.2.1 Studies carried out in Chuo U. and Davis U 3.3 Laboratory Investigations on Void-Redistribution 3.4 Numerical Studies on Void Redistribution 3.5 Data from Case Histories 3.6 Summary and Main Findings  46 46 50 55 72 74 75 80  V  CHAPTER 4: MODELiNG OF 1NJECTION FLOW AND VOID REDISTRIBUTION 4.1 Introduction 4.2 Principles of the FLAC Program 4.3 Stress-Strain Model for Sands Principles of the UBCSAND Constitutive Model 4.3.1 Elastic Properties 4.3.2 Plastic Properties 4.3.3 Model Prediction of Laboratory Element Tests 4.4 Soil Profile Used in the Analyses 4.5 Analyses and Results 4.5.1 Sloping Ground without Barrier, Case I 4.5.2 Sloping Ground with Barrier, Case II 4.6 Significance of the Permeability of Liquefiable Soil Layer 4.7 Summary and Main Findings  83 83 84 93 94 95 98 100 100 102 107 112 124  —  CHAPTER 5: LOCALIZATION AND FLOW-SLIDE FROM VOID REDISTRIBUTION 5.1 Introduction 5.2 Mesh Size Effects 5.2.1 Effects of Base Element Thickness Characteristic 5.3 Response of a Fully Liquefied Layer with Perfect Barrier 5.3.1 Elastic Materials with Tensile Strength 5.3.2 Materials without Tensile Strength 5.3.3 Effect of Permeability Contrast (kBarrier / kSand) on Level-Ground Response 5.4 Maximum Soil Expansion and Flow Failure Conditions Proposed Approach for Modeling Localized Flow-Slides 5.5 5.6 Post-Liquefaction Strength Loss from Void Redistribution Summary and Main Findings 5.7  ...  126 126 129 129 135 138 140 151 153 161 165 167  CHAPTER 6: FACTORS AFFECTiNG SEISMIC RESPONSE OF GENTLE LIQUEFIABLE 169 SLOPES WITH HYDRAULIC BARRIER 169 6.1 Introduction 170 6.2 Effects of Mechanical Conditions 170 6.2.1 Effects of Ground Inclination 171 6.2.1.1 Soil Profile without Barrier 172 6.2.1.2 Soil Profile with Barrier Sub-Layer 178 6.2.2 Effects of the Barrier Depth, DB 178 6.2.3 Effects of Soil Relative Density, Dr 184 6.2.4 Effects of Motion Characteristics 184 Effects of Motion Amplitude, PGA 6.2.4.1 187 6.2.4.2 Effects of Motion Duration 188 6.3 Effects of Flow Conditions Liquefiable Thickness, 189 6.3.1 Effects of the Layer TL 195 6.3.2 Effects of Decrease in Liquefiable Layer Permeability 196 6.3.3 Effects of Permeability Contrast within the Sand Layer, ki. / kB 197 6.3.3.1 Effects of Permeability Contrast on Excess Pore Water Pressure 199 6.3.3.2 Effects of Permeability Contrast on Surface Displacements 200 6.3.4 Effects of Thickness of Barrier Layer, T 5 201 6.4 Summary and Main Findings  vi CHAPTER 7: BARRIER EFFECTS IN LIQUEFIABLE PARTIALLY SATURATED SOILS 203 7.1 Introduction 203 7.2 Facts pertaining to the Partially Saturated Condition 203 7.3 Modeling Pore Air Fluid 208 7.3.1 Bulk Modulus of Water-Air Mixture and its Pressure-Level Dependence 208 7.3.2 Skempton ‘s B Value for Partially Saturated Soils 211 7.4 Analyses Results 213 7.4.1 Element Tests 214 7.4.2 Soil Profile without Barrier 217 7.4.3 Soil Profile with Barrier 220 Observations from a Liquefied Site: Wildlife Liquefaction Array Case Study 223 7.5 7.5.1 General Information about the WLA Site 224 7.5.2 WLA Ground Conditions and Instrumentation 225 7.5.3 Ground Response in the 1987 Superstition Earthquake 227 7.5.4 Characterization of the WLA Site 229 FLACModeloftheWLASite 231 7.5.5 Earthquake Input Motion 7.5.6 233 Results of Analyses 7.5.7 233 7.6 Summary and Main Findings 240 CHAPTER 8: MITIGATING LOCALIZATION EFFECTS OF HYDRAULIC BARRIER IN LIQUEFIABLE GROUNDS: PRINCIPLES 242 8.1 Introduction 242 8.2 Implication of Seismic Drains and Analysis Approach 243 8.3 Analyses Results for Treated Models 245 8.3.1 Fully Penetrated Drain, Case I 246 8.3.2 Partially Penetrated Drain, Case II 248 8.3.3 Minimum Penetrated Drain, Case III 248 8.3.4 Discussion on Drain Depth Effects 253 8.4 Effects of Drain Permeability Reduction 257 8.5 Summary and Main Findings 261 CHAPTER 9: SUMMARY AND CONCLUSIONS 262 9.1 Introduction 262 9.2 Summary 263 9.3 Key Findings and Contributions 265 9.4 Recommendations for Further Studies 267  REFERENCES  270  APPENDIX I: CURRENT PRACTICE FOR LIQUEFACTION ASSESSMENT Al. Introduction Al. 1 Liquefaction Triggering Assessment, Current Practice AI.2 Stress Path, Anisotropy and Fabric AI.3 Rotation of Principal Stresses AI.4 Mixing AI.5 Post-Liquefaction Volume Change AI.6 Strain History AI.7 Ageing  310 310 310 313 318 319 321 323 324  vii Al. 8 Multi-Directional Loading AI.9 Gradation and Fines Content AI.9. 1 Liquefaction of Soils with Fine Grained Materials Al. 10 Current Practice for Estimating Residual Strength Al .11 Post-Liquefaction Stiffness  .325 326 327 347 353  APPENDIX II: PREVIOUS PHYSICAL MODEL STUDIES ON VOID REDISTRIBUTION 357 AII.1 Introduction 357 AII.2 Studies done in Chuo U. and Davis U 368 APPENDIX III: CASE HISTORIES OF DELAYED GROUND FAILURES AIlI. 1 Introduction  384 384  APPENDIX IV: BULK MODULUS OF WATER -AIR MIXTURE  414  APPENDIX V: SKEMPTON”SB VALUE FOR PARTIALLY SATURATED SOILS  418  APPENDIX VI: GROUND CHARACTERIZATION OF WILDLIFE LIQUEFACTION ARRAY SITE AVI. 1 Introduction AVI.2 Evaluation of CSR for Sandy Layer AVI.2 Estimation of Sand Layer Permeability  421 421 422 424  viii  LIST OF TABLES  Table 2-1: Range of k (mis) for different soils, as suggested in textbooks  42  Table 3-1: Model tests details for lateral spreads of bridge abutments (Kutter et al., 2004) Table 3-2: Findings of Davis U. and Chou U. joint research program on void redistribution  63 71  Table 4-la: Materials properties used in the analyses Table 4-lb: Properties associated with UBCSAND model applied to sand layer Table 4-2: Barrier effects on lateral displacements  101 101 111  Table 5-2: emin, emax and potential maximum expansion (%) values of sands at Dr = 50% .160 Table 6-1: Effects of various factors on the response of liquefiable slopes with barrier sub-layer. 201 Table 7-1: Material properties used in the WLA analyses  232  ix  LIST OF FIGURES  Fig. Fig. Fig. Fig.  1-1: Key elements of soil liquefaction engineering  2 1-2: Back calculated residual strength from failed case histories 6 1-3: Undrained residual strength of Lower San Fernando dam from laboratory tests 6 1-4: (a) Mechanism B globally undrained but with local volume changes; (b) Mechanism C global and local volume changes 7 Fig. 1-5: Effect of sand seems on slope stability by transferring consolidation pore pressures (Terzaghi, et al. 1996) 8 -  -  Fig. 2-1: Sand state in e-p’ space 14 Fig. 2-2: Typical response of a dense sand to shear loading tested by Taylor (1948), (a) sample loading condition, (b) sand response, i.e., lateral and vertical displacements 15 Fig. 2-3: Casagrande’ s critical void ratio concept: (a) & (b) hypothesis of critical void ratio derived from drained direct shear tests, and (c) Wroth’s (1958) simple shear test results on 1 mm diameter steel beads, a’ = 138 kPa, in terms of specific volume, v (v = 1+ e) and shear displacement, x (adapted from Park, 2005) 15 Fig. 2-4: Monotonic drained test results of Toyoura sand in terms of stress ratio and volumetric strain vs. axial strain (Fukushima & Tatsuoka, 1984) 17 Fig. 2-5: Response of Ottawa sand in drained monotonic simple shear test, reported by Vaid, et al. (1981) in terms of: (a) stress-strain; and (b) volumetric strain vs. shear strain (adapted from Park, 2005) 17 Fig. 2-6: Typical dilation and contraction regions for sands: (a) in strain space, vs. y; (b) grains distortion; and (c) stress space, q vs. p’ 18 Fig. 2-7: Stress path and phase transformation line for a tailings sand, showing its independence from initial state variables, i.e., void ratio, confining stress, stress ratio, K: (a) key , + Jh)/ 1 (cr diagram, and (b) test results (q = (a h)/ , p’ 2 2 (data from Vaid & Sivathayalan, 2000) 19 Fig. 2-8: Characteristic behavior of dense and loose sands in a monotonic undrained stresscontrolled triaxial test: (a) deviator stress vs. axial strain; (b) excess pore pressure vs. axial strain 20 Fig. 2-9: Effect of density on undrained stress-strain behavior of water pluviated Fraser River sand in simple shear test with a’ = 200 kPa; solid dots denote PT condition (data from Vaid & Sivathayalan, 1996) 21 Fig. 2-10: Fraser River sand respose change due to major principal stress rotation in undrained HCT test: b = (a2 3)/(a1 a3) (Vaid & Sivathayalan, 2000) 22 Fig. 2—11: Effect of fabric on undrained monotonic response of Fraser River sand with nominal 22 Dr = 40%, in simple shear test (Vaid et al., 1995) -  -  -  x Fig. 2-12: Cyclic drained simple shear response of loose Fraser River sand Dr = 40% in terms of (a) stress-strain, (b) & (c) volumetric strain vs. shear strain and shear stress, respectively (Sriskandakumar, 2004) 24 Fig. 2-13: Responses of dense and loose samples of air-pluviated Fraser River sand in cyclic drained simple shear test in terms of (a) stress-strain, (b) & (c) volumetric strain vs. shear strain and shear stress respectively (modified from Sriskandakumar, 2004). 25 Fig. 2-14: Responses of dense air-pluviated Fraser River sand in cyclic undrained simple shear test in terms of (a) stress-strain, (b) R 0 vs. No. of cycles.(Sriskandakumar, 2004). 26 Fig. 2-15: Response of Fraser River sand to cyclic undrained loading in simple shear test in terms of: (a) stress path, and (b) stress-strain (modified from Sriskandakumar, 2004). ..28 Fig. 2-16: Conceptual illustration of different stages in a typical response of a liquefied sand in undrained cyclic simple shear testing: (a) applied stresses in a simple shear test, (b) stress-strain curve, and (c) stress path (note dilaton is invoked after poit A when loading occurs) 29 Fig. 2-17: Cyclic cylindrical torsional test results for Toyoura sand (Dr = 55%, K 0 = 0.5, °‘yo = 100 kPa), (a) cyclic shear, (b) shear strain, (c) effective stress ratio, and (d) excess pore pressure ratio (Ishthara, 1996) 30 Fig. 2-18: Cyclic response of Toyoura sand in terms of: (a) stress path, (b) stress-strain (modified from Ishihara, 1996) 30 Fig. 2.19: Cyclic (a) stress path and (b) stress-strain response of loose sand with initial static shear stress (modified from Sriskandakumar, 2004) 31 Fig. 2-20: CSR to cause liquefaction vs. relative density for Toyoura sand at 100 kPa confining stress (Ishihara, 1996) 32 Fig. 2-21: Control of volumetric constraint in triaxial testing, (a) no-flow (undrained), (b) freeflow (drained), (c) in-flow (partially drained, expansion), and (d) out-flow (partially drained, contraction) 33 Fig. 2-22: Transformation of dilative response under constant volume condition into strain softening in volume expansion condition (modified from Eliadorani, 2001) 34 Fig. 2-23: Range of imposed volumetric strain change ratio comparing to that of undrained and fully drained conditions (da’r = 0), (modified from Eliadorani, 2001) 35 0 (modified from Eliadorani, 2001) Fig. 2-24: Effective stress paths for various zi / Ac 35 Fig. 2-25: Triaxial injection testing, (a) stress path, (b) & (c) effect of relative density on volumetric strain over the flow failure path due to pore water inflow in terms of mean effective stress and shear strain, respectively (modified from Sento et. al., 2004, with permission from ASCE) 36 Fig. 2-26: Comparison of dilatancy characteristics in CD and injection tests (Sento et al., 2004, with permission from ASCE) 37 Fig. 2-27: V-CSH tests results for Dr =36, 57, and 79%, (a) volumetric strain and (b) void ratio vs. shear strain (Sento et al., 2004, with permission from ASCE) 38 Fig. 2-28: Volumetric strain for various initial Dr required for reaching different levels of deformation (Yoshimine et al., 2006) 39 Fig. 2-29: Steady-state line of Touyora sand (Verdugo & Ishihara, 1996) 40 Fig. 2-30: Steady-state strength of Tia Juana silty sand vs. consolidation stress (Ishihara, 1996). 41  xi Fig. 2-31: Normalized residual strength with and without void redistribution involvement (Idriss & Boulanger, 2007) 41 Fig. 2-32: Cyclic stress ratio vs. No. of cycles for Toyoura sand with different degrees of saturation (Ishihara et al., 2004, reproduced by permission of Taylor & Francis Group) LLCion of Informa Plc) 43 Fig. 3-1: Liquefaction foundation failure, (a) Overturning and (b) settlement of structures resulting from liquefaction of foundation soils in Adapazari, Turkey, 1999 (adapted from Kammerer, 2002) 47 Fig. 3-2: Modes of liquefaction-induced vertical displacements (Seed et al., 2001) 48 Fig. 3-3: Modes of “Limited” liquefaction-induced lateral displacements (Seed et al., 2001) 48 Fig. 3-4: Examples of liquefaction-induced global instability and/or “Large” lateral spreading (Seed et al., 2001) 49 Fig. 3-5: Ground deformation and damage to buried pipelines (Rauch, 1997) 50 Fig. 3-6: Observation of water interlayer by Huishan & Taiping (1984) in shaking table test of stratified (alternating coarse sand and fine sand) deposit (test R-5, dimensions in cm) 52 Fig. 3-7: Formation of trapped water interlayer, and delayed sand boil following a hydraulic fracture mechanism 52 Fig. 3-8: Four stages (i.e. a, b, c and d) in centrifuge test model of two-layer deposit, (modified from Kulasingam, 2003) 54 Fig. 3-9: Lateral displacement patterns in centrifuge tests models of mildly sloping layered grounds, (a) homogenous sand, (b) layered soil (Fiegel & Kutter, 1 994b, with permission from ASCE) 56 Fig. 3-10: Sketch of 1D tube test device (Kokusho, 1999, with permission from ASCE) 57 Fig. 3-11: Photograph of Water Film Consisting of Clear Water Formed beneath Silt Seam (Kokusho, 1999, with permission from AS CE) 57 Fig. 3-12: Time-dependent variations in sand settlement (a) and pore pressure, (b) at different depths (Kokusho, 2003) 58 Fig. 3-13: Effect of sand relative density on water film thickness (Kokusho, 1999 with permission from ASCE) 58 Fig. 3-14: 2-D model tests with silt layer (Kokusho, 1999, with permission from ASCE) 60 Fig. 3-15: Soil deformation vs. elapsed time for representative points in sloping ground (a) case 1, with silt arc; (b) case 2, without silt arc; (c) location of representative points (Kokusho, 1999 with permission from ASCE) 61 Fig. 3-16: Cross-sectional deformation for slopes (a) & (b): with buried silt arc. (c) & (d) without silt arc. (a) & (c) during shaking. (b) & (d) after the end of shaking (Kokusho, 2003) 62 Fig. 3-17: Time-dependent flow displacement at target points shown in (d); a) without silt arc by PGA 0.34g. (b) with silt arc by PGA 0.34g. (c) with silt arc by PGA 0.18g. (Kokusho, 2003) 62 Fig. 3-18: General model configuration for lateral spreading study of bridge abutment (Kutter et al., 2004, with permission from ASCE) 63 Fig. 3-19: Deformation pattern of tested models, see Fig. 3-18 and Table3-1 for details (Kutter et al., 2004, with permission from ASCE) 64  xii Fig. 3-20: Discontinuous lateral deformations in the clay sand interface (adapted from Kulasingam, 2003) 65 Fig. 3-21: Typical model configuration and prototype equivalent using im-radius centrifuge with rigid container of 560 x 280 x 180 mm tested at Davis U. (Kulasingam et al., 2004, with permission from ASCE). Note that the base of the model in prototype scale is curved due to great variation in revolution radius within the model 67 Fig. 3-22: Typical model configuration using 9m-radius centrifuge with rigid container of 1759 x 700 x 600 mm tested at Davis U. (Malvick et a!., 2002) 67 Fig. 3-23: Shake table model (a) before testing and (b) after testing (Malvick et al., 2005) 68 Fig. 3-24: Centrifuge model configuration (a) before shaking, (b) after shaking, (c) close up of silt-sand interface after shaking (Kulasingam et a!. 2002) 69 Fig. 3-25: Initial state of sand beneath silt arc at mid-slope relative to steady-state line for Nevada sand (Kulasingam et al., 2004) 70 Fig. 3-2 6: Displacement time history above silt arc in models as shown in Fig. 3-22: (a) a 1 -g shake table test and, (b) an 80-g centrifuge test (Malvick et a!., 2005) 70 Fig. 3-27: UBC-CCORE model of submerged slope with barrier layer failed after end of shaking (prototype scale, Ng = 70g) 70 Fig. 3-28: Field condition of a stratified slope (a) sandwiched sub-layer silt, (b) laboratory simulation using torsional apparatus (Kokosho, 2003) 74 Fig. 3-29: Time histories of shear stress, strain, U, axial stress water film thickness/settlement for (a) with vertical restraint, and (b) without vertical restraint (Kokosho, 2003). 74 Fig. 3-30: Time histories of shear stress, strain, Ue, axial stress water film thickness for sample of 75 Dr = 28% with static shear bias. (Kokusho, 2003) Fig. 3-31: Lateral displacement vectors at area few hundred meters from the Shinano River in Niigata (Hamada, 1992 and Kokusho, 2003) 79 Fig. 3-32: Soil profile at Niigata Hotel area, Niigata (Kokusho & Fujita, 2002, with permission from ASCE) 80 Fig. 3-33: Liquefaction-induced bearing capacity failures of the Kawagishi-Cho apartment buildings (EERC, Un., Cal, Berkeley) 80 Fig. 4-1: Basic explicit calculation cycle used in FLA C 86 Fig. 4-2: Application of a time-varying force to a mass (concentrated in node), resulting in acceleration, velocity, and displacement (FLA C mass-spring system) 86 Fig. 4-3: Principles of UBCSAND mode!, (a)moving yield loci and plastic strain increment vectors, (b) dilation and contraction regions 95 Fig. 4-4: Plastic shear increment and shear modulus 97 Fig. 4-5: Comparison of predicted and measured response for Fraser River Sand, Dr = 40% & j’ = 100 kpa (a) stress-strain, CSR= 0.1, (b) R vs. No. of cycles (liquefaction: R> 0.95), (c) CSR vs. No. of cycles for liquefaction 98 Fig. 4-6: Prediction of soil element response in undrained and partially drained (inflow) triaxial tests for Fraser River Sand, Dr = 82% 99 4-7: Fig. Soil profile used in the analyses 101 Fig. 4-8: Acceleration time history for base input motion 101 Fig. 4-9: Analyses meshes used in the two cases with different materials types, (a) case j, profile without low permeability sub-layer, (b) case Ij, profile with low permeability sub layer 102  xlii  Fig. 4-10: Excess pore water pressure ratio Ru vs. time at selected points with increasing depth (case I) 103 Fig. 4-11: Deformation pattern of soil profile without barrier, case I (with max. lateral displacement of 0.95m after 14 s) 103 Fig. 4-12: Isochrones at certain time intervals for (a) lateral displacement, (b) excess pore water pressure (case I) 104 Fig. 4-13: Centrifuge model of a 1 Om infinite slope, (a) model configuration (model scale), (b) base motion, (c) & (d) isochrones of measured lateral displacement and excess pore water pressure at different time intervals, (e) acceleration time history measured at 2.5m depth with AH4 (modified from Sharp & Dobry, 2002 and Sharp, et al., 2003a, with permission from ASCE) 105 Fig. 4-14: Predicted time history of volumetric strain for various depths (case]) 106 Fig. 4-15: Predicted time history of horizontal displacement at top surface (case]) 106 Fig. 4-16: Excess pore water pressure ratio Ru vs. time at selected points with increasing depth (case II) 107 Fig. 4-17: Deformation pattern of soil profile with barrier, Case II (with max. lateral displacement of l.75m after 30 s) 109 Fig. 4-18. Surface lateral displacement vs. time for profiles with and without barrier 109 Fig. 4-19: Change of volumetric strain isochrones beneath the barrier over times, (a) initial stages, (b) longer time stages (case II) 110 Fig. 4-20: Predicted time history of volumetric strain for various depths (case II) 110 Fig. 4-21: Flow pattern after 2s shaking within (a) soil layer without barrier, case j, (b) soil layer with barrier, case II 111 Fig. 4-22: CSR vs. relative density for Fraser River sand under different isotropic consolidation pressures (reproduced based on data from Vaid, et al., 2001) 113 Fig. 4-23: Overburden reduction factor, K for CRR (adapted from Idriss & Boulanger, 2006). 113 Fig. 4-24: (a) single-column mesh of 20 elements of 0.25m x 0.5m size, (b) Base acceleration time history 114 Fig. 4-25: Acceleration time history at surface for two cases compared to input base motion... 114 Fig. 4-26: Time history of excess pore water pressure ratio, R for Flow-on and Flow-off conditions analyses 116 Fig. 4-27: Time histories of volumetric strain for Flow-on condition at various depths 117 Fig. 4-28: Imposed volumetric strain paths with No. of cycles for a sample in cyclic simple shear test 117 Fig. 4-29: Predicted excess pore water pressure ratio with No. of cycles for a sample in cyclic simple shear test 117 Fig. 4-30: Time history of excess pore water pressure at different depths measured in centrifuge test (Sharp & Dobry, 2002) 118 Fig. 4-31: Pattern of excess pore water pressure generation, (a) k = 8.81 x 1 06 mis, and (b) 8.81 nils 4 xlO 120 Fig. 4-32: Effects of liquefied soil permeability reduction (a) time histories of R at shallow depth, and (b) ground surface lateral displacement 121 Fig. 4-33: Displacement vectors for (a) undrained condition (b) partially drained condition 121  xiv Fig. 4-34: Effect of soil permeability on lateral displacement in centrifuge tests (Sharp, et al., 2003a, with permission from ASCE) 122 Fig. 4-35: Effect of soil permeability on liquefaction depth in centrifuge tests (Sharp, et al., 2003a, with permission from ASCE) 122 Fig. 4-36: Permeability reduction of concrete sand with silt content (data from Eigenbrod, et al., 2004) 123 Fig. 5-1: Single-column model of the 10 m-layer profile 128 Fig. 5-2: (Magnified) deformation pattern of the 100g model. (Note: in model scale, the length and permeability are 1/100 that of the prototype) 128 Fig. 5-3: Model of lOm soil profile with 0.25m width and different thicknesses for the base element, (a) 0.25m, (b) 0.5m, (c) 0.125m, and (d) 0.0625m 130 Fig. 5-4: Predicted time history of surface lateral displacement for models with various base element thicknesses 130 Fig. 5-5: Maximum volumetric strain of base element vs. its normalized thickness (singleprecision) 131 Fig. 5-6: Model of soil profile with embedment of a fine mesh of width/height = 1 beneath the barrier: (a) 0.125m, (b) 0.0625m, and (c) close-up of case b 132 Fig. 5-7: Maximum surface lateral displacement vs. normalized base element thickness in two modes of analyses 132 Fig. 5-8: Maximum volumetric strain of the base element vs. its normalized thickness (doubleprecision) 133 Fig. 5-9: Profile of volumetric strain for the meshes of different analyses: (a) 0.5m, 0.25m, and 0.l25m base elements; (b) 0.0625m, 0.031m, and 0.015m base elements (doubleprecision) 133 Fig. 5-10: Profile of volumetric strain for different analysis meshes close to the barrier base 134 Fig. 5-11: (a) Fully liquefied sand layer with impervious barrier, (b) initial excess pore water pressure within the liquefied layer, and (c) inflow and outflow of an element.... 136 Fig. 5-12: Fully liquefied soil layer with perfect barrier and its model used in analyses 138 Fig. 5-13: Profile of excess pore water pressure after stabilization time (1.0 s) 140 Fig. 5-14: Profile of (a) e, at 1 s, (b) vertical specific discharge at different time intervals (levelground, instantaneously liquefied, elastic model) 141 Fig. 5-15: (a) Profile of s for mesh with base element height of 0.0625m (at ls), (b) Specific discharge time histories for the base element of 0.5m and 0.0625m thickness (level-ground, instantaneously liquefied, elastic model) 141 Fig. 5-16: Excess pore water pressure isochrones at various time intervals and after stabilization time (20s) for the Mohr-Coulomb model 142 Fig. 5-17: Isochrones at different time intervals for the Mohr-Coulomb model with 0.5m base element thickness: (a) volumetric strain, (b) vertical specific discharge (level ground, instantaneously liquefied) 144 Fig. 5-18: Isochrones at different time intervals for the Mohr-Coulomb model with 0.0625m element thickness: (a) volumetric strain, (b) vertical specific discharge (level ground, instantaneously liquefied) 144 Fig. 5-19: Time history of (a) vertical specific discharge, (b) volumetric strain, and (c) excess pore water pressure ((level-ground, instantaneously liquefied, Mohr-Coulomb model) 145 ...  xv Fig. 5-20: Conceptual pattern for excess pore pressure isochrones at different time intervals: (a) 146 materials with tensile strength, and (b) materials without tensile strength Fig. 5-21: Isochrones at different time intervals for UBCSAND model with 0.5m element thickness: (a) volumetric strain, (b) vertical specific discharge (level-ground, 146 instantaneously liquefied) Fig. 5-22: Isochrones at different time intervals for the UBCSAND model with 0.0625m element thickness: (a) volumetric strain, (b) vertical specific discharge (level-ground, 147 instantaneously liquefied) Fig. 5-23: Enlarged isochrones at different time intervals for the UBCSAND model with 0.0625m element thickness: (a) volumetric strain, (b) vertical specific discharge (level147 ground, instantaneously liquefied) Fig. 5-24: Volumetric strain time history for the barrier base element having various thicknesses for level-ground condition with impervious barrier (level-ground, instantaneously liquefied, UBCSAND model) 148 Fig. 5-25: Time histories of (a) volumetric strain rate for bottom and base elements showing zero value at stabilized time (no-hydraulic gradient) for the UBCSAND model of levelground with 0.1 25m base element thickness: (b) specific discharge for the base element of 0.5m and 0.0625m thicknesses (level-ground, instantaneously liquefied, UBCSAND model) 148 Fig. 5-26: Max. volumetric strain rate vs. base element thickness: (a) in natural scale, and (b) in logarithmic scale (UBCSAND model with impervious barrier) 149 Fig. 5-27: Time histories of volumetric strain for the base element with various normalized thicknesses (UBCSAND model) 150 Fig. 5-28: Max. expansion rate vs. normalized base element thickness, (a) natural scale, (b) semilog scale (UBCSAND model) 150 Fig. 5-29: Isochrones of volumetric strain at different time intervals for the Mohr-Coulomb model with 0.5m element thickness for (a) kBarrier = 10 X kSand (b) kBarrier = 1 01 X 152 kSand Fig. 5-30: Isochrones of vertical specific discharge at different time intervals for the Mohr Coulomb model with 0.5m element thickness for kBarrier = 1 01 X kSand condition (level-ground with impervious barrier, instantaneously liquefied) 152 Fig. 5-32: Conceptual diagram of void ratio change due to excess pore water pressure redistribution in a liquefied layer beneath hydraulic barrier 154 154 Fig. 5- 31: Idealized infinite slope with low permeability sub-layer Fig. 5-33: Typical predicted response of sand at upper part of the liquefied layer in terms of: (a) volume change with vertical effective stress, and (b) effective stress path 155 Fig. 5-34: Typical predicted response of sand at lower part of the liquefied layer in terms of: (a) 155 volume change with vertical effective stress, and (b) effective stress path Fig. 5-35: Conceptual diagram showing increase in void ratio as a result of pore water migration due to liquefaction beneath the hydraulic barrier 157 Fig. 5-36: Void ratio change due to water injection in triaxial compression test for Toyoura sand (modified from Yoshimine, et al., 2006) 159 Fig. 5-37: Volumetric strain (expansion negative) vs. Dr to reach 30% axial strain in triaxial injection test for Toyoura sand (Yoshimine, et al., 2006) 159 Fig. 5-38: Maximum expansion potential vs. initial relative density for sands (based on Table 5-1 data and Eq. 5-13) 161 ,  xvi Fig. 5-39: Estimate of (&v )max for a base element with 1 0Do (0.003m) thickness (ETR = 0.0005) for Fraser River sand using extended trend of (, )m with element thickness ratio, 163 ETR 164 Fig. 5-40: Time histories of surface lateral displacement for two events 164 Fig. 5-41: Time histories of surface lateral velocity for two events Fig. 5-42: Void ratio and effective stress change at the barrier base due to undrained shaking and 166 pore pressure redistribution Fig. 6-1: Idealized infinite slope with low permeability sub-layer 170 Fig. 6-2: Predicted surface lateral displacement vs. ground inclination (profile without barrier 171 layer, 0.25gPGA) 171 Fig. 6-3: Surface lateral displacement vs. ground inclination in centrifuge tests Fig. 6-4: Increase of surface lateral displacement with ground slope (profile with barrier layer). 172 Fig. 6-5: Surface lateral displacement time histories for different ground slopes (profile with barrier layer) 172 Fig. 6-6: Surface lateral velocity time histories for the two slopes 173 173 Fig. 6-7: Excess pore water pressure time histories for the barrier base element Fig. 6-8: Ru vs. No. of cycles for Fraser River sand of Dr = 40% without static shear stress indicating post-liquefaction excess pore water pressure for (a) CSR = 0.08, (b) CSR = 0.1 and (c) CSR = 0.12 (test data from Sriskandakumar, 2004) 175 Fig. 6-9: Ru ys. No. of cycles for Fraser river sand of Dr = 40% with static shear bias indicating post-liquefaction excess pore water pressure for, (a); 0.05 a and (b) ; = 0.1 176 Fig. 6-10: Typical stress path of a soil element to liquefaction and subsequent dilation and 177 contraction during loading and unloading, respectively Fig. 6-11: Typical idealized seismic shear stress variation within an earth structure for level177 ground condition Fig. 6-12: Specific vertical discharge, Y-Flow for the base element, (a) 1°-slope and (b) 2°-slope. 179 Fig. 6-13: Surface lateral displacement time histories for different barrier depths (1°-slope). 179 181 Fig. 6-14: Increase of surface lateral displacement with barrier depth (1°-slope) 180 Fig. 6-15: Displacement vectors within the dense sand profile with barrier sub-layer Fig. 6-16: Excess pore pressure vs. time for the bottom and the base element of the dense soil layer 181 Fig. 6-17: Time histories of surface lateral displacement for dense soil layer 181 181 Fig. 6-18: Maximum surface lateral displacement vs. liquefiable soil layer Dr Fig. 6-19: Undrained torsional shear behavior of Fuji River sand at Dr = 75% (Ishihara, 1985) (a = mean effective confinement; a = initial mean effective confinement; r 182 and y in-plane shear stress and strain, respectively) Fig. 6-20: Accumulated lateral displacement vs. deformation index (Kutter et al., 2004, with permission from AS CE) 183 history 1, PGA = 2.5 2, Fig. 6-21: Applied acceleration time of(a) event 2 of 7 s, (b) event mIs PGA = 1.25 rn/s 2 of7 s, (c) event 3, PGA = 1.25 rn/s 2 of 14 s 185 ‘  ...  ‘,,,  xvii 2 and event 2, Fig. 6-22: Surface lateral displacement time histories for event 1, PGA = 2.5 rn/s PGA= 1.25 rn/s 2 186 186 Fig. 6-23: Maximum sueface lateral displacement vs. motion amplitude Fig. 6-24: Volumetric strain profile for event 1 and event 2 187 Fig. 6-25: Acceleration time history at 8 m depth for (a) event 1, PGA = 2.5 (mIs ) and (b) event 2 188 2, PGA = 1.25 (mIs ) 2 189 Fig. 6-26: Surface lateral displacement vs. time for event 2, and event 3 189 Fig. 6-27: Maximum surface lateral displacement vs. motion duration event 189 Fig. 6-28: Volumetric strain profiles for 1, event 2 and event 3 Fig. 6-29 Models used in analyses with position of elements for (a) 12 rn liquefiable layer, (b) 6 190 m liquefiable layer, and (c) 1 m liquefiable layer Fig. 6-30: Time histories of volumetric strain for elements at various depths (a) 12 m liquefiable 192 layer, (b) 6 rn liquefiable layer Fig. 6-31: Time histories of surface lateral displacements for 12 m, 6 rn and 1 rn-liquefiable 192 layer thicknesses Fig. 6-32: Time history of (a) excess pore pressure, (b) specific discharge of bottom element, and 193 (c) surface lateral velocity (12 m liquefiable layer case) Fig. 6-33: Time history of (a) excess pore pressure, (b) specific discharge of bottom element, and 198 (c) surface lateral velocity (6 m liquefiable layer case) Fig. 6-34: Time history of (a) excess pore pressure, (b) specific discharge of bottom element, and 194 (c) surface lateral velocity (1 m layer liquefiable case) Fig. 6-35: Time history of volumetric strain for elements at various depths of the 1 m liquefiable 195 layer 195 Fig. 6-3 6: Isochrones of volumetric strain along normalized liquefiable layer depth 196 Fig. 6-37: Max. surface lateral displacement vs. (TL)° ) 5 5 (in m° Fig. 6-38: Increase of surface lateral displacement with reduction in permeability of liquefiable 196 soil (profile with barrier layer, PGA = 2.5 mIs ) 2 Fig. 6-39: Time histories of R at different depths of the soil layer for different permeability contrast, (a) kJJkB = 1000, (b) kJ/kB = 100, (c) kJ/kB = 10, and (d) kJJkB = 1 (no 198 barrier) Fig. 6-40: Effective stress path for the base element for permeability contrast of (a) k =1, no /kB 1 barrier, (b) kilkB 10, (c) kjJkBlOO, and (d) kj/kB =1000 198 lateral displacements for different permeability contrasts Fig. 6-41: Time histories of surface 199 (kJJ7cB) Fig. 6-42: Surface displacement difference relative to uniform soil profile (%) with permeability 199 contrast (kJ/kB) Fig. 6-43: Change of surface displacements with barrier layer thickness for different permeability 200 contrast (kjj’kB) Fig. 6-44: Surface lateral displacement vs. product of permeability contrast (kL/kB) and barrier 200 thickness  xviii Fig. 7-1: (a) schematic profile of saturation condition in a typical soil layer, (b) profile of shear wave and compression wave velocity compared with that of water (V = 1500 mIs). 204 Fig. 7-2: Measured compression wave velocity in various soil types (Ishihara et al., 2004, reproduced by permission of Taylor & Francis Group, LLC, a division of Informa Plc.) 205 Fig. 7-3: Distribution of recorded peak accelerations with depth in three components (Yang & Sato, 2001) 206 Fig. 7-4: Cyclic stress ratio vs. No. of cycles for Toyoura sand (Ishihara et al., 2004, reproduced by permission of Taylor & Francis Group, LLC, a division of Informa Plc) 206 Fig. 7-5: Variation of air-water mix bulk modulus for different pore air pressures vs. saturation degree, (a) for saturation degree higher than 90%, (b) near fully saturation (> 99%). 211 Fig. 7-6: Bulk modulus of water-air mix vs. saturation for 100 kPa pore fluid (gauge) pressure derived from rigorous and approximate relationships represented by circles and triangles, respectively 211 Fig. 7-7: Variation of Skempton ‘s B value with saturation for different skeleton bulk modulus (u =0.2,u=lOOkPa) 213 Fig. 7-8: Variation of Skempton ‘s B value with saturation for different Poisson’s ratio, ,u (G = 43830 kPa, u = 100 kPa) 213 Fig. 7-9: Trend of model prediction for CSR with No. of cycles required for liquefaction for fully saturated (B = 0.95) and partially saturated Toyoura sand (B = 0.61) compared to test data 215 Fig. 7-10: Effect of saturation change during cycling on (a) R, (b) saturation, (c) Skempton B value and (d) pore fluid bulk modulud 215 Fig. 7-11: Typical predicted response of partially saturated soil sample to cyclic shearing, (a) R, (b) saturation, (c) Skempton c B value, and (d) pore fluid bulk modulus 216 Fig. 7-12: R rise vs. normalized No. of cycles for different initial saturation conditions predicted by element test FLA C simulation 217 Fig. 7-13: Maximum lateral displacement vs. soil saturation predicted for top surface of the shown mesh 218 Fig. 7-14: Predicted time histories of excess pore fluid pressure ratio, Ru for different initial saturations at shallow to deep points in a uniform gentle slope 219 Fig. 7-15: Time histories of surface lateral displacement for different initial saturation condition for soil layer with barrier 221 Fig. 7-16: Surface lateral displacement vs. initial saturation for soil layer with barrier 221 Fig. 7-17: Time histories for excess pore fluid pressure ratio, Ru for different initial saturation, from deep to beneath the barrier in a liquefied soil profile 222 Fig. 7-18: Map of Imperial Valley with marked location of WLA site and epicenters of the following pertinent earthquakes: 1981 Westmorland (M = 5.9), 1987 Elmore Ranch (M=6:2) and 1987 Superstition Hills (M=6.6) (Hoizer et a!., 1989)....226 Fig. 7-19: Oblique photo of Wildlife area showing localities of 1982 and new WLA sites (Youd et al., 2004a, by courtesy of Professor Youd) 226 7-20: WLA Fig. soil profile and instrumentation (modified from Bennett et al., 1984) 227 Fig. 7-21: Time histories of measured acceleration and excess pore pressure during 1987 Superstition earthqauke (modified from Hoizer et al. 1994) 228  xix Fig. 7-22: Time histories of excess pore pressure ratio, R, recorded by piezometers in sandy 230 layer of WLA site (data from Dobry et a!., 1989) Fig. 7-23: (a) profile of P-wave velocity measured at the new WLA site (data from Youd et a!., 231 2004), (b) model used in the analysis Fig. 7-24: Typical variation of Vp in a porous medium with a saturation range of 90% to 100% with (a) medium porosity and (b) Poisson ‘s ratio (Yang et a!., 2004) 232 Fig. 7-25: NS component (360 deg.) of Superstition 1987 Earthquake acceleration time history recorded by SM1 in down-hole and input motion applied to the model base in the analysis 233 Fig. 7-26: Predicted surface acceleration time histories compared to the measured record for (a) fully saturated condition and (b) partially saturated condition 235 Fig. 7-27: Predicted surface spectral acceleration (D = 5%) compared to that measured for (a) fully saturated condition and (b) partially saturated condition 236 Fig. 7-28: Predicted excess pore pressure ratio, R for P3 and P5 piezometers along with measurements 237 Fig. 7-29: Predicted excess pore pressure build-up after main shock for piezometer P5 238 Fig. 7-30: Predicted long-term record of R for piezometers P5 and P3 239 Fig. 7-31: Shear stress-strain curve, (a) prediction, (b) interpreted from measured data (Zeghal & Elgamal, 1994) 240  Fig. 8-1: Testing set-up for the: (a) no drain test and (b) drain test (Chang, et al., 2004) 245 Fig. 8-2: Measured R in the field liquefaction test for the case without drain and with drain (data 245 from Chang, et al., 2004) Fig. 8-3: Meshes used in analyses of drain effects with (a) full penetration, (b) half penetration, and (c) minimum penetration 246 Fig. 8-4: Distribution Of (Ru)m in the model with drain and flow vectors at 3.5 s 247 Fig. 8-5: Surface lateral displacement time history of the profile with barrier treated by drain 247 compared to that of profile without barrier Fig. 8-6: Predicted time history of R at mid-depth of loose sand: (a) uniform profile, (b) treated with drain (fully penetrated) 247 Fig. 8-7: Displacement and flow vectors within the model after 12 s (case I) 247 Fig. 8-8: Distribution of volumetric strain within the model, Case 1(12 s) 249 Fig. 8-9: Distribution of (Ru)m over time, during and after shaking (at 12 s), for the layer treated with the partially penetrated drain 249 Fig. 8-10: Displacement and flow vectors within the model with partially penetrated drain after lOs 250 Fig. 8-11: Surface lateral displacement time history of the profile with partially penetrated drain (case II) 250 Fig. 8-12: Contours of (Ru)max within the model treated by drain with: (a) minimum penetration, (b) half penetration, and (c) complete penetration 251 Fig. 8-13: Displacement and flow vectors within the model with minimum penetration drain after 16s 252 Fig. 8-14: Time history of surface lateral displacement for case III with minimum drain penetration 252 Fig. 8-15: Comparison of surface lateral displacement time histories with that of uniform layer. 253  xx Fig. 8-16: Variation of maximum surface lateral displacement vs. drain penetration depth ratio. 253 Fig. 8-17: Effects of penetration depth of the seismic drains in terms of time history of (a) R at mid-depth (element 1, 5), and (b) vertical specific discharge at barrier base (element 1, 13) 255 Fig. 8-18: Predicted stress-strain response for the barrier base element, [1,13] in the 3 cases. ..256 Fig. 8-19: Deformation profile for the profile withlwithout barrier and with drain of various depths i.e. full penetration, half penetration, and minimum penetration 256 Fig. 8-20: Acceleration time history at the barrier base (1, 14) for model treated by drain of (a) full penetration, (b) half penetration and (c) minimum penetration 258 Fig. 8-21: Time histories for the three cases with reduced drain permeability 259 Fig. 8-22: Open crack in liquefied soils in an abandoned channel of the Salinas River, Loma Prieta, California (earthquake: October 17, 1989) (adapted from Yang & Elgamal, 2001) 259 Fig. 8-23: Drain of minimum k (a) deformation pattern of the model with cracked barrier, maximum lateral displacement of 1.3 m, and (b) counters of (Ru)m within the soil profile 260  xxi  LIST OF SYMBOLS  B: Skempton  coefficient for pore pressure (ziu/Acrm)  CRR: cyclic resistance ratio CSR: cyclic stress ratio  —  —  —  Dr: relative density DB:  Depth of barrier layer  50 mean size of soil grains (50% passing) D : e: void ratio em:  maximum void ratio  emin:  minimum void ratio  e: initial void ratio e: intergranular void ratio : interfine void ratio 1 e F C. fines content i. hydraulic gradient IRD:  dilatancy index (Bolton, 1986)  LL: liquid limit LI: liquidity index  ) 2 u: fluid dynamic viscosity (e.g., units of N-sec/m k: soil permeability kBarrier:  barrier layer permeability  ksd: sand layer permeability kFMC: mobility coefficient used by FLAC for porous medium permeability v. volume v: volume of voids V specific discharge (in Darcy ‘s law)  J’,: compression wave velocity V: shear wave velocity  xxii g: the gravitational acceleration pw: the fluid mass density . at-rest soil pressure coefficient 0 K K: consolidation stress ratio K: correction factor for overburden K: bulk modulus K: bulk modulus of fluid (water) Km bulk modulus of air-fluid mixture M: constrained bulk modulus Km: earthquake magnitude correction factor N: Standard Penetration Test, SPT blow count, N-value  Nj: SPT blow count normalized for a reference overburden pressure (i.e. 100 kPa) 60 SPT blow count normalized for theoretical 60% energy N : : SPT blow count normalized for energy and overburden 60 (Nj) (NJ)60cs: SPT blow count normalized for clean sand (NJ)6OUBCSAND:  UBCSAND model N-value correlated to basic soil parameters  OCR: overcondoilidation ratio P1: soil plastic index  Q: empirical constant in Bolton ‘s dilatancy Eq. q: deviatoric stress R: contraction ratio (Verdugo & Ishihara, 1996) R,’: failure ratio  G: shear modulus Ge: elastic shear modulus G°: plastic shear modulus Giiq: shear modulus of liquefied soil U: pore pressure Ue: excess pore pressure n:  porosity  Fa. atmospheric pressure P ‘m: mean effective stress Sr: saturation Sr: residual undrained strength  xxiii S: steady state strength SPT: Standard Penetration Test TB:  thickness of barrier layer  TL:  thickness of liquefied soil layer beneath barrier layer  PGA: peak ground acceleration Y-Flow: vertical specific discharge, vertical flow rate  : element inflow rate 1 q : element outflow rate 0 q t:  time  a: ground inclination, sand placement direction o stress m.  mean stress  : effective initial verical stress 0 a’ a: verical stress a’: effective stress Id:  dynamic shear stress  : strain c: axial strain Sa:  axial strain  e: volumetric strain (e) *: Equivalent volumetric strain for an element corrected for mesh size (8v)max. e• 8  potential maximum volumetric strain  elastic strain  s°: plastic strain ço: soil friction angle p: friction angle at phase transformation condition q: friction angle at constant volume condition pp: peak friction angle Pcs/ss.  quasi/steady-state friction angle  y. shear strain elastic shear strain  xxiv “: plastic shear strain Yw. water unit weight ij:  stress ratio, tI a’  u: Poisson  ratio  u: fluid dynamic viscosity (e.g.,  units  of N-sec/rn ) 2  p: unit density r shear stress R:  relative state parameter (Boulanger, 2003 a) dilation angle and state parameter in e-p’ space (Been & Jefferies, 1985)  2D: two-dimensional  xxv  ACKNOWLEDGEMENTS  I learned from several years engagement in engineering practice that the best way to grasp cutting-edge technical knowledge is to return to student-status. However, this change in life style was a challenge and indulgent. This could happen with support from many people. It was my fortune and privilege of working under the supervision and advice of Professor Peter M. Byrne who made it possible for me to do that. I express my sincere appreciation for his continuous support and passion throughout my time at UBC to pursue a fundamental understanding of soil behavior and geomechanics. I would also like to thank Dr. John Howie my co-advisor for his guidance and in-depth comments. Grateful appreciation is extended to Professor D. Anderson, Dr. D. Wijewickreme, Professor 0. Hungr, Professor J. Fannin, and Dr. L. Yan who served on my final/qualifying exam committee. Special thanks go to Professor Y. Vaid for his generosity and helpful discussion I had in the early stage of my research. I should also thank Professor L. Finn for his encouragement I received from him. Financial supports provided by BC-Hydro and National Science and Engineering Research Council of Canada (NSERC) are gratefully acknowledged. I had also the opportunity to work at BC-Hydro office during my studies; I had valuable discussions with Dr. M. Lee, I wish to thank him. I also extend my thanks to Mr. Al Imrie, Mr. K. Lum and his colleagues at the Geotechnical group of BC-Hydro. Over the last three years, I have returned to my profession at Golder Associates Ltd., where I had constructive discussions with Drs. U. Atukorala, H. Puebla, J. Ji, G. Wu and other colleagues which are acknowledged. In particular, supports and invaluable comments from Dr. Upul Atukorala on the manuscript are deeply appreciated. I also would like to express my appreciation to Professors H. Poorooshasb, A. Afshar, A. Kaveh and Dr. P. Brenner for their encouragement in perusing my studies.  xxvi During the course of this research at UBC, I had helpful discussions with my fellow graduate students Ken, A. Amini, S. Sriskandakumar, S. Park and M. Sanin, I thank them. Particularly, I thank E. Naesgaard for his constant willingness to discuss on mutual interests in variety of technical issues. In preparation of this thesis, I have used a number of figures from other sources which I hereby acknowledge the permissions granted me by publishers and individuals, namely: —  —  —  —  —  —  —  —  —  —  -  —  -  —  —  -  -  —  —  American Society of Civil Engineers American Association for the Advancement of Science Professor John Berrill BiTech Publisher Ltd. University of California at Davis, Center for Geotechnical Modeling Earthquake Engineering Research Center Elsevier Ltd. John Wiley & Sons Inc. National Research Council Canada Oxford University Press Sung-Sik Park Professor Shamsher Prakash Dr. Alan Rauch Somasundaram Sriskandakumar Taylor & Francis Group, LLC Thomas Telford Ltd. Dr. Jun Yang Professor Mitsutoshi Yoshimine Professor Leslie Youd  The last but by no means the least, I would like to extend my deepest gratitude to my parents and sisters and other family members for their support and patience. Finally, the contribution and understanding of my wife, Naghrneh and my son, Puya and my lovely little daughter, Noura that would not be possible to describe with words are fully appreciated. Nothing would become true without God willing who gives us every thing. Thanks to God.  xxvii  DEDICATION: To my Parents  1  CHAPTER 1  INTRODUCTION  1  Background The effects of liquefaction on foundations of buildings, bridges, port facilities, and  lifelines continue to cause large economic and human losses after earthquakes. Following the devastating 1964 Niigata earthquake in Japan, and the 1964 Good Friday earthquake in Alaska, USA, many geotechnical earthquake engineering research programs on liquefaction were initiated in Japan and North America. These have provided researchers with better insight into the liquefaction phenomenon and associated failures. Nevertheless, recent earthquakes, e.g. 1994 Loma Prieta (USA), 1995 Northridge (USA), 1999 Kocaeli (Turkey), and 1999 Chi-Chi (Taiwan) indicate the need for further research into the complex behavior of liquefying soils. Over the past four decades, significant progress has been made in understanding the factors that cause soil liquefaction and the consequences of liquefaction. Initially, progress was largely confmed to improving the ability to assess the likelihood of initiation (or “triggering”) of liquefaction in clean, sandy soils. As the years passed, researchers became increasingly aware of the liquefaction susceptibility of both silty and gravelly soils, stratification, post-liquefaction shear strength, and the deformation behavior of liquefied soils. Currently, the area of “soil liquefaction engineering” is emerging as a semi-mature field of practice in its own right (Seed et al., 2003). This area now involves a number of discernable sub-issues, or subtopics, as illustrated schematically in Fig. 1-1. As the figure shows, the first step in most engineering treatments of soil liquefaction is the assessment of “liquefaction potential” or the risk of “liquefaction triggering”. Some recent advances in this area have been described by various authors (Youd et al., 2001; Seed et al., 2003; Byrne et al. 2006 and Idriss & Boulanger, 2006).  Chapter 1: Introduction  2  I  I  1. Triggering Assessment  I 0  2. Post-Liquefaction StrengthlStability .c 4-  .Q.O  ZedDefoatio7  0  Tsequessessmenfl  >  Iii 9  I tigationases  Fi.g. 1-1: Key elements of soil liquefaction engineering  Once liquefaction is determined to be a potentially serious hazard, the next step is to assess the potential consequences of liquefaction. This would likely involve an assessment of the available post-liquefaction strength/stifffiess, and the resulting post-liquefaction overall stability (flow-slide). The post-liquefaction strength (residual strength) is a key factor in this process and controls the scope of further actions (see Fig. 1-1). The soil strength is affected by void redistribution, which is involved in all stages of the process (Fig. 1-1) and this is the prime focus of the present  study.  If post-liquefaction stability is  found to be low,  then the  deformation/displacement potential is large, and engineered remediation measures would be warranted. When the post-liquefaction overall stability is acceptable (no occurrence of flow slide), an assessment of the anticipated displacements is required. This area of research is still immature, and much needs to be done with regards to the development and calibration/verification of the engineering tools and methods. The tools range from empirical and simplified methods (e.g., Youd et al., 2002 and Newmark, 1965) to sophisticated numerical procedures using total stress and effective stress approaches (e.g., Beaty & Byrne, 1999; and Byrne et a!., 2004). Similarly, a few engineering tools and guidelines are available for assessing the effects of liquefactioninduced deformations and displacements on the performance of structures and other engineered  Chapter 1: Introduction  3  facilities. Establishing criteria for “acceptable” performance are more frequently considered in various design standards, though they are not fully developed or well-established. Finally, in cases where the engineer(s) conclude that a satisfactory performance cannot be counted on, engineered mitigation of liquefaction risk is generally warranted. This is also a rapidly evolving area, and one which is rife with potential controversy. The ongoing evolution of new methods for mitigation of liquefaction hazard is providing an ever-increasing suite of engineering options, but the efficiency and reliability of some of these remain contentious. Accurate and reliable engineering analyses, to confirm the improved performance provided by many of these mitigation techniques, continue to be difficult. Our understanding of soil behavior, and in particular, liquefaction, has been improved from: •  Observations of field case histories;  •  Extensive laboratory testing of soil samples (or elements) under monotonic and cyclic loading conditions;  •  Model testing of earth structures under simulated earthquake loading; and  •  The development of numerical modeling procedures. Numerical procedures have proven to be particularly useful tools for studying soil  liquefaction and associated displacements caused by earthquakes. Two key aspects that control the response of an earth structure to earthquakes are: 1. Mechanical conditions. 2. Flow of water within and between soil layers (flow/hydraulic conditions). Mechanical conditions that encompass soil properties (i.e., soil density, stiffness, strength, etc.) and the characteristics of applied loads (i.e., static and cyclic stresses) are primarily responsible for generating excess pore water pressures during earthquake shaking. Flow (hydraulic) conditions; i.e., drainage path, soil hydraulic conductivity/permeability and its spatial variation (permeability contrast) within the soil layers control excess pore pressure redistribution during and after earthquakes. Most, if not all, of the previous liquefaction studies have been based on the assumption that undrained conditions exist within the soil layers (i.e., no flow occurs during or after  Chapter 1. Introduction  4  earthquake loading) and were therefore focused on the mechanical behavior of soils without accounting for the flow conditions. Liquefaction was defmed in the proceedings of the NCEER (1997) workshop, adapted from Marcuson (1978), as: the transformation of a saturated granular material from a solid to a liquefied state as a consequence of increased pore-water pressure and reduced effective stress. In this thesis, seismic liquefaction refers to a sudden loss in stiffness and strength of soil due to the effects of cyclic loading from an earthquake. The loss arises from a tendency for granular soil to contract under cyclic loading and, if such contraction is prevented or curtailed by the presence of water in the pores that cannot escape, it leads to a rise in pore water pressure and a resulting drop in effective stress. If the effective stress drops to zero (100% pore water pressure rise), the strength and stiffness also drop to zero and the soil behaves as a heavy liquid. However, unless the soil is very loose, it will dilate with the continued application of shear strains and regain some stiffness and strength. The change of state occurs most readily in loose to moderately dense granular soils with poor drainage. As liquefaction occurs, the soil stratum softens, allowing large cyclic deformations to occur. Liquefaction and the associated excess pore water pressures results in a pore pressure redistribution within the soil strata driven by the hydraulic gradient developed both during and after earthquake shaking. The liquefaction manifestation and consequences are typically divided into two classes: •  Level ground conditions, and  •  Sloping ground conditions. In level ground conditions (without shear stress bias), liquefaction causes settlement from  the reconsolidation and sedimentation (Florin & Ivanov, 1961; Scott, 1986; Ragheb, 1994; Butterfield & Bolton, 2003; and Miyamoto et al., 2004). Structures supported on, or in, such liquefied materials, may experience large displacements or (bearing) failure. In sloping ground conditions (with shear stress bias), liquefaction leads to lateral displacements/spreading and, if the available post-liquefaction strength is lower than the driving stresses, it leads to flow failure.  1.1  Post-Liquefaction Strength and Void Redistribution  The state-of-practice for assessing the post-liquefaction strength of soil relies on the pre earthquake soil properties and an estimation of residual shear strength, Sr, based on values that are back-calculated from case histories (e.g., Seed & Harder, 1990; Mesri & Stark, 1992; and  Chapter 1: Introduction  5  Olson & Stark, 2002), which involved flow-slides. Fig. 1-2 shows the relationship between the residual strength and the normalized Standard Penetration Test, (Nj) o for clean sands 6 developed by Idriss (1998) from a reevaluation of Seed & Harder (1990) data. These values are generally much lower than the values derived from laboratory tests on (undisturbed) soil samples, based on the undrained steady-state strength approach (Poulos et al., 1985). This issue has been pointed out by a number of investigators (e.g., Seed, 1987; Byrne & Beaty, 1997; Seed, 1999; Kokusho, 2003; and Seid-Karbasi & Byrne, 2004a among others). Fig. 1-3, for example, shows the undrained residual strength of undisturbed samples (solid symbols) from the Lower San Fernando dam that failed after the 1971 earthquake. The test results suggest much larger strengths (at the initial void ratio) than those obtained from back analysis and shown in Fig. 1-2 (shown with an arrow in the figure). The void redistribution mechanism, occurring during, and after, an earthquake, can explain these differences in residual strengths. The significance of the void redistribution mechanisms was conceptually outlined by Whitman (1985), though detailed experimental studies to investigate the mechanism have been performed only recently. If a liquefiable soil layer is overlain by a (practically) impermeable layer, earthquake-induced liquefaction can cause loosening of a zone of soil below the impermeable layer. The lower portion of the liquefied soil layer densifies as the earthquakeinduced pore pressures dissipate by upward water flow, while, the upper portion of this layer loosens because of the impedance to the water flow, caused by the impermeable layer. These local volume changes (void redistribution) can take place without global volume changes, referred to as “Mechanism B” by the NRC (1985). A soil that is initially dense (comparing to the critical state void ratio) can expand due to water migration (injection) and loosen by Mechanism B, so that its shear strength, Sr becomes smaller than the static shear stresses, and flow liquefaction develops (see Fig. 1 -4a). High excess pore water pressures in liquefied zones can cause flow of water into other zones with initially low or negligible excess pore water pressures (see Fig. 1-4b). This can cause loosening of cohesionless soils and the cracking of cohesive soils. This process takes place with both local and global volume changes and was named “Mechanism C” by the NRC (1985). Mechanism C causes reductions in the available shear strength of different soil zones, and can also lead to flow liquefaction in soils that are initially dense (comparing to the critical state void ratio).  6  Chapter 1: Introduction  40 Case History Data  (‘3 0  30 • EQ-Induced (SPT Measured)  -c -I D)  20  Cl)  o EQ-Induced  (‘3 D  (SPT estimated)  U)  10  • Construction Induced  0 0  4  12  8  16  20  1 -6o N Fig. 1-2: Back calculated residual strength from failed case histories.  0.9  w 0  0  Silty sand, Lower San Fernando Dam • Seed et al. (1989) V Castro et al. (1989) Li Baziar and Dobry (1995) C] Reported by Marcuson et  >  500 1000 Undrained residual strength at steady state, (kPa)  0.2  0.5  1  2  5  10  20  50 100  Fig. 1-3: Undrained residual strength of Lower San Fernando dam from laboratory tests (adapted from Yoshimine & Koike, 2005).  7  Chapter I. Introduction  Flow-Induced Effective Stress Reduction; Cracking  Sand Loosened by Flow Low-Permeability Layer Loosening  Excess Pore Water  Contracting  (b) Mechanism C  (a) Mechanism B  Fig. 1-4: (a) Mechanism B globally undrained but with local volume changes; (b) Mechanism C global and local volume changes. -  -  Any of the above mechanisms on their own, or in combination, can cause flow liquefaction. For example, different parts of a given slope may become unstable due to different mechanisms, and together, can cause an overall flow failure. Experience from past earthquakes indicates that lateral displacements (or spreads) and flow failures have occurred in liquefied soils in coastal regions, river deltas, and near river banks, in many regions of the world, including: Alaska (US), Niigata (Japan), and Turkey. Movements may exceed several meters, even in gentle slopes of less than a few percent (Kokusho, 2003). Submarine slides have been seismically triggered in many regions, as reported by Scott & Zukerman (1972) and by Hamada (1992). More interestingly, lateral spreads or flow slides have occurred not only during, but also after, earthquake shaking has stopped. These large movements are mainly driven by gravity, though the initial triggering of liquefaction is caused by seismic stresses. The slopes in these slides were gentle, normally less than 5° and sometimes less than 1° (Hampton & Lee, 1996). Although lateral flow failures have been reported in past earthquakes, causing damage to structures, the mechanism leading to large lateral displacements is poorly understood. Sand and silt deposits often comprise many sub-layers as a result of the sedimentation process. A number of researchers have examined the effect of layering on post-liquefaction sliding, including: Scott  Chapter 1. Introduction  8  & Zukerman (1972); Huishan & Taiping (1984); Liu & Qiao (1984); Elgamal et al. (1989); Adalier & Elgamal (1992); Fiegel & Kutter (1992); Kokusho (1999, 2000); Kulasingam et al. (2001); Malvick et a!. (2002, 2005, & 2006); Yang & Elgamal (2002); Kulasingam (2003); Seid Karbasi & Byrne (2004a, 2007); Sento et al. (2004); Kulasingam et a!. (2004); and Yoshimine et al. (2006). Based on physical model tests and site investigations, Kokusho (1999) and Kokusho & Kojima (2002) concluded that liquefaction failure can be caused by the formation of a waterrich zone at the base of a sub-layer leading to a zone of essentially zero strength. Such failures can only be explained by the void redistribution mechanism. This mechanism influences all processes involved in engineering of earth structures for seismic safety (see Fig. 1-1). The use of residual strength from undrained laboratory tests on undisturbed samples (if possible) taken before earthquake shaking does not represent the conditions that develop during and following void redistribution. The mechanism of void ratio change due to pore pressure redistribution has been addressed in a general sense by pioneering researchers as a possible cause of embankment failure. Terzaghi & Peck (1967) suggested a possible mechanism for pore pressure redistribution in a clay foundation with sand seams under a fill embankment (see Fig. 1-5). The high pore pressures, induced in the middle of the embankment foundation from the construction of the fill, can be transferred by a preferred drainage path provided with higher permeability sand seams, to the critical toe region of the slope, to create instability.  .S//a’i7 AS//Q’flCE-’.-..  :.;.:.‘“°‘  Fig. 1-5:  Effect of sand seems on slope stability by transferring consolidation pore pressures (Terzaghi, et al. 1996).  The mechanism of void redistribution needs to be thoroughly understood to be able to account for its effect on the shear strength and deformations. Natural and man-made soil deposits  Chapter 1: Introduction  9  are heterogeneous in nature. Heterogeneities can be present at both macro and micro scales. Pore pressure increases, due to an earthquake, cause hydraulic gradients and associated pore fluid flow during, and after, earthquake shaking. Stratifications affect the pore fluid flow due to the permeability contrasts. These features can therefore result in void redistribution, with certain zones becoming loosened and others becoming densified. The result is that the state of soil properties changes during, and after, shaking. The change in properties implies that the current practice of estimating a design (residual) shear strength, based on pre-earthquake soil properties, has a high degree of uncertainty. This can lead to highly unreliable or unsafe designs that are not supportable from a fundamental soil mechanics point of view. A major difficulty associated with either field or physical model data (e.g., centrifuge tests), is the lack of direct measurements of void redistribution. Recent experimental investigations, such as those by Sento et al. (2004) and Yoshimine et al. (2006) using laboratory testing and Malvick et al. (2005) employing physical models have improved the understanding of void redistribution, though they still lack the exploration of all factors and conditions needed for flow failure, especially in regards to the context of volume change driven by flow conditions. Numerical modeling, using the effective stress approach, and based on the fundamentals of soil mechanics, could be a unique alternative that provides good insight into such problems. This approach is used in this thesis to develop a sound explanation for the mechanism.  1.2  Objectives and Scope of Work  The prime objective of this research is to gain a concrete understanding of the void redistribution mechanism involved in the seismic behavior of earth structures and to understand how this mechanism controls the low residual strength and large deformations and/or failures in gentle slopes of sandy soils. To achieve this purpose, a coupled stress-flow analysis procedure based on an effective-stress approach is used to numerically investigate the phenomenon, and the results are supported by observations from field, physical models, and laboratory test data. The insight gained from this study provides a rational basis for designing remedial measures for liquefiable earth structures and foundations. Several researchers, using physical test models (e.g., Elgamal et al., 1989; Dobry & Liu 1992; Kokusho 2003; Kulasingam 2003; and Malvick 2005) and numerical modeling (Yang & Elgamal 2002) have also noted the occurrence of void redistribution in the presence of inclusions,  Chapter 1. Introduction  10  but their conclusions were not justified by a framework based on the characteristic behavior of sands in the context of volume changes arising from the flow/hydraulic conditions, as observed in laboratory element testing. Furthermore, these authors did not investigate the required conditions for a flow-slide. Therefore, the mechanism is still poorly understood or unknown. This thesis presents the results and fmdings of a numerical study of seismic behavior for layered, infmite, and gentle slopes using the UBCSAND constitutive model. The fmdings are not limited to these situations only. The employed constitutive model can capture the element sand behavior under various boundary conditions (i.e. drained, undrained, or partially drained), subjected to different loading types (i.e. monotonic or cyclic). The main purposes of this study are: • •  • •  1.3  To investigate the conditions that lead to development of localized shear strains in slopes of liquefiable soils. To explore the characteristic behavior of gentle liquefiable slopes (with a low permeability sub-layer) in earthquakes to obtain a coherent explanation for observations from field data (e.g. low residual strengths). To investigate the effects and significance of flow (hydraulic) conditions on the seismic behavior of liquefiable grounds. To study the requirements for liquefaction-induced flow-slide.  Organization of the Thesis  The thesis is organized into nine chapters and six appendices, as follows: Chapter 1:  Background and scope of the research and general organization of the thesis.  Chapter 2:  Characteristic behavior of sands in monotonic and cyclic loading, using element test data.  Chapter 3:  Review of previous studies on void redistribution and description of a typical case history from past earthquakes as evidence in support of the occurrence of void ratio redistribution.  Chapter 4:  Principles of the applied numerical procedure, demonstrating its ability to capture the void ratio redistribution mechanism and associated localization; highlighting of the significance of liquefiable soil permeability and flow conditions in the seismic ground response.  ChapterS:  Exploration of the seismic characteristic behavior of a liquefiable sandy slope comprised of a low permeability sub-layer. Also, the effects of mesh size involved in the numerical analysis are addressed and an approach is proposed for  Chapter 1: Introduction  11  overcoming the problem. A framework is presented for ascertaining the likelihood of lateral spreading and/or flow slide. Chapter 6:  Investigation of the effects of various factors affecting void ratio redistribution; i.e., barrier depth, liquefiable layer thickness, permeability contrast, barrier thickness, ground inclination, soil consistency, and base motion characteristics.  Chapter 7:  Presents the results of a study on the effects of partial saturation conditions on the seismic liquefiable ground response. Presents fmdings and an explanation for the behavior of the Wildlife Liquefaction Array (WLA) experimental site (California, USA), that was observed during the 1987 Superstition Hill earthquake.  Chapter 8:  Provides the results of implementing seismic drain as a remedial measure to mitigate the barrier effects and localization. The seismic drain is shown to be a promising treatment technique to alleviate associated large deformations caused by void redistribution.  Chapter 9:  Summarizes the conclusions and makes recommendations for future research.  Appendix I:  Current practice for liquefaction assessment and related issues; e.g., fmes content.  Appendix II:  List of previous studies on void redistribution using physical model testing.  Appendix III: Catalogue of case histories with void redistribution involvement. Appendix IV. Detailed derivation of bulk modulus for pore fluid of air-water mixture. Appendix V:  Detailed derivation of Skempton  B value for partially saturated soils.  Appendix VI.. Includes related geotechnical data used to characterize the WLA experimental site.  12  CHAPTER 2  CHARACTERISTIC BEHAVIOR OF SANDS AND LIQUEFACTION  2.  Introduction Any numerical approach in geo-mechanics is an attempt to simulate the actual behavior of  geo-materials under applied loads. Such simulation should capture the behavior of an element of soil under different loading conditions. Therefore, having a clear picture of sand behavior and its complex stress-strain relationship will greatly facilitate the development of a suitable modeling technique. The main features of sand behavior are stiffness and strength, both before and after liquefaction onset. Liquefaction in granular materials is associated with a large decrease in effective stress due to pore pressure rise during monotonic or cyclic loading. This leads to large reductions in the shear stiffness and strength of soils. In addition, the bulk stiffness of the soil skeleton is greatly reduced upon liquefaction and gives rise to post-liquefaction settlements, as pore water pressures dissipate. Most studies on liquefaction have focused on its triggering using undrained loading as the relevant condition. However, the sand response is controlled by the skeleton and volumetric constraint of the water as noted by Martin et al. (1975). Since water is essentially incompressible, the constraint is related to whether or not water in the pores has time to flow and cause significant volume change during and after the period of strong shaking. This can greatly affect the soil shear response. In this chapter, the characteristic behavior of clean sands is presented based on observations from laboratory element testing in monotonic and cyclic loading conditions (drained and undrained). This forms the framework for further discussions on the key factors that affect liquefaction behavior. The partially-drained condition is the most relevant condition to void  Chapter 2. Characteristic Behavior ofSands and Liquefaction  13  redistribution and is discussed in this chapter. Other experimental studies associated with void redistribution are treated in Chapter 3. For earthquake loading a simple shear test can better mimic the induced loading condition (Peacock & Seed, 1968 and Silver & Seed, 1971). During earthquake excitation, the application of cyclic shear stress results in a gradual change of principal stress direction that can be reproduced better in a simple shear test. This test can also better represent the conditions of postliquefaction flow slide. Nevertheless, most results in the literature are related to compression triaxial tests, traditionally used in many studies; therefore, the test data presented in this chapter are mainly taken from triaxial testing methods.  2.1.  Characteristic Behavior of Sands  2.1.1. Monotonic Loading Condition  Sand is a granular material and its particles are packed in states ranging from very loose to very dense as illustrated in Fig. 2-1 in terms of void ratio vs. effective mean stress (this figure is discussed in more detail later in this section). The particles are generally not bonded and, under the action of loading, they tend to rearrange themselves to cope with the load. In contrast to metals, which only exhibit volumetric deformations when the mean stress is changed, sands change in volume if they are sheared. Many researchers (e.g., Casagrande, 1936; Roscoe et al., 1963; Cole, 1967; Castro, 1969; among others) have extensively investigated the drained static behavior of saturated sands. These studies suggest that sands at very large shear strain, whether starting from an initial loose or dense state, will end up at a unique state (ultimate state) at which point the strength depends only on applied effective stress. Based on this finding, two terms, “Critical-State” and “Steady-State” were introduced by various investigators (e.g., Roscoe et al., 1968; and Poulos et al., 1981) to describe the ultimate sand strength. In fact, as noted by Poorooshasb (1989) and Verdugo (1992), the two terms are essentially the same and represent the state of a sand element at large shear strain. Casagrande (1936) observed that sand experiences significant volumetric deformations during shearing. This phenomenon, known as shear-induced volumetric strain, is a key feature of sand behavior.  Chapter 2: Characteristic Behavior ofSands and Liquefaction  emax  14  —  0  •D  0  Very Loose, Upper Bound Steady-State  —  Very Dense, Lower Bound  Mean Effective Stress, P’  Fig. 2-1: Sand state in e-p’ space.  The term, dilatancy, was first suggested by Reynolds (1885) to describe the shear-induced expansion. One of the earliest attempts to account for the increased shear strength due to dilatancy in dense sand, was made by Taylor (1948), who used the term, “interlocking” to  describe the effects of dilatancy. Fig. 2-2 shows the response of a dense sand to shear loading, in experiments conducted by Taylor (1948), using a direct shear apparatus (Schofield & Wroth, 1968). In fact, the results represent the coupling between shear and volumetric strains, which leads to very different responses to drained and undrained loading. Casagrande (1936), from test results on loose and dense sands using a shear-box device, concluded that sand reaches a limit void ratio wherein deformation continues under constant volume (with corresponding friction angle, q,,) and load. He postulated the existence of a unique critical void ratio for a sand, that depends only on confining stress, to which loose sands would compress and dense sands would dilate (Fig. 2-3). He defmed “critical density” or “critical void ratio” (the horizontal line, M, in Fig. 2-3b) as a state at which shear deformation occurs without volume change. Wroth (1958) used 1 mm diameter steel beads to justify Casagrande’s “critical void ratio” concept (Fig. 2-3c). The typical drained response of a dense sand, at different confming stresses, in terms of stress ratio and volumetric strain vs. axial strain, as observed in triaxial tests, is shown in Fig. 2-6 (Fukushima & Tatsuoka, 1984). The relatively dense sand is seen to initially exhibit a contractive behavior, which changes to dilation with further straining (as depicted in Fig 2-4).  Chapter 2: Characteristic Behavior ofSands and Liquefaction  15  7  J 7  x  4  x  (b)  (a)  Fig. 2-2: Typical response of a dense sand to shear loading tested by Taylor (1948), (a) sample loading condition, (b) sand response, i.e., lateral and vertical displacements.  LOVSf 5AND CONTPACTL SPONS  I I  10  2 (1Q;) en (5/cm  X,  mm  Fig. 2-3: Casagrande’s critical void ratio concept: (a) & (b) hypothesis of critical void ratio derived from drained direct shear tests, and (c) Wroth’s (1958) simple shear test results on 1 mm diameter steel beads, c’ = 138 kPa, in terms of specific volume, v (v = 1 + e) and shear displacement, x (adapted from Park, 2005).  Chapter 2. Characteristic Behavior ofSands and Liquefaction  16  A very loose sand would contract throughout its loading path from the initial loading stages. Lee & Seed (1967) reported similar behavior for sands from drained triaxial tests. The same pattern of sand response is observed in simple shear tests (Fig. 2-5) (Vaid et al., 1981). As may be seen (from Fig. 2-4 and Fig. 2-5) in triaxial tests the strength ratio drops after (axial) strain of about 5% whereas in simple shear tests, drop in strength ratio is noted only for the very dense sand. This difference in response may be due to localization that can occur in triaxial tests (Byrne, 2007). Roscoe et al. (1958) extended Casagrande’s work and defmed the critical-state as “the condition at which a soil shears at constant stress and constant void ratio  ‘  Based on this  concept, and using plasticity theory, Roscoe and coworkers (e.g., Wroth, 1958; Schofield, 1959; and Poorooshasb, 1961) founded a school of thought called “Critical-State Soil Mechanics”. Casagrande and his students (e.g., Castro, 1969; Poulos, 1981; and Poulos, et al., 1985) at Harvard University, US, used undrained tests and introduced the “steady-state” concept. The steady-state strength represents the constant stress condition, while the material is straining at constant volume and constant strain rate, and such behavior is known as (static) flow liquefaction failure (Poulos, 1981). While the critical-state data is commonly related to the drained condition, its corresponding steady-state data are mainly derived from undrained tests (Poulos, 1981). In general, sand behavior can be expressed in tenus of void ratio, e, and mean effective stress, p regarding the two extreme limits, namely: a dense state corresponding to a lower bound void ratio, and loose state, corresponding to an upper bound void ratio (Fig. 2-1). In this figure, the band between these two bounds is seen to narrow with increases in p’ and these limit lines and the steady-state line are not parallel. The two bounds correspond to pure compression (no shear stress), whereas, the steady-state (Poulos, 1981) represents a condition at which a soil sample is subjected to a critical stress ratio (deviator stress to effective mean stress, q/p’). The granular material is observed to contract when subjected to shearing if the stress ratio (i=  v/u) is lower than a certain value and dilate when the stress ratio exceeds that value. The  stress ratio value/line at which the change from contraction to dilation occurs is called “Phase Transformation” ratio/line (Ishthara et al., 1971 and Ishihara, 1993). This concept is illustrated in Fig. 2-6 showing that when the mobilized shear stress ratio, i, exceeds this particular state (sin pt),  the material dilates.  Chapter 2.’ Characteristic Behavior ofSands and Liquefaction  “S  17  IS  DRAINED TRIAXIAL COMPRESSIoN TEST SATURATED TOVOURA SAND, AIR-PLUVIATED ISOTROPICALLY CONSOLIDATED  in  -  0  U. w  z  Jo.5  o  12  0.2 w  0 U.  I.  U  /  a,  f  4.0  -B z  w  1.0  0.2  bo  I  in  0.1  U  2.0 4.0  -4  it I US -J  0  3 . 0 C  >  (kgt!cm) w  I,-  .  -Sw 0.3mm 0 1 0—  0.1 0.2 0.5 1.0  0.650 0.058 0.056 0.871  2.0 4.0  0.677  0  0.679  5 10 AXIAL STRAIN, Ca(  15  Fig. 2-4: Monotonic drained test results of Toyoura sand in terms of stress ratio and volumetric strain vs. axial strain (Fukushima & Tatsuoka, 1984). 0.9 0.8 0.7  .  0.5 0.4  )  0.  0.2  : :  0.1  :  0 0  : :  : : :  ADrc46% • Drc61% • Drc 93% 1  I  10 20 Shear strain, y (%)  ADrc 46% • Drc 61% • DrC 93%  .  I I  2 30  0  10 20 Shear strain, y (%)  30  Fig. 2-5: Response of Ottawa sand in drained monotonic simple shear test, reported by Vaid, et al. (1981) in terms of (a) stress-strain; and (b) volumetric strain vs. shear strain (adapted from Park, 2005).  ____  Chapter 2. Characteristic Behavior ofSands and Liquefaction  18  (a)  \ \ I  0, (b)  ?  ‘  :. -  So q  bIiuitY\\D.It  (c)  JDiIatjoflPt  Fig. 2-6: Typical dilation and contraction regions for sands: (a) in strain space, y; (b) grains distortion; and (c) stress space, q vs. p’.  vs.  Fig. 2-7 shows the stress paths for a tailings sand tested in the undrained condition with different initial state variables, i.e., relative density, confming stress, and shear stress bias (Ks),  Chapter 2: Characteristic Behavior ofSands and Liquefaction  19  along with the PT line (Vaid & Sivathayalan, 2000). It indicates that before the commencement of Phase Transformation state, shear-induced excess pore pressure increases, whereas it decreases after PT state due to material dilation.  Steadystate point  I  a)  Effective stress path durin9 undrained loading  Initial point, aftor  isotropic consolidation  (a) Mean effective stress (p’)  2400  Maximum Obliquity Ca  0  1600  D= 87%  Cl) U)  =  a)  2  C’)  0 >  (b)  800  0 0  1000  2000  3000  4000  Mean effective stress, p’ (kPa)  Fig. 2-7: Stress path and phase transformation line for a tailings sand, showing its independence from initial state variables, i.e., void ratio, confming stress, stress ratio, K: (a) key diagram, and (b) test results (q = (o c)/2, p’ = (o + c)/2 (data from Vaid & Sivathayalan, 2000). -  The Phase Transformation state separating shear induced contraction and shear induced expansion states is well established in the literature (e.g., Bishop 1966; Castro, 1975; Hanzawa,  Chapter 2. Characteristic Behavior ofSands and Liquefaction  20  1980; Been et al., 1991; Konrad, 1990 and Vaid & Thomas, 1995). In addition, test data from triaxial and hollow cylinder tests suggests that the Phase Transformation state (P1) line is a characteristic property of a granular material and is essentially independent of initial variables, stress path, and the shearing mode (e.g., Vaid & Sivathayalan, 1996; and Uthayakumar, 1996). Negussey et al. (1988) and Vaid & Thomas (1995) demonstrated that friction angles, at the phase transformation state , with constant volume condition,  and steady-state, q all are identical.  In fact, during undrained loading, the excess pore pressure reflects the contraction tendency of (loose) granular soils when subjected to shearing. This leads to effective stress reduction, and as soil stiffness is a stress-level dependent property, this reduction results in material softening. The strain softening behavior following initial peak shear strength is considered as liquefaction condition by NCR (1985). Fig. 2-8 shows a typical response of dense 1000 900 Sand B, dense  800  (a)  ..—  700 600 °  20mm  500  0 .  400  200  A, loose  4,  100 0  5  10  15 Axial strain (%)  20  SteadY-state Ud  25  30  500 Consolidation stress u  400  (b) 300 ,  Steady-state U’ 3 Sand A, loose  200  0  100 —SandB,dense  -100 0  5  10  15  20  25  30  Axial strain (%)  Fig. 2-8: Characteristic behavior of dense and loose sands in a monotonic undrained stress-controlled triaxial test: (a) deviator stress vs. axial strain; (b) excess pore pressure vs. axial strain  Chapter 2: Characteristic Behavior ofSands and Liquefaction  21  and loose sands to undrained monotonic loading as observed by Castro (1969). He conducted stress-controlled triaxial tests on two sands at different void ratios (called sand A and B) at the same confining stress. Sand A exhibited a continuous increase in excess pore pressure during shearing (Fig. 2-8b) with sudden strength loss after a peak. Sand B showed a strain-hardening response (after initial contraction), with decreasing excess pore pressure that became negative, and strength increased to values even higher than those obtained in the drained condition. Other investigators, e.g., Vaid & Sivathayalan (1996) performed simple shear tests (as shown in Fig. 29) and reported the same effect of density (void ratio) on the undrained behavior of sands.  .  100  e=0.836  80  e=0.861  60  U)  e=0.888 40 ‘I’  -c  (I)  20  e  =  0.902  0 0  5  10 Shear Strain (%)  15  20  Fig. 2-9: Effect of density on undrained stress-strain behavior of water pluviated Fraser River sand in simple shear test with u’. = 200 kPa; solid dots denote PT condition (data from Vaid & Sivathayalan, 1996). 2.1.2  Stress Path, Anisotropy, and Fabric  Stress-strain response and strength of sand at a given state (i.e., Dr and c) also depends on loading path and direction of principal stresses, as addressed by many researchers (Arthur & Menzies, 1972; Bishop, 1971; Kuerbis & Vaid, 1989; Vaid & Thomas, 1995; Riemer & Seed, 1997). Different responses of sand can be due to the inherent material properties or the anisotropic consolidation loading (Wijewickreme & Vaid, 1993). Vaid & Sivathayalan (2000) reported data from a hollow-cylindrical torsion, HCT test (Fig. 2-10) and demonstrating that a given sand exhibits a wide range of behavior (dilative to contractive) depending on the principal stress direction relative to sand placement direction  Chapter 2: Characteristic Behavior ofSands and Liquefaction  (angle of a.). In this figure where b a  =  =  (a2  -  a3)/(31  -  (33)  the condition of b  22 =  0, a  =  00  and b  =  1,  90° represent triaxial compression and extension test conditions that give the upper and lower  bounds of shear strength, respectively. At a given initial state, a gradual transformation of the sand response occurs from dilative to strain softening, reflecting the sole influence of a as it increases from zero to 90° at constant b  =  0 (Uthayakumar & Vaid, 1998).  Particle orientation and particle contacts within the sand matrix is referred to as the fabric (Oda, 1972; Oda et al., 1978). Various sample placement techniques, i.e., moist tamping (MT), air pluviation (AP), and water pluviation (WP) give rise to a considerable different behavior. The moist tamped sample shows the lowest strength and the water pluviated sample shows the highest strength (see Fig. 2-11). However, Mulilis et al. (1977) reported that cyclic undrained strength (in terms of CRR) from CT tests for MT samples are higher, compared to the resistance in AP samples.. Data from cyclic simple shear tests (Sriskandakumar, 2004) suggests that WP samples exhibit greater CRR than that of AP samples. Other investigators (e.g. Ishthara, 1996) have also noted the effects of sample placement method on sand liquefaction resistance. As mentioned earlier, regardless of these contributing effects, the contractive and dilative response, before and after the phase transformation condition, respectively, is a characteristic behavior exhibited by sands in various conditions and fabrics.  150  lCD  ‘cci 50  0  0 -C (%) 1 £ 3  (%)  Fig. 2-10: Fraser River sand respose change due to major principal stress rotation in undrained HCT test: b = (a2 33)/(CY1 (33) (Vaid & Sivathayalan, 2000). -  -  Fig. 2—11: Effect of fabric on undrained monotonic response of Fraser River sand with nominal Dr = 40%, in simple shear test (Vaid et al., 1995).  Chapter 2: Characteristic Behavior ofSands and Liquefaction  23  2.1.3. Cyclic Loading Condition Liquefaction may also occur during dynamic (cyclic) loading due to the material contractive response. Laboratory strain-controlled drained cyclic simple shear tests on sand by Silver & Seed (1971), Seed & Silver (1972), Youd (1972), Martin et al. (1975), and Finn et al. (1982) have shown that a progressive decrease in volume occurs with the applied number of load cycles. When the test is conducted in the undrained condition, the tendency of the soil towards contraction results in the generation of excess pore pressure. Similar to the monotonic condition, the skeleton controls the sand response and the pore fluid contributes as a volumetric constraint. Silver & Seed (1971) and Youd (1972) performed drained cyclic tests and concluded that the level of confining stress does not have a significant effect on volumetric compression and that the volumetric strains also increase linearly with increasing cyclic strain amplitude. Youd (1972) reported that the frequency of shear strain application has no effect on the shear-induced volumetric compression. Fig. 2-12 presents the results of drained strain-controlled cyclic simple shear, CSS, tests performed on air-pluviated Fraser River sand from a study reported by Wijewickreme et al. (2005). The sand samples had Dr  =  40% and were subjected to a cyclic shear strain amplitude,y,  of 2%. As may be seen from stress-strain curve (Fig. 2-12a), the material shows softer response in the first time loading; however, over the cycling, the larger shear strain amplitude causes more degradation. Fig. 2-12b and Fig. 2-12c indicate that shear-induced volumetric strain is accumulating (with decreasing rate) upon loading and unloading during cyclic shearing and reaches to more than 2.5% after 6 cycles. The effects of Dr on sand behavior in the drained cyclic loading condition can be seen from Fig. 2-13, which compares the sand response to cyclic loading with 4% shear strain amplitude at loose (Dr = 40%) and dense (Dr = 80%) states. From Fig. 2-12b and Fig. 2-13b, it is inferred that an increase in shear strain amplitude results in larger volumetric strain. This is in agreement with findings by Martin et al. (1975) that the shear-induced volumetric strain is proportional to the applied cyclic shear strain amplitude. In contrast to the loose sample, the dense sample shows significant dilation (after PT) during loading cycles (see Fig. 2-13c) and relatively small cumulative volumetric strains. As can be seen in Fig. 2-1 3b, the dense sample also shows a progressive increase in cumulative volumetric strain with the number of shear cycles but to a lesser extent compared with loose sand (e.g.  6 <  0.5% after 2 cycles comparing to  Chapter 2. Characteristic Behavior ofSands and Liquefaction >  24  2% in the loose case). Although dense sands may dilate during a portion of a cycle of loading,  the overall effect is a reduction in volume during any cycle of loading and a net contraction in volume with number of cycles as seen in Fig. 2-13b. This observation is also in accord with the undrained cyclic shear response of sands where the excess pore water pressure gradually increases with the number of cycles, despite the larger dilation spikes in the loading cycles for dense sands (see Fig. 2-14).  (a)  -4  (b)  -3  -2  -1  y I(%)  01.2 0—  a’=1OOkPa; D=4O%  3 =  4 2%  —3  60 ‘=100kPa D=4O%  (c)  6  I(%)  Fig. 2-12: Cyclic drained simple shear response of loose Fraser River sand Dr = 40% in terms of (a) stress-strain, (b) & (c) volumetric strain vs. shear strain and shear stress, respectively (Sriskandakumar, 2004).  Chapter 2. Characteristic Behavior ofSands and Liquefaction  25  (a)  y I(%) -4  -8  0  8  4  —  (b)  Dense Sample (Type 2)  Loose Sample (Type 1)  ---3--  80 60  (c)  40 20  -20 -40 -60 -80  c  Fig. 2-13: Responses of dense and loose samples of air-pluviated Fraser River sand in cyclic drained simple shear test in terms of (a) stress-strain, (b) & (c) volumetric strain vs. shear strain and shear stress respectively (modified from Sriskandakumar, 2004).  Chapter 2: Characteristic Behavior ofSands and Liquefaction  26  (a)  I Shear Strain, y (%) (b) 0.8  0.6  0.4  0.2  0 0  5  10 15 NO OF CYCLES  20  25  Fig. 2-14: Responses of dense air-pluviated Fraser River sand in cyclic undrained simple shear test in terms of (a) stress-strain, (b) R vs. No. of cycles. (Sriskandakumar, 2004).  Commonly, undrained cyclic tests, i.e., cyclic triaxial (CT) test, cyclic simple shear (CSS) test, and the cyclic hollow-cylindrical tortional (CHCT) test have been extensively utilized by many researchers to investigate soil liquefaction triggering (e.g., Seed & Lee, 1966; Finn & Vaid, 1971; Ishihara, 1972; and Vaid & Chern, 1985, among others). As mentioned earlier, with regards to the stress path that can be applied during testing, the CSS test and the CHCT test can better mimic the change of shear stress (and principal stress) direction that occurs during an earthquake excitation. In any case, most of the test data available in the literature is from CT tests.  Chapter 2: Characteristic Behavior ofSands and Liquefaction  27  Fig. 2-15 shows the results of an undrained cyclic simple shear test on air-pluviated Fraser River sand  OfDr  =  44% (Sriskandakumar, 2004). The stress path followed is shown in Fig.  15a where it may be seen that starting from an initial vertical effective stress of 200 kPa, the effective normal stress drops with each cycle until the phase transformation line (denoted by dashed line), or constant volume friction angle p  33° is reached after 4 cycles. Once this has  occurred, loading and unloading takes place close to the q line, with loading involving an increase in effective stress and unloading involving a decrease in effective stress. It may be seen from Fig. 2-1 Sb that the shear stress-strain response is stiff for a number of cycles in the pre liquefaction stage, with shear strain less than 0.2%, followed by an abrupt change to a post liquefaction stage with very much softer response and strains greater than 15%. This typical liquefaction response is illustrated in more detail in Figure 2-16 schematically where it is divided into five phases. During phase 1 prior to liquefaction, the stress path is below the PT line (before point A) and pore water pressure rises gradually causing the soil stiffness to decrease slowly upon cyclic loading. Once the PT line is reached (phase 2), further loading causes dilation as the stress point moves up just above the PT line (point B). Upon unloading (phase 3), the stress point drops slightly below the PT line and the soil contracts, driving the stress point back to the origin or zero effective stress (momentarily R =100%) and liquefied state (phase 4). Upon reloading (phase 5) the soil dilates, moving up just above the PT line gaining strength (de-liquefies). In subsequent unloading and reloading cycles, the pattern repeats itself Note that although the soil liquefies during cyclic unloading, it recovers its criticalstate strength at large strain as it is loaded. The post-liquefaction strength and stiffness depends very much on its density. Higher densities will have much higher post liquefaction stiffness and critical-state strengths. The cyclic strains are small while the stress point is below PT line and  become large once the stress point reaches and exceeds PT line. The same characteristics for undrained cyclic sand response was reported by Ishihara (1996) using cyclic hollow cylinder test with a lateral deformation constraint that reproduces the infmite level-ground condition (no axial and lateral strain). He showed that the increase of excess pore water pressure and liquefaction bring a sample (from an anisotropically consolidated stress condition, K 0  1) to the isotropic stress condition (K 0  =  1). Fig. 2-17 shows the test results of a  sample of Toyoura sand with Dr  =  55% anisotropically consolidated to a vertical stress of cr’  100 kPa and a lateral stress  =  50 kPa (K 0  ‘ho  =  0.5), and then subjected to 10 cycles of uniform  Chapter 2: Characteristic Behavior ofSands and Liquefaction torsional stress with an amplitude of  rd  =  28  15 kPa. It may be seen from Fig. 2-1 7b that the shear  strain, after 9 cycles increases rapidly associated with high excess pore water pressure ratio, R (Fig. 2-1 7d). Fig. 2-1 7c shows that the lateral stress ratio, K 0 continues to increase during cyclic loading until the lateral stress becomes equal to the initial vertical stress (K 0  =  1.0). This is  accompanied by the concurrent build-up of pore pressure which also becomes equal to the initial vertical stress. Same fmding was observed by Vaid & Chern (1985) from cyclic triaxial testing.  60  40  (a)  • Point of’=3.75% (i.e. Assumed triggering point of liquefaction for comparison purposes)  ‘=200kPa; D=44% tc,y,ja’y=O. 12; ;/a’ 0 .0  2O 2  0 -20 .-.  PT Line -40  Vertical  Effective Stress, a’,, (kPa)  -60  60 • Point of y=3 .75%  (b)  (i.e. Assumed triggering point of liquefaction for comparison purposes)  40  c’=200kPa; Drc=44% t/a=O. 12; t/a’ =0.0  20 Ci) Ci)  C,)  I  5  00-5  10  15  )  I) C,)  -40 L( -vu  Shear Strain, ‘y  (%)  Fig. 2-15: Response of Fraser River sand to cyclic undrained loading in simple shear test in terms of: (a) stress path, and (b) stress-strain (modified from Sriskandakumar, 2004).  Chapter 2. Characteristic Behavior ofSands and Liquefaction  (a)  (b)  29  t  Phase 1  Phase4 C (Liquefaction)  1  Phase 2  C D Phase 4  Phase 5  E 4.  (c) Fig. 2-16: Conceptual illustration of different stages in a typical response of a liquefied sand in undrained cyclic simple shear testing: (a) applied stresses in a simple shear test, (b) stress-strain curve, and (c) stress path (note dilaton is invoked after poit A when loading occurs).  The test results in terms of effective stress path and stress-strain curve is shown in Fig. 218, where p’  =  0 (cr’  +  u’ho)/ and 2 , 3  Td  are the effective mean stress and the (dynamic) cyclic  shear stress, respectively. This behavior is quite comparable to what was observed in the simple shear tests presented earlier. Fig. 2-19 shows the results for an undrained cyclic simple shear test with a shear stress bias that represents sloping ground conditions. Again, the same characteristic behavior  Chapter 2. Characteristic Behavior ofSands and Liquefaction  (a)  Tojaura sand  Torsional stress  30  30  WMA/V\/\tft 30  60  (b)  120  180  240  ( mi n.  300  Tosionat rcin  3.C  z:zzzi  (c)  (d)  60  120  1BO  A3O  240 I fl  Fig. 2-17: Cyclic cylindrical torsional test results for Toyoura sand (Dr = 55%, K 0 = 0.5, 100 kPa), (a) cyclic shear, (b) shear strain, (c) effective stress ratio, and (d) excess pore pressure ratio (Ishihara, 1996).  30j-  30  AC0T-test,K Q 0 5, Dr55%  Dr55%  ci  ‘1[A  0  N  0  :j.—::I  —.  t‘ Q \I  30  ACOT-tst 0.5 0 K  Phase Transformation  25  50  p’ (kpa)  75  30  I 2.0  (b) 0 y (%)  2.0  Fig. 2-18: Cyclic response of Toyoura sand in terms of (a) stress path, (b) stressstrain (modified from Ishihara, 1996).  4.0  Chapter 2. Characteristic Behavior ofSands and Liquefaction  31  30 c’=100 kPa; Drc40% 10; t/a’., =0.05  Point of y= S% (i.e. Assumed 7 . 3 triggering point of liquefaction for comparison purposes) PTline  1 a 20  10 19  rJ) CM  5)  5 5)  Vertical Effective Stress, o, (kPa)  “ -s  ‘5  -20  -30 30  (b)  • Point of’=3.75% (i.e. Assumed  100 kPa Drc=40% 10; tIo’ =0.05  20  triggering point of liquefaction for comparison purposes)  10  I  5  -10  -5  5  I 10  I  1  -10 11)  -20  Shear Strain, y (%)  Figure 2.19: Cyclic (a) stress path and (b) stress-strain response of loose sand with initial static shear stress (modified from Sriskandakumar, 2004). indicates a pore pressure rise in each cycle before PT line and subsequent liquefaction and de liquefaction upon unloading and loading (after PT). As noted earlier, sand contractiveness decreases with (relative) density and as a result, its resistance to liquefaction increases. This is seen in Fig. 2-20 that shows results for a cyclic triaxial test, in terms of the cyclic resistance ratio, CRR vs. Dr for Toyoura sand. This conforms with observations what was inferred from liquefied case histories where CRR increases with normalized penetration resistance (e.g., Seed & Idriss, 1971; and Youd et al., 2001).  Chapter 2. Characteristic Behavior ofSands and Liquefaction  32  OA Air pIuv.alion =1OOKP N.20cycIes  o  100 Rfativ density D %)  Fig. 2-20: CSR to cause liquefaction vs. relative density for Toyoura sand at 100 kPa confming stress (Ishihara, 1996).  2.2.  Impact of Partially-Drained Condition on Sand Behavior  Under conditions in the field, excess pore water pressures generated by seismic loading will induce flow of water and change in volume leading to void expansion or contraction (void redistribution) during or after shaking and this should be considered. A saturated soil mass is a two-phase material, i.e., grains skeleton, and water. The presence of pore fluid only provides the volumetric constraint on the soil skeleton, and it is the behavior of the skeleton; in terms of effective stresses at near constant volume, that is the basis for our understanding. Based on this concept, undrained (simple shear) tests can be simulated using dry sands under constant volume conditions (Finn et al., 1978) and the effect of void redistribution can be simulated by controlling the volume. When using triaxial testing, the volumetric constraint (flow condition) during shearing can be controlled through drainage system as depicted in Fig. 2-21. This system can mimic the spectrum of volume change condition (drainage) that may apply to a sample in (triaxial) testing to account for different volumetric constraint conditions (flow conditions). This implies that the conventional testing procedures (i.e., fully drained and undrained) are just two particular cases of a wide range of possible conditions for volume change. To understand the physics of liquefaction, a knowledge of the stress-strain behavior of the soil skeleton alone as well as that of the soil and pore fluid phases in combination is required, as follows:  _______  Chapter 2: Characteristic Behavior ofSands and Liquefaction  (a)  I  °i  (b)  No-Flow  (c)  LI  Free-Flow  33 (d)  [1ElIIn-Flow  UI  II u  It>Out.F1ow  Fig. 2-21: Control of volumetric constraint in triaxial testing, (a) no-flow (undrained), (b) free-flow (drained), (c) in-flow (partially drained, expansion), and (d) out-flow (partially drained, contraction).  1. The behavior of soil skeleton, representing the drained condition; 2. The behavior of (fully) saturated undrained soil, assuming that the pore water is completely incompressible (no flow, constant volume), and 3. The behavior of partially-drained (saturated) soil, to account for various volumetric constraint conditions (driven by flow conditions). The first two cases were discussed earlier; the third case (partially-drained) is treated in this section. This case is the most relevant loading condition to the void redistribution mechanism. Other investigation methods employed to study void redistribution (including physical model testing) are discussed in Chapter 3. The majority of the previous liquefaction studies are based on the assumption that no flow (undrained condition) occurs during or after earthquake loading. However, this condition may not represent the real situation since, during and after shaking, water migrates from zones with higher excess pore pressure towards zones with lower excess pressure. Transient flow may temporarily increase or decrease the pore pressure in a zone. This pore pressure redistribution results in different flow conditions and, as a result, the volumetric constraint changes in soil deposits during a seismic event  .  Thus, shear strength and other measures of sand behavior may be  enhanced or degraded. To investigate this effect, the imposed volumetric conditions must be controlled during the testing, in tenus of shear and volumetric strain, simultaneously, which is not the usual practice in element laboratory testing. Recently, a few researchers have reported results of their work on sand behavior under partially-drained conditions (Chu, 1991; Lo & Chu,  Chapter 2. Characteristic Behavior ofSands and Liquefaction  34  1993; Vaid & Eliadorani, 1998; Eliadorani, 2000; Bobei & Lo, 2003; Lancel ot et al., 2004; Sento et al., 2004; Yoshimme et a!., 2006; and Sivathayalan & Logeswaran, 2007). Fig. 2-22 illustrates the consequences of partially-drained loading (dashe d line) as reported by Eliadorani (2001) from traixal tests that can be compared to the results from conventional undrained monotonic triaxial testing (solid lines). In partial ly-drained tests, the specimen is forced to expand proportionally to the axial strain (/iSv/A 0.6). The figure shows 8a that a strain hardening and dilative material under undrained condition (no volum e change) can be strain-softening because of the water injection (volume expansion) in the partially-drained condition.  Stress Path  I  1/ 0  o  Drained,  =  0.6  1  i  2  AxiaI*in (%) Fig. 2-22: Transformation of dilative response under constant volume condit ion into strain softening in volume expansion condition (modified from Eliadorani, 2001).  As mentioned earlier, the shear strength of sand, under a partially-drained condition can vary widely depending on volumetric constraint. Results of a series of partially-drained triaxial tests, with the strain paths depicted in Fig. 2-23 (expansion as negative) are shown in Fig. 2-24, in terms of the effective stress path, in comparison to that of the special cases, i.e., undrained and drained conditions (Eliadorani, 2001). The figure shows that the ratio of volumetric strain increment to that of the axial strain (/18/LiSa) has significant impact on sand reponse. It demonstrates that the partial drainage condition is not bounded betwee n drained (dJ’r = 0) and undrained conditions  (/18/LiSa  =  0), and can be more destructive to sand behavior. Vaid &  Eliadorani (1998) also demonstrated that a (dense) sand with dilative behavi or under undrained  Chapter 2: Characteristic Behavior ofSands and Liquefaction  35  conditions exhibits strain-softening behavior under (inflow/injection) partially drained condition when the injection rate exceeds the dilation rate. In field conditions the imposed volume change 8v/&a) 1 (1  can be variable, and produce different senarios. The in-flow condition in which the  element expands can result in a very large reduction in soil resistance.  d/dei —-1.0  -0.6 -  0.1  -  0.2 -  ‘  0  -  0.  0.05 Undrained  ,  W  +02  —-  r0 Drained +0:  +0.  0  4 (%) I Fig. 2-23: Range of imposed volumetric strain change ratio comparing to that of undrained and fully drained conditions (dU’r = 0), (modified from Eliadorani, 2001). E  1Eh 1 (d ) j  Li  =2XkPa -.4.  1.G  •  + L4  ,(  4-C.2  ii  00  =  / •  E  Undrained  +  .0  *  .10  100  Al ..  /  / I  .4L4  ,,dJI1UIr=0  /  F  100  / Drained  F  F  O0 (1’  a1)it2(kPa)  Fig. 2-24: Effective stress paths for various zi /&a (modified from Eliadorani, 2001).  Chapter 2: Characteristic Behavior ofSands and Liquefaction  36  Recently, Sento et al. (2004) reported results of an experimental study on Toyoura sand under constant shear and partially drained condition using triaxial and torsional hollow cylinder apparatus. This test can represent a sloping ground subjected to inflow condition. Fig. 2-25 shows injection triaxial test results followed by drainage for various relative densities with the same initial (bias) shear stress. The samples reached the failure line (point C), at volumetric strain from about 0.5% to 1.0% and then large shear strains (limited to less than 8% due to apparatus  7  Falure  (a)  C  /7  InaI statk shear Stress 0, 2 37, 54lcPa  Draênage  D  Pore waler injechon ,vPrnrw  ntIirtP Inn  I QJP  Rdave deisiIy (%)  (b)  -0-30 -& 85  -D—6O D  1! E 0  >  A 0  100 50 150 Eflective mean stress (kPa)  2X  6  (c)  Reatwe density %) -0-30 -0-60 ‘-&- 85  C  4  E  C,  ___  D  2  0 0  2  4 Shear strain  6  {%)  8  A 2-25: Triaxial injection testing, (a) stress path, (b) & (c) effect of relative density on volumetric Fig. strain over the flow failure path due to pore water inflow in terms of mean effective stress and shear strain, respectively (modified from Sento et. aL, 2004, with permission from ASCE).  Chapter 2: Characteristic Behavior ofSands and Liquefaction  37  constraints) developed with continuation of inflow at constant shear and effective stresses. As may be seen, looser sands develop larger shear strain when equivalent volumetric strain was applied (see Fig. 2-25c path C to C’). The results shown in Fig. 2-25b in terms of  vs. P’  suggest that the drainage volume (volume change from C’ to D) during effective stress recovery (path C’ to D) after flow-slide is independent of initial sand density. However, such failure is a runaway type, and hence the drained path (C’ to D) cannot represent the real failure condition as noted by Chu (2006). In addition, Fig. 2-25c indicates that shear strain was essentially constant during drainage process (path C’ to D). Fig. 2-26 compares consolidated drained triaxial, CD test results for the same relative densities with that of injection tests (solid symbols) in terms of volumetric strain vs. shear strain. As may be seen the expansion rate 1 1d6 for both tests are almost the same. Yoshimine et al. (d6 ) (2006) reported similar results from triaxial injection tests. This suggests that development of shear strain during failure is governed by dilatancy characteristics. Consequently, to develop the same level of shear strain, denser sand requires much more inflow pore water. This means that a denser sand has more resistance to injection flow failure due to greater expansion potential.  -0- Iose. CD test {)- medkin. CL) bet -- dense. CD test  0  2  4  --  bose. ijecton  medium, injecvn A- dense, ânjectioi,  6  Shear strain (%)  8  10  Fig. 2-26: Comparison of dilatancy characteristics in CD and injection tests (Sento et al., 2004, with permission from ASCE). Regarding practical difficulties involved in triaxial testing to maintain a constant volumetric strain rate by increasing the back pressure, they performed torsional hollow cylinder (volumetric strain-controlled, constant shear stress, V-CSH) tests to study the dilation limits of  Chapter 2: Characteristic Behavior ofSands and Liquefaction  38  sand specimens subjected to pore water inflow. In these tests, the volumetric strain rates and initial static shear stress were constant (r = 10 kPa, o’ = 100 kPa) and the pore water injection volume was continuously increased until shear strain of 80% developed. Fig. 2-27 shows the test results in terms of volumetric strain and corresponding void ratio vs. shear strain, (up to y y= 80%) for Toyoura sand of various relative densities. Fig. 2-27 implies that for a given shear stress there is a limiting void ratio, at which no further dilation is possible in the sample. This limit is related to the critical-state void ratio. The figure denotes that required volumetric strain for the Dr =36, 57, 79% samples, were 4.7, 6.4 and 10%, respectively for a shear strain of 80% at which shearing was stopped due to equipment limitation. As the void ratios did not reach the same value at 80% shear strain thus, the steady-state should correspond to larger strain levels. Based on a similar study (using triaxial injection test under constant shear stress), Yoshimine et al. (2006) proposed Fig. 2-28 to estimate the volumetric strain required to reach different distortion levels including steady-state condition (6j cz) for Toyoura sand. This suggests that a volumetric strain of 6% brings a typical sloping ground of loose sand (e.g. Dr = 40%) to steady-state and flow-slide. They also reported that effective stress was essenti ally constant during distortion (path C to C’ in Fig. 2-25b). The same fmding was reported by Sivathayalan & Logeswaran (2007) from triaxial inflow test with constant injection rate (ZlSiM6a). This suggests that an injected soil at steady-state can fail due to a minimal applied stress.  12  .  8  >  0 0  20  40  Shear strain Y (%)  60  80  0  20  40  60  80  Shear strain (%)  Fig. 2-27: V-CSH tests results for Dr =36, 57, and 79%, (a) volumetric strain and (b) void ratio vs. shear strain (Sento et al., 2004, with permission from ASCE).  Chapter 2: Characteristic Behavior ofSands and Liquefaction  39  0  w t  -p  40 60 Initial relative densty,  80  (%) Fig. 2-28: Volumetric strain for various initial Dr required for reaching different levels of deformation (Yoshimine et aL, 2006).  2.3.  Post-Liquefaction Response and Flow Slide  The behavior of a softened material after liquefaction onset is called post-liquefaction response. The post liquefaction strength is crucial as the flow slide in liquefied grounds usually takes place after shaking due to applied static shear stresses. Extensive attempts have been made to describe the post liquefaction strength of sands, based on the undrained steady-state strength concept. Fig. 2-29 shows the steady-state line (curve) for Toyoura sand along with the upper and lower bound of the compression line reported by Ishihara (1996). Laboratory data from a number of investigators (e.g., Baziar & Dobry, 1995) suggest that residual strength is normalized with respect to consolidation stress. Fig. 2-30 shows the undrained residual strength, S with depth, for Tia Juana silty sand (Ishthara, 1996). In accordance with this fmding from element testing, a few researchers (e.g. Stark & Mesri, 2002 and Mesri, 2007) have also suggested normalized residual strength correlations, back-calculated from failed case histories. During cyclic loading (earthquake shaking) in a typical loose sand element, the stress path may reach the zero effective stress/zero shear strength origin, and true liquefaction occurs (Phase 4 in Fig. 2-16). Upon continued monotonic shearing to large strains, however, the soil will dilate, and move up the failure envelope, gaining strength. If the undrained condition continues, the so called (undrained) residual strength will not be reached until:  Chapter 2: Characteristic Behavior ofSands and Liquefaction  40  1.2 TOYOURA SAND  emi  1.014  Ie )  0.8  IsGtropc consoidaUon Looet .tat.  0.913 Steady state  emin  0  0 >  0.6 0.597  Isotropic con5ofldatbr) densest state  -  0.0  0.1  0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Effective mean stres8, p (MPa)  1.0  Fig. 2-29: Steady-state line of Touyora sand (Verdugo & Ishihara, 1996). Fig. 2-30: Steady-state strength of Tia Juana silty sand vs. consolidation stress (Ishihara, 1996). (i) The pore-water cavitates and thus allows the sample to increase in volume and reach the steady-state, or (ii) The high mean effective stress generated by dilation suppresses the dilation and the soil reaches its critical-state strength, or  (iii) The sand grains crush and the soil reaches a critical-state of the crushed material. The strength of the sand reached in (i), (ii) or (iii) is generally much higher than the commonly accepted undrained residual strengths, back-calculated from case histories, and is likely much higher than the drained strength (Naesgaard et al., 2006), hence, a flow slide would not occur. However, as shown earlier, if; in lieu of undrained loading, a small inflow of water occurs, it will reduce or eliminate the strength gain from dilation. When the inflow volum e exceeds the shear-induced dilation, then the soil quickly reaches the state of zero effective stress and is truly liquefied. More recently, a few investigators, recognizing the void redistribution (pore water migration) effects, have proposed correlations for residual strength to account for this mecha nism (Kokusho & Kabasawa, 2003; Idriss, 2006 and Idriss, & Boulanger, 2007). These authors developed suggestions based on physical model tests (i.e., shaking table and centrifuge models ) of slopes with a barrier layer. Fig. 2-31 shows the correlation suggested by Idriss and Boulan ger  Chapter 2. Characteristic Behavior ofSands and Liquefaction  41  (2007) for conditions where a void redistribution mechanism is involved and for situations without void redistribution effects.  Field-based strengths may be reasonable postulated to reflect all factors involved in previous failures that could also be the case in future probable failures, and should be recommended for current engineering design, as noted by Byrne et al. (2006). The issue of post-liquefaction strength of deposits comprising barrier layers needs to be further explored. Current practice for estimating residual strength is found in Appendix I.  Ct)..  0  Oi  Cl) 1.  Cl) 04  •  C, 10  15  20  • e  Sqd&Harder  G  O1onStat*(2002) 25  Equivalent Clean Sand SPT Corrected Blowcount, , 5 ) 1 (N ,  Fig. 2-31: Normalized residual strength with and without void redistribution involvement (Idriss & Boulanger, 2007).  2.4.  Flow Properties  Pore water migration within an earth structure, leading to soil element expansion or contraction is controlled by its flow characteristics. Therefore, in addition to mechanical conditions the seismic response of an earth structure depends on flow conditions that include: 1. Soil permeability (hydraulic conductivity, k). 2. Permeability difference within the soil layers (permeability contrast). 3. Spatial distribution of different soils types (flow path).  Chapter 2: Chamcteristic Behavior ofSands and Liquefaction  42  The hydraulic conductivity, or coefficient of permeabilty, k (in Darcy ‘s law) can vary in a wide range. Table 2-1 presents typical values of k, as suggested in textbooks for various materials (e.g., Lee et al., 1983; and Coduto, 1999). For sands, the recommended values range from 10 to 1 0 mis, depending on gradation and fines content. This permeabilty is sufficient for excess pore pressure dissipation in a (relatively) short time, in many cases, when subjected to earthquake loading. The range can decrease by 100 times or more, for silty sand and silt materials. Hence, a liquefiable deposit with lower permeability will experience large excess pore pressures for a longer time in earthquakes. Thus, the response of a liquefiable deposit to a given earthquake will vary with its permeabilty. This cannot be investigated using conventional element testing procedures and will be explored by numerical modeling in more detail in Chapter 4. Table 2-1: Range of k (mis) for different soils, as suggested in textbooks. Soil type  Gravel Sand Silty sand Silt Clay  Reference Lee, White, & Ingles, 1983a 102 102 to10 5 2 x i0 5 to 1O 5 x 106 to iO 7 <1O8  Coduto, 1999 to1O 1 1O l02 to iO 10 to i0 5 lO to 1O iO to 1012  a Proposed values based on Harr, 1977; Terzaghi and Peck, 1967; and Lambe and Whitman, 1969.  2.5.  Partial Saturation  The majority of investigations on liquefaction of granular soils have been centered on fully saturated soil. In situ test results, including compression wave velocity measurements, 1’,, indicate that partial saturation conditions may exist below ground water level for a few meters due to the presence of air bubbles (Ishihara et al., 2001; and Nakazawa et al., 2004) or gas bubbles in marine sediments and oil sands, as noted by Mathiroban and Grozic (2004). Some investigators (e.g., Kokusho, 2000; Yang & Sato, 2001; Pietruszczak et al., 2003; Atigh & Byrne, 2004; Mathiroban & Grozic, 2004; Seid-Karbasi & Byrne, 2006a; and Yegian et al., 2007) have recently addressed the effects of partial saturation conditions on the liquefiable ground response. The saturation condition of soil samples in the laboratory can be evaluated by measuring Skempton B value andlor the compression wave velocity, V, as suggested by Ishihara et al. (2001). Laboratory test data have shown that the resistance of sands to liquefaction onset increases as saturation decreases (Ishthara et al., 2001 & 2004; Yang, 2002; and Yang et al. 2004). Fig. 2-32 shows the cyclic stress ratio, CSR, vs. number of cycles required for liquefaction  Chapter 2: Characteristic Behavior ofSands and Liquefaction  43  of Toyoura sand at different saturation states, Sr, that is evaluated in terms of Skempton ‘s B value. The effects of partial saturation are discussed in more detail in Chapter 7.  0.3  0.25  b  0.2  0.15  0.1 U  0.05  Toyoura sand Dr=40% kP D.A. axaI strain=5%  \ \..\  :  Sr99  vp8o  -  \  -  :Bo.9.srIoo%  0  100 Number of cycles. Nc  1000  Fig. 2-32: Cyclic stress ratio vs. No. of cycles for Toyoura sand with different degrees of saturation (Ishihara et al., 2004, reproduced by permission of Taylor & Francis Group)  2.6.  Summary and Concluding Remarks  This chapter presents a literature review of characteristics and behavior of sands in connection with the liquefaction problem based on data from laboratory element tests. The main factors related to the scope of this study were addressed. Other issues, including current practice in liquefactuion engineering e.g. liquefaction triggering assessment, residual strength, post liquefation settlement, and fmes content effects are treated in Appendix I for the sake of completeness. The main conclusions from this overview are as follows: 1. Key issues in sand behavior  •  Volume change in granular materials is coupled with applied shear strain that results in dilation or contraction.  •  The amount of dilation increases with sand relative density and reduces at higher normal stress values.  •  The stress-strain behavior of sand is controlled by its skeleton and the volumetric constraint of the pore fluid. The volume change condition can vary in a broad range, and  Chapter 2: Characteristic Behavior ofSands and Liquefaction  44  the undrained (constant volume) and the fully drained (free) conditions are just two special cases within this wide range. A given sand, depending on the volumetric constraint conditions, exhibits significantly different responses to loading. These fundamental features of sands behavior are reflected in both monotonic and cyclic laboratory element test data. To capture seismic response of an earth structure, numerical modelling should be able to predict a soil element behavior in different loading conditions. 2. Excess pore pressure build-up and redistribution Characteristic undrained sand behavior and recent data from partially-drained laboratory tests were reviewed. From this review, the following points are inferred: •  Generation of excess pore pressure in saturated granular soils during undrained loading is a reflection of the tendency of sand to contract when loaded. The fluid in soil pores when saturated with water provides a near constant-volume condition when no flow takes place, and causes normal stress to be transferred from the skeleton to the water.  •  Pore pressure rises in each cycle of undrained shearing and if the stress path reaches the zero-effective stress state, liquefaction occurs momentarily. Further shear loading will cause the stress path to follow up the failure envelope and dilate regaining stiffness and strength  •  When undrained loading exceeds the phase transformation state while moving up the failure line, pore pressure reduces due to the dilation effects.  •  Element tests suggest that a small amount of water injected into the soil sample results in large strength loss and eventually instability. This strength loss depends on the volume of injected water (fmal void ratio) and corresponding effective stress. This effect suppresses the strain hardening effect of dilation.  •  When a sand element is brought to steady-state by inflow expansion (flow threshold) it deforms with minimal driving shear force and the subsequent deformations are not controlled by the initial soil state (i.e., Dri, and act,).  3. Post-liquefaction behavior and residual strength  Post-liquefaction stability of earth structures (flow-slide) and resulting deformations are significantly affected by residual strength. Two possible senarios arise in determining the post earthquake deformations of earth structures i.e.: a)  Cases where the void redistribution effect (i.e., soil expansion) is not significant, e.g., practically homogenous deposits (with uniform permeability), such as clean sands that exhibit strain hardening behavior and gain strength while deforming after liquefaction. A  Chapter 2. Characteristic Behavior ofSands and Liquefaction  45  flow-slide is unlikely to take place in these situations, as the residual strength can be large or even greater than the drained strength. b)  4.  Cases where the void redistribution effect (i.e., soil expansion) is significant, e.g., stratified deposits with permeability contrast. For these cases, the standard practice approach is to determine the residual strength based on data that is back-calculated from failed case histories.  Partial saturation  •  Sands in the partially saturated condition exhibit greater resistance to liquefaction.  46  CHAPTER 3  LIQUEFACTION INDUCED-GROUND FAILURES  3.1  Introduction  Liquefaction induced-defonnations are influenced by several mechanisms and factors. Flow failures, lateral spreads, and differential settlements are some forms of liquefaction deformations that can cause very severe damage. Understanding the underlying mechanisms that cause liquefaction deformations is essential for the successful prediction of performance and selection of suitable mitigation methods. The consequences of liquefaction vary for level ground and slopes. Level ground sites undergo ground oscillations accompanied by opening and closing of fissures and settlements (NRC, 1985). Surface manifestations of level ground liquefaction include bearing failure, cracks, settlement and sand boils (see Fig.3-1). Sand boil formation seems to occur only in the presence of a low permeability soil layer above the liquefied sand layer (e.g. Scott & Zuckerman 1972; Fiegel & Kutter, 1 994a). For sloping ground or embankments liquefaction can result in ‘flowslide” or “lateral spreading  “.  Flow-slides (or flow-failure) with very large movements occur  during or after shaking when the post-liquefaction strength drops below the “static driving shear stresses  “.  Lateral spreads occur intermittently (and progressively increase even more than lm)  essentially during earthquake shaking when the combined “static and inertial driving forces” exceed the soil strength. However the post-liquefaction strength is greater than the “static driving shear stress” and movements stop when shaking ceases (Byrne et al., 2006). Fig.  3-2 to Fig.  3-4 illustrate examples of liquefaction-induced deformations  corresponding to situations of vertical displacements and also limited and global instability or large lateral spreading (even more than 1 Om), respectively. Such large deformations can be very destructive and lead to catastrophic failure in structures or lifelines (Fig. 3-4 and Fig.3-5).  Chapter 3: Liquefaction-Induced Ground Failures  47  Fig. 3-1: Liquefaction foundation failure, (a) Overturning and (b) settlement of structures resulting from liquefaction of foundation soils in Adapazari, Turkey, 1999 (adapted from Kammerer, 2002).  Experiences from past earthquakes indicate that many of these large lateral displacements have taken place in sloping grounds with very gentle inclination during or after the main shock. Recent evidences have revealed that in all these cases, soil stratification and low-permeability sub-layer causing a void redistribution mechanism (as described in Chapter]) were involved. In this chapter, physical model test studies (using shaking table and centrifuge dynamic testing) are first discussed followed by results of laboratory element tests. Afterwards, some  Chapter 3. Liquefaction-Induced Ground Failures  48  /N  ci (bJ Secondary Ground Loss Due to Erosion  (a) Ground Loss Due to Cyclic Densification and/or Volumetric Reconsolidation  of Bcr Elects  -+r -i--  2__ (c) Global Rotational or Tranltionat Site Displacement  (d) ‘Slumping or Limited Shear Deformations  (e) Lateral Spreading and Resultant PullApart Grabens  (f) Locakzed Lateral So Movement  (9) Full Bearing Failure  (h) Partial Beanng Failure or Limited Punching  (i) Foundation Settlements Due to Ground Softening Exacerbated by Inertial Rocking”  Fig. 3-2: Modes of liquefaction-induced vertical displacements (Seed et aL, 2001).  -  Liq.atadzme  (a) Stxeadng Thede a Free Face  lt Sreaig  tiotr&ipe  c  .  (c) Lbe t’bn-drsdiur4ly Pr€faierêal  ih lerR £sØacensets  Fig. 3-3: Modes of “Limited” liquefaction-induced lateral translation (Seed et al., 2001).  Chapter 3: Liquefaction-Induced Ground Failures  49  case histories are reviewed and mechanism described. At the end of the chapter some related numerical investigations are discussed. A more complete list of physical model tests data and case histories are described in Appendix II and Appendix III respectively.  -  Liquefied zone with low residual undraned strength  (a) Edge Fai[ureiLateral Spreading by flow  (b) Edge Failure/Laterat Spreading by Translation  -  (c) Flow Failure  (d) Translationa’ Displacement  (e) Rotational and/or Translational Sliding  Fig. 3-4: Examples of liquefaction-induced global instability and/or “Large” lateral spreading (Seed et al., 2001).  Chapter 3: Liquefaction-Induced Ground Failures  50  Before Earthquake) Cayey Soil  Buried Water Pipe  Stream Bank  H I  Broken Lifeline  uefid  (a) (b) Fig. 3.5: Liquefaction induced lateral spreading, (a) gently sloping ground, (b) free face area (Rauch, 1997). 3.2  Physical Model Studies on Void-Redistribution  A number of researchers have investigated the void redistribution mechanism using model tests on layered soil profiles with permeability contrasts. These model tests included onedimensional sand column, 1 -g shake table, and centrifuge tests. Formation of water inter-layers were observed in some tests, whereas loosening due to void redistribution was inferred using photographs and instrument recordings in others. In some of the earliest studies, void redistribution observations were made on tests that were carried out to study some other problems. Later, researchers designed tests to study void redistribution specifically. After the pioneering work of Kokusho (1999) that demonstrated significant impact of low permeability sub-layer on liquefiable ground flow-slide, recently this issue has drawn more attention. This led to more experimental studies on this phenomenon and in particular by Kokusho and his co-workers at Chuo University in Japan and at the University of California, Davis, U.S as well as a joint work by University of British Columbia and C-CORE, Canada. Table All-i of Appendix II summarizes the results of past model tests and some of them will be examined in more detail in this chapter (complete description for all of them are provided in Appendix II). The results of a recent joint research program between Chuo U. and Davis U. (Kulasingam, 2003 and Malvick, 2005) that focused on void-redistribution will be also discussed in this chapter.  Chapter 3: Liquefaction-Induced Ground Failures  51  Huishan & Taiping (1984) reported results of shaking table tests on homogeneous deposits and horizontally stratified deposits in the presence or absence of a model foundation. A rigid model container with Plexiglas sidewalls was used. The sand was water pluviated and brought to the desired density by vibration. The sand had a D 10 of 0.053 mm and a D 60 of 0.114 mm. The models were prepared by pluviating sand in about 2 cm layers and waiting for it to consolidate before pluviating the next layer in order to form a stratified deposit. This resulted in each of these layers having a coarser bottom layer and a finer top layer. The model of this stratified deposit was constructed and tested for two relative densities (i.e. 14% and 28%). A sinusoidal excitation of 3-5 Hz frequency was applied to the models and continued until evidence of liquefaction was observed. The sinusoidal motion applied to the stratified models had a 0.3 g acceleration. The observations from the test with 14% relative density are shown in Fig 3-6. Huishan and Taiping (1984) described the observations as follows, “When the pore pressure increases, the small horizontal fissures filled with water appear symmetrically or asymmetrically outside the foundation. If vibration continues, the fissures grow up rapidly to form water interlayers or water lenses. With further build up of pore pressure water lenses located at the same elevation will be interconnected to form a long water interlayer. Meanwhile, the other fissures may appear somewhere. With increasing thickness of water interlayer the ground surface is uplifted. Once the first water interlayer reaches its maximum thickness, the water burst out with a noise through the overburden stratum and boiling occurs. After boiling the water interlayer soon disappears and the fissure is closed”. The maximum thickness of the observed water inter-layers for the 14% and 28% relative density sands were 2.5 cm and 1.5 cm respectively”. Elgamal et a!. (1989) performed a series of qualitative 1 -g shake table tests to investigate the effect of stratification of soil deposits on liquefaction. Three different models, a uniform silty sand layer, a silty sand layer underiying a silty clay blanket and an inter-layered clay-loose sand stratum were tested (no specific materials density/relative density was noted). The models were prepared by water pluviation. Water inter-layers were observed to form below the less permeable layers in the second and third models. These water inter-layers continued to grow as the dynamic excitation progressed and reached a maximum thickness of about 5% of the underlying sand layer. Finally after about 100 seconds of continued dynamic excitation the water inter-layers gradually  shrunk and a combination of sand and clay boils erupted to the surface. They addressed two points in this regard i.e. the relatively large thickness of the water inter-layers and the long time  _________  ____________  Chapter 3: Liquefaction-Induced Ground Failures  52  duration during which this thickness is sustained following the end of dynamic excitation. Fig. 37 depicts their observation from the test.  —36 ——  q=5+25g/cm’  Initial Stratification  FRONT ViEW  Fig. 3-6: Observation of water interlayer by Huishan & Taiping (1984) in shaking table test of stratified (alternating coarse sand and fine sand) deposit (test R-5, dimensions in cm).  Sand (mostly from upper layer), clay, and water  [  i..  SAND (upper layer) CLAY Trapped water interlayer  +  ...“  .4—  SAND (lower layer)  .......  .-..-.....-  %..  Fig. 3-7: Formation of trapped water interlayer, and delayed sand boil following a hydraulic fracture mechanism.  Fiegel & Kutter (1991 and 1 994a) reported results of centrifuge model tests carried out to study the liquefaction mechanism for layered level-grounds. Four models were tested with the first model having homogeneous Nevada sand (k  5 x 1 0 cm/s) air pluviated at 60% relative  Chapter 3: Liquefaction-Induced Ground Failures  density and the next three models with a non-plastic silt layer (k  53 =  3 x 10.6 cm/s) on top of the  Nevada sand. The silt was placed in a slurry form and consolidated in-flight. Water was used as the pore fluid. During the last three tests, the accelerations in the silt layer followed the base shaking (and the acceleration in the sand layer) only for a few cycles and then damped out, indicating that the silt layer became isolated from the base. Pore pressure records showed that pore pressure ratio remained at 100% at the sand-silt interface for a relatively long time. Surface settlement recordings indicated that the silt surface bulged first before finally settling. These observations were not obsereved for the homogeneous Nevada sand test. Based on these test results they concluded that an overlying, relatively impermeable soil tends to restrict the escape of pore water produced by the settlement of an underlying liquefiable sand layer. This can result in the formation of a water gap or a very loose zone of soil at the interface between the two soil layers. Dobry & Liu (1992) presented two centrifuge tests results conducted on layered soil deposits representing level-ground condition. In the first test, sand was placed at a relative density of 40% with a silt layer on top. These soils were the same as used by Fiegel & Kutter (1991 and 1 994a) for their tests. Based on the pore pressures and accelerations measured in these tests, they inferred four stages of behavior, which included the formation of a water interlayer. These are shown in Fig. 3-8a to Fig.3-8d. The first stage lasted 2 seconds where pore pressure generation took place with resulting upward water flow. The second stage lasted from 2 seconds to the end of shaking at 5 seconds, and extended a little bit beyond shaking (initial part of consolidation). Initial liquefaction had been reached at the upper part of the sand layer and a water film at the sand-silt interface grew during this stage, most of upper part of the sand layer experienced complete liquefaction, R l 00% (see Fig. 8-3b). The third stage lasted for about 4 minutes during which the only point of the sand layer that had a R of 100% was at the interface of the two layers (Fig. 3-8c). During this stage the water film was shrinking. After this the fourth (last) stage took place where there was no water film and coupled consolidation of the two layers took place (Fig. 3-8d). The second test had a model with a very similar two-layer horizontal soil deposit. The main difference was that a shallow foundation was placed on the soil surface. The relative density of the sand was 45%. Dobry & Liu (1992) reported that a water interlayer formed in this case also. The thickness of the water interlayer was thought to be larger in the free field than under the structure, since the weight of the structure was forcing the water out towards the free field. Water was used as pore fluid in the two tests described above.  _ ____  Chapter 3. Liquefaction-Induced Ground Failures  54  (a)  During Shaking LI  SI’  SendH L-s W• fl  ,  (b) During Shaking or Shortly After Shaking U  SR U  2  (c)  After Shaking --  w  i  a  (d) Long After Shaking  UI kiS.nd F  F  t,.TFrrrTTTT  Fig. 3-8: Four stages (i.e. a, b, c and d) in centrifuge test model of two-layer deposit, (modified from Kulasingam, 2003).  Chapter 3: Liquefaction-Induced Ground Failures  55  Fiegel & Kutter (1 994b) reported details of two centrifuge model tests carried out to study  the liquefaction-induced lateral spreading of mildly sloping ground (slope angle 2.6 degrees). The first model consisted of homogenous Nevada sand and the second consisted of a layer of Nevada sand overlain by a layer of non-plastic silt. The Nevada sand was air pluviated at a relative density of 60%. Silt was placed in a slurry form and consolidated in-flight. Water was used as the pore fluid. Both models were subjected to a base motion with a 30 s duration. The homogenous and layered models had maximum base accelerations of 0.9 g and 0.7 g respectively. Pore pressure records during the test indicate that they remained high for a longer duration for the layered model than for the homogeneous model. In both tests approximately 0.8 m of prototype lateral displacement was measured at the surface. As shown in Figure 3-9 in the homogeneous sand model this lateral displacement was distributed throughout much of the layer, whereas in the layered model displacement was concentrated along the interface between layers. Almost all the lateral displacements occurred during shaking for both the tests. Based on Newmark sliding block calculation and previous lab tests (Kutter et al., 1994) they pointed out that the undrained steady state strength of the sand far exceeds the strength required to prevent lateral displacement of a 2.6 degree slope, even with 0.7g of lateral acceleration. They attributed the reduced sliding resistance between the silt and the sand layers and the concentration of displacement to the redistribution of voids at the interface. In an attempt to investigate the mechanism involved in the extensive lateral slides reported from the 1964 Alaska earthquake (e.g. Seed, 1968), Zeng & Arulanandan (1995) conducted a centrifuge model of silty slope with a seam of liquefiable sand. They demonstrated that liquefaction of the sand seam led to slope failure due to pore water redistribution.  3.2.1  Studies carried out in Chuo U. and Davis U. An experimental research program was conducted by professor Kokusho at Chuo  University in the late 90s to investigate the mechanism involved in liquefactionflow-slide and in particular in gently sloping grounds. Kokusho (1999) reported results of layered soil column liquefaction models tested to study the mechanism of water film formation in level-ground condition.  Chapter 3: Liquefaction-Induced Ground Failures  (a)  56  (b)  Fig. 3-9: Lateral displacement patterns in centrifuge tests models of mildly sloping layered grounds, (a) homogenous sand, (b) layered soil (Fiegel & Kutter, 1 994b, with permission from ASCE).  An instant shock was used to liquefy a tube of a water-sedimented sand. The test was conducted for a uniform soil with and without a thin non-plastic silt seam (of 4cm thick at z  =  96cm) sandwiched between sand layers (see Fig. 3-10). A water film started developing below the silt seam, reached a maximum thickness of 8% of the under-lying loose sand layer (Dr  39%)  shown in Fig. 3-11, and then slowly disappeared. Fig. 3-12 depicts typical time-dependent settlement curves at the surface as well as at interior points in the fine sand. The sand instantaneously liquefied by hammer impact at the benchmark bi and the settlement started from the bottom. As may be observed from Fig. 3-12 the settlements increase with time linearly until kinks indicated by the benchmarks b2, b3 and b4, where the sedimentation of sand particles suspended in the water take place. Kokusho (1999) carried out a parameter study by varying the relative density of the lower layer. The maximum thickness of water film varied with sand relative density as depicted in Fig. 3-13. Kokusho & Kojima (2002) reported details of similar tests for three 3-layer systems (fine sand-silt-fine sand, coarse sand-fine sand-coarse sand, and coarse sand-fme sand-unsaturated fine sand crust) and a 2-layer system (coarse sand-fme sand). A stable water film was observed in all 3-layer system tests. In the 2-layer test fierce turbulence was observed at the layer interface, with larger void ratio near the bottom of the upper fine sand layer. A stable water film did not develop in the 2-layer test.  Chapter 3: Liquefaction-Induced Ground Failures  x  57  P lezometer Upper sand layer  of silt  sand layer cal  (Un i t : cm) Fig. 3-10: Sketch of ID tube test device (Kokusho, 1999, with permission from ASCE).  Fig. 3-11: Photograph of Water Film Consisting of Clear Water Formed beneath Silt Seam (Kokusho, 1999, with permission from ASCE).  _________  ___  ___  ____  Chapter 3: Liquefaction-Induced Ground Failures  58  A  (a)  —0—  Soil urie;  z.1 99.cni  z=144.lcrn —0—:  A  C  A  A  A  A  E  0  2L  (h)  --  40 ELapsEd time (s)  )  100  .  I  10  I  S’ ifrne tn  2c  I•  b  I  U  10 ..  (a)  2,5  1f  2  0  4-  0  —  ‘  —-  I  2U iJ  LL  t—’i  Ui  “—  oE  1.5  —  E)  1, ‘  ru  1  x  10  0  20  40  U  ped 1irr (si  80  100  C  *c; 20  30  40  50  60  70  80  Relative densityDr(%)  Fig. 3-12: Time-dependent variations in sand settlement (a) and pore pressure, (b) at different depths (Kokusho, 2003).  Fig. 3-13: Effect of sand relative density on water film thickness (Kokusho, 1999 with permission from ASCE).  Chapter 3. Liquefaction-Induced Ground Failures  59  Kokusho (1999, 2000) carried out two-dimensional model tests on the shake table to further investigate the water film mechanism and its effect on overall deformations. Fig. 3-14 shows the three different types of geometries tested. All models were prepared by water pluviation and had loose soils with Dr of 21%, 14%, and 35% for models in Fig. 3-14a, 3-14b, and 3-1 4c, respectively. For each of these tests, companion tests with the same geometry but without any silt seams were conducted to compare the behavior. The models were subjected to a very short duration motion applied in the transverse slope direction. This motion caused liquefaction and limited soil deformations during shaking. Deformations continued after shaking and caused flow failures for models with silt seams. Fig. 3-15 shows displacement time history for case “a” shown in Fig. 3-14 for certain representative points (see Fig. 3-1 Sc for their positions) along with its corresponding case without a silt arc. As may be seen the deformation at the end of shaking for the case with silt arc is less than that of without silt arc case, whereas the former continues to deform after shaking. This deformation was mainly concentrated at the bottom of silt seam-sand interface. A hair-like water film was observed at the toe parts of this interface. In the case of sloping ground with horizontal seams of silt, breakage of the silt seams occurred followed by boiling of the overlying sand leading to a mudflow avalanche. This series of tests illustrates the important role of void redistribution in the failure mode and timing of lateral spreads and flow failures. Kokusho (2003) reported results of a similar set of model test results with and without silt arc and their deformation patterns after failure are shown in Fig. 3-16 which indicates most of the deformation occurs at the silt-sand interface when the silt arc is present. These results are for an input acceleration of 0.3 1g. In Fig. 3-17c, the time histories of flow deformation of the same model subjected to weaker input acceleration of 0.1 8g are shown. Much larger post-shaking flow occurs in this case than when the acceleration was 0.34g; but minimal deformation takes place during shaking. This is because in the weaker motion, the slope remains steep during shaking and so the driving forces are larger during post-shaking flow along the interface. Concurrently to the studies in Japan, several research model programs were conducted at University of California, Davis, U.S. to investigate low permeability sub-layer effects on seismic behavior of liquefiable soils namely, pile foundation, bridge abutments and sloping grounds using a small 1 m and large 9m-centrifuge facilities. The results can be found in a number of reports and publications (e.g. Balakrishnan & Kutter, 1999; Gajan & Kutter, 2002; Kutter et al., 2004, and Malvick et al., 2006) that were interpreted in few PhD theses i.e. Kulasingam (2003)  Chapter 3: Liquefaction-Induced Ground Failures  60  —  (a) Slope with  si’  Ilf  arc  31t  (b) Houo4iLai røinid with ar  (a) Slope with lwrizsmiai sik  embankmem Fig. 3-14: 2-D model tests with silt layer (Kokusho, 1999, with permission from ASCE).  and Malvick (2005). Fig. 3-18 shows a test model of a river flood plain used to study the effect of relative density and thickness of sand layers on the amount of settlement and lateral spreading near bridge abutments. The models had a river channel with clay flood banks underlain by layers of sand with varying relative densities and thickness. The layers had a gentle slope with one of the banks having a bridge abutment surcharge. The models were constructed by air pluviating the sand and placing the clay in a slurry form consolidated at 1 g under a vacuum pressure of about 80 kPa. Water was used as the pore fluid. The models were subjected to three large shaking events. Discontinuous lateral deformations at the clay-sand interface (interface slip  1.2 m), with  the clay layer moving more than the top of the sand layer, were observed for two of the models  where the relative densities of the sand layer were high and/or the thickness of the looser layer was small.  Chapter 3: Liquefaction-Induced Ground Failures  61  (a) case I 8  SIikirg  —  -o-OoO  :  Clapsed hme is)  (b)case2 Sktng  Elapsed time (s)  (c)  -  Fig. 3-15: Soil deformation vs. elapsed time for representative points in sloping ground (a) case 1, with silt arc; (b) case 2, without silt arc; (c) location of representative points (Kokusho, 1999 with permission from ASCE).  However, in cases where the sand layer was looser or thicker the deformation patterns appeared to be continuous or the clay appeared to move less than the sand. The clay layer seems to have moved by the same amount (1.5  —  1.8 m) for all the tests regardless of varying densities  or thickness of the underlying sand layer (see details in Fig. 3-19 and Table 3-1). This may have been caused because of the deformations of the clay layer being limited by the river channel boundary. The observations of discontinuous deformations at the interface in some tests and the fact that the clay layer had negligible strains (almost moved as a rigid block) indicate that void redistribution played an important role in the deformation mechanism.  Chapter 3: Liquefaction-Induced Ground Failures  62  1SlIn9nc1m8I 0.340 —  10  End  1  50 40 30 30 10  0 50 70  —  de*rme0  I  td ur bh.J  •  TEt± eo  16  Elapsed lime  EIEE1EE1EE1E[EIE 10 70 0 4(1 50 50 70  10  5  70  ) (b)  [aknomisl to ar.cipiIg cirecj  80 WOl Ci  IS m 10  sols  50  -.-EIawj  .—[d of shebid  end aF .Idefurwelvn .  0  U  i1  (a)  b&orhmwig  70  ICiiieCioci  1(1  S  20  IS  2  Eised time {s}  102C04.050507090W010  BkgnonnaitosIcplngdIrec1i  70 o i  ---v  --.  —  -  -  1C U  I”--f  I:  --  -—  —r  -  -  —  —  .-IEncicshakin  aJ 0  1U2304G5050080O1D0u10  10  S  1T._’  o 50 50 40  --.  •r:lLIc.,m5Qfl  O Fig.  70 60 50 40  -.  hz::..  102030 8 50807080 0iuGi10  3-16:  slopes (a)  0  Cross-sectional deformation for  & (b):  with buried silt arc. (c)  :  (d  sweatie p  __Cot5iII  I  .  —  1TTJT!EF1  -.--  :HiZ’  20  (8)  is’  (d)  •—I  25  IS  Elap5ed lime  ‘-  &  (d) without silt arc. (a) & (c) during shaking. (b) & (d) after the end of shaking (Kokusho, 2003).  Fig.  10 20 30 4.0 SO  3-17:  70 80 90 luOiiO  Time-dependent  flow  in (d); a) without silt arc by PGA 0.34g. (b) with silt arc by PGA 0.34g. (c) with silt arc by PGA 0.18g. (Kokusho, 2003).  displacement at target points shown  Chapter 3: Liquefaction-Induced Ground Failures  63  PLAN  — — — —  ELEVATION ON A- A  Fig. 3-18: General model configuration for lateral spreading study of bridge abutment (Kutter et al., 2004, with permission from ASCE). Table 3-1: Model tests details for lateral spreads of bridge abutments (Kutter et al., 2004).  Model code (‘80 LtSO U50 4.5  U50_4.5S 1.33134.5  1j304.5M  Model deta1s in o Di=80%. H2l5 1 = 50%, HI = 9 oh Dr =80%. H2=6 01 2 Dr = 50%, HI 4.5 rn 1 Dr =0%. H2= 10.5 in 2 Dr Drt = 50%. HI =4.5 m Dr=80%. H2=7.5rn 1 = 30%. HI = 4.5 m Dr Di=0%. H2=7.5 in 1 30%. HI ‘4.Sin Dr =80%. H2=7.5 in 2 Dr  Note: U30_4.5M stands for Unimproved Dr30% sand  of 4.5  Height of water table (HI  slope 0 f cloy (C)  slope of nd (S)  9.3%  3.3%  1.2  9.0%  3.0%  1.2  9,3%  3.3%  1,2  3.0%  3.0%  .2  9.3%  3.3%  1.2  9.3%  3.3%  —0.3—1.3 (variable  flt)  m thickness with input motion (M) varied. C, S and Hare marked in Fig. 3-20.  Chapter 3: Liquefaction-Induced Ground Failures  64  (d) U50_4.55  (b)1J50  (c) LJO_45  (c)U304.5  (1) U30_4SM  Fig. 3-19: Deformation pattern of tested models, see Fig. 3-18 and Table3-1 for details (Kutter et al., 2004, with permission from ASCE). Kutter et al. (2004) also examined the empirical correlation proposed by Youd et al. (1999) for lateral spreading that only considers the thickness of soil layers that have (N 60 <15; against ) 1 their test results. They showed that thick soil layers with (N 60 >15 (approximately Dr ) 1  =  55%)  can also produce significant lateral movement. Davis U. research group reported results of another set of model tests to study the behavior of piles in laterally spreading ground (Singh et al., 2000, and 2001; Brandenberg et al., 2001). The models had a top, moderately over consolidated clay, layer underlain by a middle loose sand layer (Dr  20-30%) and a bottom dense sand layer (Dr  70-90%). Some models had  a thin coarse sand layer on top of the clay layer. All layers had a 3° 4.5° general slope. The clay -  had a 25° sloping river channel at one end. All models had single and group piles embedded in them. The models were constructed by air pluviating the sand and placing the clay in a slurry form consolidated at 1 g under a vacuum pressure of about 80 kPa. Water was used as the pore  Chapter 3: Liquefaction-Induced Ground Failures  65  Fig. 3-20: Discontinuous lateral deformations in the clay sand interface (adapted from Kulasingam, 2003).  fluid. The models were subjected to several (more than 3) large shaking events. Lateral deformation patterns after the shaking events show a clear discontinuity at the clay-loose sand interface as shown typically in Fig. 3-20 (photo taken by Brandenberg, 2001). This was attributed to loosening due to void redistribution driven by the upward hydraulic gradients produced by the excess pore pressures in the underlying sands. Malvick et al. (2005) presented results of a U.S.-Japan cooperative research project conducted jointly at Chuo University in Tokyo, by Professor Kokusho and his coworkers and University of California at Davis to collaborate on a project studying the effects of void redistribution and water film formation on shear deformations due to liquefaction in layered soils. They employed 1 g-shake table, small 1 m-radius centrifuge and large 9m-radius centrifuge facility in a 2-D study of slopes with various relative density of liquefiable sand layer comprising silt sub-layer subjected to 1 to 3 subsequent events. The typical shake table model had a 4H:1V slope that was 0.3m high and consisted of Tokyo Bay sand (see Fig. 3-14). Models were typically shaken transverse to the slope by a harmonic motion (Kokusho, 2003). The typical centrifuge model had a prototype 2H: 1V slope that was 6m high and consisted of Nevada sand (shown in Fig. 3-21 and 3-22 for small and large centrifuge models, respectively). Models were typically shaken along the slope by a modified earthquake ground motion (Kulasingam et a!., 2004). A few tests were performed at both institutions to control operation and procedures effects. Fig. 3-23 shows the shake table model configuration before and after shaking. This model consisted of a loose slope of Tokyo Bay sand with embedded silt arc. The model failed after being shaken transverse to the slope (normal to the  Chapter 3. Liquefaction-Induced Ground Failures  66  view shown) by a 3 Hz harmonic motion for 1 s with a peak base acceleration of 0.3 g. Approximately 50% of the deformations and localization occurred for 9 seconds after shaking stopped. This shake table test is similar to other tests completed at Chuo University and described in Kokusho (1999 and 2000), Kokusho & Kojima (2002), and Kokusho (2003). For comparison, some of the tests described in these references showed 50% to 85% of the movements occurring up to 20 s after shaking stops. The base acceleration during shaking for these models ranged from approximately 0.15 g to 0.35 g. Fig. 3-24 shows typical centrifuge model configuration before and after shaking along with a close up of silt-sand interface showing localization. Kulasingam et al., (2004) demonstrated that a slope model of Dr  =  20% without a silt sub-layer can withstand the applied  shaking event whereas a similar model with greater relative density e.g. 50% failed when a silt layer is present in the slope as shown in Fig. 3-24. Fig. 3-25 shows the initial states for the sand they used compared to the sand’s steady-state line. The steady-state line is based on isotropically consolidated undrained and drained triaxial compression tests by Castro (2001). Initial states for the sand are shown for the confining stresses just below the silt arc near the middle of the slopes. This suggests that even the initial Dr  20% models would be dense of critical and have sufficient  undrained shear strength for stability. They inferred that water film formation is the extreme condition of localization that it may not be manifested during failure of a slope with barrier layer. Kulasingam (2003) back calculated shear strengths using limit equilibrium and Newmark (1965) sliding block method from test models experiencing localization and showed that they are much lower than that inferred from the steady-state condition. He also argued that the extent to which void redistribution affected the apparent residual strength, Sr in the few case histories that control current empirical procedures is unknown. Thus it is not clear whether these field-based correlations (e.g. Seed 1987; Seed & Harder and Olson & Stark, 2002) are conservative or unconservative in their implicit accounting for void redistribution effects. He concluded that numerical modeling is an appropriate approach to account for void redistribution effects in post liquefaction strength.  Fig. 3-26 shows a typical displacement time history obtained in 1 g-shaking table test and 80g-centrifuge test of the model with configuration given in Fig. 3-22 (Malvick et al. 2005). The authors concluded that timing of localization occurrence and the portion of post shaking displacement depend on model configuration and motion characteristics i.e. level of excitation and its duration.  Chapter 3: Liquefaction-Induced Ground Failures  67  Post-shaking failure also took place in centrifuge model of a submerged slope (with configuration given in Fig. 3-27) including a sub-layer silt barrier designed by UBC and tested at C-CORE,  after  N.F.  end  of  shaking  (Phillips  et  al.,  2005  available  at  www civil. ubc .ca/liguefaction). Malvick et al. (2005) concluded that several key factors including: barrier shape, sand relative density, thickness/volume and permeability of liquefied layer, and earthquake characteristics control void redistribution and ground deformations. A summary of their findings is listed in Table 3-2 with a footnote for main references to specific factors. It indicates that looser materials experience larger displacements and more susceptible to localization. It also Model  Approximate prototype  .  ShIthg  Fig. 3-21: Typical model configuration and prototype equivalent using im-radius centrifuge with rigid container of 560 x 280 x 180 mm tested at Davis U. (Kulasingam et al., 2004, with permission from ASCE). Note that the base of the model in prototype scale is curved due to great variation in revolution radius within the model.  0  10  _I  200  DIRECTION OF SHAKING  —  Fig. 3-22: Typical model configuration using 9m-radius centrifuge with rigid container of 1759 x 700 x 600 mm tested at Davis U. (Malvick et al., 2002).  Chapter 3: Liquefaction-Induced Ground Failures  68  shows that thicker liquefiable layers aggravate the effect of low permeability sub-layer. The lower permeability of the liquefied layer can increase the potential for localization or water films to form after shaking. The delays of ground displacement until after shaking were most dramatic when the ground motion was small enough to minimize earthquake-induced deformations but strong enough to trigger high excess pore pressures throughout the slope. They also concluded that the residual shear strength of liquefied soil that would be appropriate for use in a stability analysis does not depend solely on the soil’s pre-earthquake state (i.e. density and confining stress), because instability may form along a zone of soil that has become loosened during void redistribution or along interfaces that have trapped water films.  (b)  Fig. 3-23: Shake table model (a) before testing and (b) after testing (Malvick et al., 2005).  Chapter 3. Liquefaction-Induced Ground Failures  69  I3eiore Shaking: (a)  (b)  •  :  •.LuL1 ’‘ • — Photos from test RKS1 I (D 1  50% Sand  ssrith  Silt Arc I.  (c)  Fig. 3-24: Centrifuge model configuration (a) before shaking, (b) after shaking, (c) close up of silt-sand interface after shaking (Kulasingam et al. 2002).  Chapter 3. Liquefaction-Induced Ground Failures  70 a  12  a  a  o!S  4 0  I  08 80 8 U 0.7  0.6 10 100 1000 Effec*êe Moor PrtricpaI Sts 4kPa  10000 0  Fig. 3-25: Initial state of sand beneath silt arc at mid-slope relative to steady-state line for Nevada sand (Kulasingam et al., 2004).  100  200 300 Time(s)  400  500  Fig. 3-26: Displacement time history above silt arc in models as shown in Fig. 3-22: (a) a 1-g shake table test and, (b) an 80-g centrifuge test (Malvick et a!., 2005).  Saturation Drainage Layer Fig. 3-27: UBC-CCORE model of submerged slope with barrier layer failed after end of shaking (prototype scale, Ng 70g).  Chapter 3: Liquefaction-Induced Ground Failures  Table 3-2: Findings of Davis U. and Chou U. joint research program on void redistribution.* Factor Influence Shape of low-permeability 2 barrier ” 8 7 ’ ”I  .  Relative density of the liquefied ” 7 ’ 2 layer”  . .  .  .  .  Thickness (volume) of the liquefied 2 .” 9 ’ 7 . 5 layer”  •  • Hydraulic impedance of barrier 9 6 3 ’ 2 layer” • Permeability contrast between liquefied and barrier soils . Thickness of barrier layer .  •  •  .  Permeability of liquefying 7 ’ 6 layer”  .  • Earthquake” 9 7 6 5 4 ’ 2 • Frequency content . Amplitude and duration of motion . Direction of shakin g • 3lIaKing sequence anu history  .  •  •  • •  *Specific references for the factors are:  When the shape of the low-permeability layer coincides with a kinematically admissible failure surface, it is more likely to contribute to localization and large deformations. Looser soils trigger liquefaction sooner during shaking. Looser soils experience larger consolidation strains, thereby expelling more water that can drive localization or water film formation elsewhere in the slope. Looser soils require less water inflow (dilation) at the contact with a low permeability layer before they will localize and/or form a water film. Looser soils develop larger shear strains during shaking and larger total displacements (includes displacements along localizations or water films). The magnitude of ground displacement depends on whether or not localization forms with the transition between these cases occurring over a small range of relative density. Thicker layers expel more water to drive localization or water film formation beneath an overlying low-permeability barrier layer. Thicker layers take longer to reconsolidate, which increases the potential for localization or water films to form after shaking. The hydraulic impedance of the barrier layer increases with increasing thickness and decreasing permeability. Greater hydraulic impedance restricts pore water flow across the interface between the liquefied soil and the overlying barrier soil. This allows more water to accumulate, thereby making localization or water film formation more likely. A lower permeability for the liquefied layer reduces the rate of pore pressure dissipation and consolidation, which can increase the potential for localization or water films to form after shaking. A lower permeability for the liquefied layer reduces the permeability contrast with the overlying barrier layer, and could reduce the potential for water to accumulate at the interface if the contrast is small enough. The proportion of the total ground displacement that occurs after shaking depends on how much displacement is induced during shaking versus how much occurs due to pore water flow after shaking. Delays of ground displacement until after shaking were most dramatic when the ground motion was small enough to minimize earthquake induced deformations but strong enough to trigger high excess pore pressures throughout the slope. Larger amplitude and/or duration motions increase shear strains, which increases volumetric strains in the liquefying layer, thereby making localization more likely. Shaking transverse to the slope direction may reduce inertial stresses down slope which could reduce deformations during shaking. Prior shaking can increase the cyclic resistance of the liquefying sand, thereby reducing the potential for localization. At the same time, prior shaking can cause loosening below the barrier layer, which increases the potential for localization in subsequent shaking events.  1. Kokusho (1999), 2. Kokusho (2000), 3. Kokusho & Kojima (2002), 4. Kokusho (2003), 5. Kulasingam et al. (2001), 6. Kulasingam (2003), 7. Kulasingam et al. (2004), 8. Kutteret al. (2002), 9. Malvick et al. (2002a), 10. Malvick al. (2002b), et ii. Malvick et al. (2003), 12. Malvick et al. (2004).  71  Chapter 3: Liquefaction-Induced Ground Failures  3.3  72  Laboratory Investigations on Void-Redistribution  Void redistribution was observed in laboratory sand specimens (Casagrande & Rendon 1978 and Gilbert, 1984). However, Casagrande (1980) suggested that void redistribution observed in the laboratory element tests are the result of test boundary conditions and may not reflect in-situ soil behavior. Recently, it was recognized that void redistribution can occur during an earthquake due to pore water flow (NRC, 1985), and a few investigators have attempted to simulate this condition by using element testing in partially drained condition (e.g. Vaid & Eliadorani, 1998 and Eliadorani, 2000) as discussed earlier. Chu & Leong (2001) showed that instability occurs in both loose and dense sands when injection rate (called “imposed strain rate”) is greater than their corresponding dilation rate. Bobei & Lo (2003) reported strain softening behavior for silty sand under partially drained (strain-controlled) loading condition similar to that reported for sands (e.g. Eliadorani, 2000). Boulanger & Truman (1996) and Boulanger (1999) conceptualized the void redistribution mechanism in an infinite slope with a lower permeability top layer, by stress path testing in a triaxial apparatus. Tokimatsu et al. (2001) conducted partially drained hollow cylinder torsional shear tests by controlling the amount of pore water injected into the specimens as a function of shear strains The pore water migration from the underlying liquefied soil layer was modeled by pore water injection into these elements. They concluded that: •  Even dilative medium dense sand exhibits very low shear strength and may undergo flow failure if a sufficient amount of pore water is injected as noted by Eliadorani (2000). Such pore water migration is confirmed to be the major cause of liquefaction induced flow slides in dilative sands.  •  If liquefied, saturated sand expands due to water injection; the mobilized shear stress tends to decrease, accompanied by large shear strain. The tendency becomes pronounced as the soil density decreases or the amount of injected pore water increases.  •  If non-liquefied, saturated sand subjected to initial shear stress expands by only 0.3  —  0.5%  due to inject flow, the shear strain tends to increase, irrespective of initial soil density. Kokusho (2003) conducted a set of cyclic undrained hollow cylinder torsional tests with and without vertical constraint (no settlement) in an attempt to simulate low permeability sub layer effects on a liquefiable soil layer behavior shown schematically in Fig. 3-28.  Chapter 3. Liquefaction-Induced Ground Failures  He tested clean sand samples of Dr sheared with  td/cC  =  73 =  40% consolidated under 98 kPa and cyclically  0.2 of 0.1 Hz under undrained conditions. The equipment had a shear strain  limit of 25% double amplitude. Fig. 3-29 shows the test results in terms of shear stress, strain, excess pore water pressure, axial (total) stress fluctuation and water film thickness andlor settlement, respectively for case with and/or vertical constraint. In both tests the results are very similar in the earlier part. However, after the excess pore water pressure ratio reaches 100%, strain development is much more drastic in the case with vertical restraint and reaches the maximum strain limit earlier than in the case without the restraint because of void redistribution at the top of the sand specimen. Variation of total vertical stress can be measured in this case as on the fourth diagram in Fig. 3-29a, indicating the periodical fluctuation due to the dilatancy effect. The water film formation is observed in the case with vertical constraint some time (i.e. at 60 s) after initial liquefaction, R = 100% (at the end of the 6th1 cycle) partly, where its thickness increases linearly in subsequent test period (see Fig.3-29a, fifth diagram). Obviously, the excess pore pressure and vertical stress cease to fluctuate after the formation of the water film in contrast with the case with no vertical restraint in Fig. 3-29b. The vertical settlement depicted on the 5th diagram of Fig. 3-29b indicates that the settlement after the onset of liquefaction occurs only at short periods of zero shear stress. This further suggests that the post-liquefaction settlement of sand particles suspended in pore water can occur at the moment of zero shear stress only. This is consistent with observation in centrifuge tests that the settlement of liquefied slopes decreases with ground inclination as reported by Taboada & Dobry (1998). Kokusho (2003) reported results of another set of cyclic tests on a sand sample of Dr 28% when consolidated under 98 kPa stress with static shear stress ratio of 0 /a’ ‘r cyclic stress ratio of ‘rd/aC  =  =  =  0.19 and  0.20. Fig. 3-30 shows time histories of stress, strain, excess pore  water pressure, axial total stress (change) and water film thickness for a test with vertical settlement constraint (clamped). Note that the excess pore water pressure has pak values when the shear stress is almost zero while it decreases considerably at all other times due to the dilatancy effect. Pore pressure builds up to 100% in the middle of the  3 t d  cycle, and the water film becomes  visible 1.5 cycles later, increasing its thickness linearly up to 5 mm eventually. The residual strain increases in the direction of the initial shear stress while changing cyclically, arrives at the strain limit of 24%.  _  ___ ___  ____plate  _ ___________ _____ _____ _  Chapter 3: Liquefaction-Induced Ground Failures  74  (a)  (b  1 L oadlng  —  Sett  1  rticai ovemnt  Fig. 3-28: Field condition of a stratified slope (a) sandwiched sub-layer silt, (b) laboratory simulation using torsional apparatus (Kokosho, 2003).  (a)  rJa=020  I—  —: .:  :--  .•‘--  J Shear • W;  P.  1-L Lr  -—  — i____.__-- I_______  I---.-’  “  t  L)  Li  I  ,J\..  Øreur  j Ur  ,..___  Axtr.  —  G  (b) ur  F  We’ fifrn  I  —  0  -  1  Watir film bervd  I  10  0  30  40  !  r0’  ,.  -•‘  ?0  .  ru  \4  SO  !  r  \-..•.  : I  1•  —-Y  zz—  109 Pore preewe 50 r 0.tI—-  !,.-.‘  -‘  -i--i  )  0  Dr41%:f0.iHz: r/O2 2O”---,  staT .  O  --—i  Pore pressure ratio100% —1  •  4  —  ---  le]  .  —.I•  •-  .  0  10  I  20  O  4  50  0  70  Fig. 3-29: Time histories of shear stress, strain, Ue, axial stress water film thickness/settlement for (a) with vertical restraint, and (b) without vertical restraint (Kokosho, 2003).  Chapter 3. Liquefaction-Induced Ground Failures  75  As may be noted, although the water film appeared after initial liquefaction in this test, this may not be the case in reality, since the sample was not allowed to displace freely due to equipment limitation (see the second graph in Fig. 3-30). The gap between liquefaction onset and water film appearance and then linearly increase in these tests may be attributed to inject flow.  0  10  20  30  40  50 time[secj  60  70  80  90  Fig. 3-30: Time histories of shear stress, strain, Ue, axial stress water film thickness for sample of Dr = 28% with static shear bias. (Kokusho, 2003).  3.4.  Numerical Studies on Void Redistribution Recently researchers have applied numerical methods to simulate the behavior of earth  structures near the interface of a low permeability top layer and liquefiable bottom layer (e.g. Yoshida & Finn, 2000; Yang & Elgamal, 2002; Bastani, 2003; Uzuoka et al., 2003; Seid-Karbasi & Byrne, 2004a and Seid-Karbasi & Byrne, 2007). The computational formulations derived from fundamental soil mechanics principles and incorporated in a stress-flow coupled analysis procedure with an account for pore water redistribution can predict deformations in stratified grounds and resulted localized shear strains at the layers interfaces.  Chapter 3: Liquefaction-Induced Ground Failures  76  Yoshida & Finn (2000) presented initial results of a numerical work to model water film formation using a joint element technique. They applied their procedure to predict a centrifuge test model of liquefiable level ground with surface barrier (Liu & Dobry, 1993). Yang & Elgamal (2002) employing an effective stress approach predicted large deformation in a mildly sloping ground of liquefiable soil with localization beneath the low permeability top layer.  They noted that the analysis results are mesh size dependent and  suggested further studies in this regard. Bastani (2003) utilizing numerical analysis evaluated static centrifuge tests subjected to seepage forces similar to those that occur post-shaking. The model showed dilation characteristics, such as void ratio increases, consistent with void redistribution although the mechanistic explanation was not fully developed. Uzuoka et al. (2003) with employing an effective stress approach demonstrated that localization may occur in a liquefiable sloping ground when an unsaturated soil layer above ground water table is present. They also addressed mesh size effects on the analysis results and needs for more studies. These studies show that numerical modeling can be employed as a tool to shed more light on the mechanism of void redistribution and flow-slides.  3.5.  Data from Case Histories  Researchers have speculated on the possible role of low permeability sub-layer (or void redistribution) in case histories of failures in earthquakes. These failures included both flow failures as well as large lateral spreads. The fact, that only very few case histories are well documented and it is very hard to find direct evidence of void redistribution during and after a failure, makes it difficult to directly observe the role of this mechanism in such failures. A comprehensive list of failed case histories with void redistribution involvement is provided in Appendix III of this thesis.  Table AIII-J of Appendix III lists case histories of post shaking  failures in a chronological order of occurrence based on information found in the literature (e.g. Hamada 1992; Kokusho, 2003 and Kulasingam, 2003). Details of geometry, soil conditions and shaking characteristics are given where available to evaluate whether void redistribution might possibly have played a role in the failure. Among them a case from Niigata 1964 earthquake,  Chapter 3: Liquefaction-Induced Ground Failures  77  Japan is described in the preceding section as a typical liquefaction induced failure in gentle slopes. Please consult with Appendix III for complete description for all cases listed in Table Alil-] along with some additional cases with less severe failure consequences. The compiled case  histories are ones where large movements were known to have started after the end of shaking or where void redistribution would be expected to be important but the timing of failure initiation is unknown. Case history records show that many post-earthquake failures took place from a few seconds after the end of shaking to days after the earthquake. In general some mechanisms, which could lead to delayed failure as noted by Kulasingam (2003), are: • • • • •  Loosening due to void redistribution. Pore pressure redistribution softening the non-liquefied portions. Shear strain accumulation due to small after shocks acting on liquefied soil (Meneses et al., 1998 and Okamura et al. 2001). Stress redistribution due to the failure of local regions of the slope during shaking, leading progressively to a global failure after shaking. Cracks formed during shaking, leading to piping and erosion. It is also possible that more than one mechanism was active for any one case or other  mechanisms e.g. mixing of layers with different gradation resulting in lower residual strength (Byrne & Beaty, 1997, Yoshimine et al., 2006 see Appendix I for more details) aggravated the resulted failure. Note that slide movements for steep slopes, which started during shaking, can continue after the end of shaking due to momentum effects.  Lateral Spreading in Kawagishi-cho and Hakusan, Niigata, Japan (1964)  The 1964 Niigata earthquake, of magnitude 7.5, caused widespread liquefaction in Niigata city, Japan (Kawakami & Asada, 1966). This event and Alaska earthquake in 1964 as benchmark events had a significant impact on geotechnical earthquake engineering. Since then a number of comprehensive investigations on liquefaction have been launched in Japan and North America. Yoshida et al. (2005) noted that using aerial photos taken after earthquake and comparing conditions before and after the earthquake revealed earthen flow-slides or large lateral spreads at various nearly level-ground sites in Japan. It was found that liquefaction-induced flow is not an extraordinary phenomenon. They also argued that applying steady-state concept to evaluate residual strength of liquefied sand cannot explain the occurredflow-slide mechanism. It should be  Chapter 3: Liquefaction-Induced Ground Failures  78  noted that in the most relevant literature the steady-state strength of a liquefied sand layer refers to undrained strength of a sample of that layer at pre-earthquake in-situ void ratio (constant volume loading). There were several lateral spreads along the banks of the Shinano River (Hamada, 1992) due to Niigata earthquake. Fig. 3-31 shows lateral displacement vectors at an area located a few hundreds meters from the river bank (insignificant free face effect). As may be noted in some locations (designated as 2b and 2c) large displacements (e.g. 4 m) occurred in the directions opposite to the river whereas the slope is less than 1% or less indicating that failure has occurred in a surface (possibly sub-layer interfaces) that does not follow the ground surface inclination. An area, located between the Echigo railway embankment and the left bank of the Shinano River in Kawagishi-cho, Hakusan district, suffered lateral displacements in the order of 7-11 m towards the river during that earthquake (Hamada 1992; Kawakami & Asada 1966; Kokusho 1999, 2000, 2003; Kokusho & Kojima, 2002, Yoshida et al., 2005). This area had a very gentle slope of less than 1%. The general soil profile in this area consisted of deep deposits of sands with a sandy clay layer sandwiched near the surface. The soil profile at the Hakusan transfonner substation consisted of a 2m thick sandy clay sandwiched between a 4 m thick sand layer on top, and a sand layer (with sub-layers of silty to gravelly sands) extending for more than 25 m at the bottom. Trenching work reported by Kokusho & Fujita (2002) and Kokusho & Kojima (2002) showed the continuous nature of the sandy clay layer and additional micro layering within the top sand layer (see Fig. 3-32). Liquefaction and lateral spreading caused the failure of several building foundations in Kawagishi-cho area. Kawakami & Asada (1966) described the case history as follows, “In the area where liquefaction of the ground had been occurred, many reinforced concrete buildings of multiple stories, which were settled or tilted with small breakage, were observed. The subsidence and the tilting of these buildings were not caused by the shear failure of soft ground, and slip plane in the ground or heaving of the ground around the structures could not be found. It took several minutes to overturn an apartment house in Kawagishi-cho, Niigata city, and the directions of the tilting of apartment houses in the area were the same, because this damage had no direct connection with vibration”. A photo of Kawagishi-cho apartment buildings after the earthquake is shown in Fig. 3-33. Lateral spreading occurred in the nearby area, which included the Meikun High school and the Hakusan transformer substation, too (Kawakami & Asada 1966; Kokusho & Kojima 2002). The area of slide was measured to be 250 m by 150 m, and the maximum  Chapter 3: Liquefaction-Induced Ground Failures  79  displacement was about 7 m. The slide mass continued to move even after the shaking ended (Kokusho, 1999). Kokusho & Kojima (2002) reported pictures taken by a high school student indicated that muddy water started to come out of the ground, and fissures gradually expanded after the end of shaking. Kawakami & Asada (1966) also described the failure as quite a different phenomena from the usual slides of sloping ground in which the movement of upper part of the ground was due to the liquefaction of the lower part of the ground.  Fig. 3-31: Lateral displacement vectors at area few hundred meters from the Shinano River in Niigata (Hamada, 1992 and Kokusho, 2003).  Chapter 3: Liquefaction-Induced Ground Failures  On SHINANO  80 lOOn  300rn  HOTEL N11GATA  RER WT5  On  -iOn  bore-hole number  44  —  45  46  47  1SE’  Less permeable  sublayer Liquefiable sand  OO1  218  57  227  Ds Water table  63  79  Clay  Silt  Fig. 3-32: Soil profile at Niigata Hotel area, Niigata (Kokusho & Fujita, 2002, with permission from ASCE).  Fig. 3-33: Liquefaction-induced bearing capacity failures of the Kawagishi-Cho apartment buildings (EERC, Un., Cal, Berkeley).  Chapter 3: Liquefaction-Induced Ground Failures  3.7  81  Summary and Main Findings  In this chapter, results of previous studies on void redistribution using physical model testing were first reviewed. Then, fundamentals of soil strength loss and instability due to injection flow under partially drained conditions based on element test data were discussed. A brief review of related numerical investigations carried out to date was presented. Finally, evidence from past earthquakes indicating the involvement of void redistribution were reviewed. The following are the main findings of this literature review: •  Liquefaction-induced flow slides have occurred in very gentle sloping ground conditions in past earthquakes.  •  Most of these failures initiated during shaking or some time after the main shock of the earthquake motion from few seconds to days.  •  Applying steady-state concepts in such cases to evaluate undrained residual strength of liquefied soils (at the pre-earthquake void ratio) suggests that failure should not occur.  •  Residual strengths back calculated from case histories reflect implicitly the void redistribution effects onflow-slides. However, the extent of this influence remains unknown.  •  Residual strengths during earthquakes are not solely controlled by pre-earthquake soil parameters.  •  Field case histories do not have the information to prove whether void redistribution took place or not. However, the review of case histories of several cases where void redistribution could have possibly played a role in the failure, highlights the need for study of void redistribution and also site investigation techniques to detect thin sub-layers.  •  In level ground condition after liquefaction onset, water film can occur beneath the barrier layer. Its occurrence is less likely in an (infinite) slope with shear stress bias as sand deforms in its path to steady-state condition before a water film can form.  •  Physical model studies of slopes with and without low permeability sub-layer indicate that sand slopes as loose as 20% relative density are stable (with limited deformation) when subjected to earthquake shaking if no barrier layer is present. However, similar test models with silty sub-layers failed with localization in sand-silt interface, even in models of denser sand layers.  •  Physical model data also suggests that the deformations of liquefied sloping ground conditions with a barrier are mainly controlled by pore water migration rather than the inertia effects of earthquakes. It is possible that a smaller earthquake that results in less displacement  Chapter 3: Liquefaction-Induced Ground Failures  82  during shaking (as a result of steeper slope at the end of shaking) causes larger post-shaking deformations due to greater driving static shear stress. •  It is difficult to determine the volume change (void ratio change) of expanding soil beneath the barrier in physical model testing. However, it is possible to observe water film formation in test models.  •  Numerical methods can be a useful tool to provide insight into the void redistribution mechanism, especially regarding limitations involved in determining volume change within soil layers in physical tests.  83  CHAPTER 4  MODELING OF INJECTION FLOW AND VOID REDISTRIBUTION  4.1  Introduction  To investigate the effects of low permeability layers on ground deformations due to earthquake loading, predictions of the generation, redistribution, and dissipation of excess pore water pressures must be made during and after shaking. A fundamental approach requires a dynamic coupled stress-flow analysis, where the volumetric strains are controlled by the compressibility of the pore fluid and flow of water through the soil elements. To predict the instability and liquefaction flow-slide, an effective stress approach based on an elastic-plastic constitutive model (UBCSAND) is used in this study. The model is calibrated against laboratory element test data as well as centrifuge data and is described in this chapter. The UBCSAND model is incorporated in the commercially available computer code FLAC (Fast Lagrangian Analysis of Continua, Itasca, 2000). In the analyses used in this investigation, version IV of the program was used in 2D plane-strain mode. In general, three forms of soil-fluid mixture coupling formula are used in geomechanics, namely: (1) u p, (2) u -  -  U and (3) u p -  -  (J as suggested by Zienkiewicz and Shiomi (1984)  based on Biot ‘s theory (1941). Here, the unknowns are the soil skeleton displacements u; the pore fluid (water) pressure p; and the pore fluid (water) displacements U The u-p form captures the movements of the soil skeleton and change of pore water pressure, and is applicable when the relative fluid (water) acceleration is not important (in-phase movement). This relative acceleration is generally small in earthquake shaking (Zienkiewicz, et al., 1999). This approach is the most popular form of a coupling formulation used by many researchers in earthquake geotechnical engineering (e.g., Prevost, 1985, Dafalias, 1986, Zienkiewicz, et al., 1990, Byrne, et al., 1995, and Elgamal, et al., 1999, among others) and has been applied in this research.  Chapter 4. Modeling ofInjection Flow and Void Redistribution  84  In the first part of this chapter, to provide an insight into the computational process followed by the computer code, FLAC’, and the constitutive model used in this study, the main features of the FLAC program and principles of the UBCSAND model are briefly described. Then, results of previous applications of this procedure related to partially drained condition (void redistribution) are presented. After demonstrating the capability of the model to capture element soil behavior, its use will be extended to analyze the response of a typical liquefiable soil profile with a low permeability sub-layer to earthquake excitation. Also, the significance of permeability of the liquefiable soils in seismic ground response is investigated and highlighted. In the following sections, the results of such studies are presented and discussed.  4.2  Principles of the FLAC Program  The solution of a stress-deformation (boundary-value) problem requires that equilibrium and compatibility be satisfied for the boundary and initial conditions using an appropriate stressstrain relationship. Finite element or finite difference techniques are routinely used to reasonably satisfy these conditions. The finite difference method is perhaps the oldest numerical technique used for the solution of sets of differential equations, given initial values and/or boundary values (see, for example, Desai & Christian, 1977). In the finite difference method, every derivative in the set of governing equations is replaced directly by an algebraic expression written in terms of the field variables (e.g., stress or displacement) at discrete points (nodes/gridpoints) in space; these variables are undefined within elements (explicit method). However, finite element programs often combine the element matrices into a large global stiffhess matrix (implicit method), which is not normally done with finite difference programs since it is relatively efficient to regenerate the fmite difference equations at each step. The computer code FLAC uses the finite difference method and satisfies dynamic equilibrium using a step-by-step explicit time domain procedure. The dynamic approach used in FLAC has the advantages of achieving a numerically stable solution even when the problem is  not statically stable, allowing for the examination of large strains and displacements prior to failure. Thus, even though for a static problem, FLAC uses the dynamic equations of motion in the formulation. Since it does not need to form a global stiffness matrix, it is a trivial matter to update coordinates at each timestep which is the case in the large-strain mode of the code. The incremental displacements are added to the coordinates so that the grid moves and deforms with the material it represents. This is termed a “Lagrangian” formulation, in contrast to an  Chapter 4: Modeling ofInjection Flow and Void Redistribution  85  “Eulerian” formulation, where the material moves and deforms relative to a fixed grid (Itasca, 2000). The constitutive formulation at each step is a small-strain one, but it is equivalent to a large-strain formulation over many steps. The geometric domain (continuum model) is  discretized by the user into a finite difference mesh (grid) composed of quadrilateral elements (zones). An element should be small enough to be representative of material with the same properties and large enough so that the fluid and porous media system can be considered as a statistical homogenous porous medium. Internally, FLAC subdivides each element into two overlaid sets of constant-strain triangular elements (four triangular sub-elements), and calculations are carried out for these sub-elements to assure more reliable numerical results. The general calculation sequence of the explicit “time-marching” scheme embodied in FLA C is illustrated in Fig. 4-1 for every cycle. This procedure can be summarized as follows:  1. The equations of motion are invoked to derive new nodal velocities and displacements from stresses and forces. 2. New strain-rates are derived from nodal velocities. 3. Constitutive equations (stress-strain laws) are used to calculate new stresses from strainrates from previous calculation. It takes one timestep for every cycle around the loop and the maximum out-of balance force in the model is monitored. This force will either approach zero, indicating the system is reaching an equilibrium state, or a constant, nonzero value, indicating that a portion (or all) of the system is at steady-state (plastic) flow of material. Importantly, each box in Fig. 4-1 updates all of its grid variables from “known” values that remain ‘fixed” while control is within the box. For example, the lower box takes the set of velocities already calculated and, for each element, computes new stresses. The velocities are assumed to be ‘frozen” for the operation of the box i.e., the newly calculated stresses do not affect the velocities. This can be done if the selected timestep is so small that physical information cannot pass from one element to another during  that period. Of course, after several cycles of the loop, disturbances can propagate across several elements, just as they would propagate physically.  Chapter 4: Modeling ofInjection Flow and Void Redistribution  86  (Fixed forces during this calculation)  4  Equilibrium Equation (Equation of Motion) (for all mass-gridpoints)  new velocities and displacements  new stresses or forces  (Fixed strain-rates during this calculation) Stress I Strain Relation (Constitutive Equation)  (for all elements)  Fig. 4-1: Basic explicit calculation cycle used in FLAC.  -ü,it,u F(t) k  m  Fig. 4-2: Application of a time-varying force to a mass (concentrated in node), resulting in acceleration, velocity, and displacement (FLA C mass-spring system).  The central concept is that the “computational wave speed” always keeps ahead of the “physical wave speed,” so that the equations always operate on known values that are fixed for  the duration of the calculation. Thus, no iteration process is necessary when computing stresses from strains in an element, even if the constitutive law is wildly nonlinear. In an implicit method (which is commonly used in finite element programs), every element communicates with every  Chapter 4. Modeling ofInjection Flow and Void Redistribution  87  other element during one solution step: several cycles of iteration are necessary before compatibility and equilibrium are obtained. This prediction is path-dependent if materials are not elastic. The disadvantage of the explicit method is in the small timestep, which means that large numbers of steps must be taken. Fig. 4-2 illustrates a simple mass-spring system used in FLA C to solve the equation of motion with application of Newton ‘s law of motion that relates the acceleration, dü/dt of a mass, m, to the applied force, F(t), which may vary with time. The figure shows a force acting on a  mass, causing motion described in terms of acceleration (ii), velocity  (ii)  and displacement (u).  Newton’s law of motion for the mass-spring system is:  m=F(t)—ku dt  [4-1]  where k is the spring stiffness and dt is the timestep which is selected by FLA C based on the problem specifications. When several forces act on the mass, Eq. 4.1 also expresses the static equilibrium condition when the acceleration tends to be zero i.e., 2F = 0, where the summation is over all the forces acting. This property of the law of motion is exploited in FLA C when solving “static” problems. In a continuous solid body, Eq. 4.1 is generalized as follows:  a. 9t  ôx  [4-2]  where p, t, x,. g 1 and u are mass density, time, components of coordinate vector, components of gravitational acceleration (body forces); and components of stress tensor, respectively. By application of the Gauss divergence theorem to the quadrilateral elements (sub-elements), the derived velocities at each mass/gridpoint (node) are used to express the strain rates of the quadrilateral elements. To solve static problems, the equations of motion must be damped to provide static or quasi-static (non-inertial) solutions. FLA C uses a form of damping, called “local damping” (non-viscous damping) in which the damping force on a node is proportional to the magnitude of the unbalanced force. This form of damping has the following advantages (Itasca, 2005): 1. Only accelerating motion is damped; therefore, no erroneous damping forces arise from steady-state motion.  Chapter 4: Modeling ofInjection Flow and Void Redistribution  88  2. The damping constant, ct, is non-dimensional. 3. Since damping is frequency-independent, regions of the assembly with different natural periods are damped equally, using the same damping constant. For “dynamic” simulations, “Rayleigh damping, as commonly used in the time-domain “  programs, is also available in FLA C. It is approximately frequency-independent over a restricted range of frequencies. Although Rayleigh damping embodies two viscous elements (in which the absorbed energy depends on frequency), the frequency-dependent effects are arranged to cancel out at the frequencies of interest (i.e., central/natural frequency). The reader is referred to consult with the FLAC users’ manual for more details. For geological materials, damping commonly falls in the range of 2 to 5% of critical (Biggs, 1964). When using a plasticity-based constitutive model (e.g., UBCSAND) that captures material nonlinear behavior in cyclic loading, a nominal Rayleigh damping of 1% to 2% can be applied. FLAC is capable of simulating groundwater flow problems, mechanical problems, and  also coupled stress-flow problems (e.g., consolidation) when the program is configured to carry out this kind of analysis. The incremental formulation of coupled deformation-diffusion processes in FLA C provides the numerical representations for the linear quasi-static Biot ‘s theory (Itasca, 2005). Two mechanical (coupling) effects related to the pore fluid/water pressure are  considered: changes in pore water pressures induced by volumetric changes, and changes in effective stresses caused by pore water pressure changes. The first effect is captured through the fluid reaction to volume variations of the grid element. This volume change can be due to confining mean stress or deviatoric stress (shear induced) which is referred to as “mechanical volume change  “.  The second effect reflects the effective stress change when the pore water  pressure is modified by the flow process (originated from mechanical or groundwater source). This is referred to ‘flow volume change.”  The groundwater formulation of the program follows the same general scheme of fmite differences and discretization of the grid for mechanical problem, and the governing equations are solved by applying transport law (Darcy ‘s law), balance (continuity) law and constitutive  law. FLAC considers pore water pressure and saturation as being associated with gridpoints/nodes. Furthermore, the groundwater equations are expressed in terms of pressures, P rather than hydraulic head, and hence, Darcy ‘s law for anisotropic porous medium is written as (Itasca, 2005):  Chapter 4: Modeling ofInjection Flow and Void Redistribution  q,  =  —ks,  where qj is the  “  -  axi  89 [4-3]  specfIc discharge vector” (discharge in unit area), P the pressure, and lc is the  “FLAC permeability” (kpMc) tensor. The program uses “mobility coefficient” (coefficient of the  pore fluidJwater pressure term in Darcy ‘s law). The relation between “hydraulic conductivity, “k (e.g., in mlsec), commonly used when Darcy law is expressed in terms of head, and kFMc (e.g., in [m /Pa-sec]) is as Eq. 4-4. Also, the property of “intrinsic permeability,” 2  K  ) is 2 (e.g., in m  related to kFJAc and k, as shown by Eq. 4-5:  kFLAC  = gp  [4-41  where g: the gravitational acceleration, Pw the fluid mass density,  FLAC allows the user to decide whether gravitational forces (stress/mechanical  computation), flow effects (hydraulic/flow computation), or both (coupled stress-flow) should be taken into account. A “Flow-on/Flow-off” switch instruction is used for this purpose. Turning “gravity” on implies that body forces will be accounted for in the analysis. The gravitational  acceleration, g is treated as a vector in FLA C formulation, so different vertical and horizontal components of g can be applied to a grid. In addition, the magnitude of g can be set to be equal to a value different from the actual Earth gravitational acceleration of 9.81 rn/s . Therefore variation 2 of g, like those in centrifuge testing, can be simulated. Turning “Flow-on” (effective stress approach) implies that the fluid within a grid is allowed to move among the elements and the bulk modulus of the fluid increases the mechanical stiffness of a saturated zone. The effect of increased mechanical stiffness is incorporated in quasistatic analysis in the density-scaling scheme already in FLAC using Biot theory (Biot’s coefficient, ci is assumed 1, neglecting soil grains compressibility comparing to that of soil  Chapter 4: Modeling ofInjection Flow and Void Redistribution  90  skeleton, Kske). The apparent mechanical bulk modulus of a saturated zone is modified by the presence of fluid as follows:  K K=KSke+•’ n  [4-5]  Depending on the boundary conditions with regard to the flow, the grid will be either an open or closed system. In an open system, fluid will enter or leave the grid, while in a closed system, no communication occurs with the outside world. In both cases, flow will occur within the geometric domain of the problem. Turning “Flow-off” (undrained condition) implies that the fluid will not enter or leave any of the elements comprising the grid, and thus, the fluid will not move at all. Flow computations also require that the timestep be less than a critical value to assure that no physical (flow) process is transferred during a computation cycle. The explicit flow timestep can be derived by imagining that one node at the center of four zones is given a pressure of P°”. The resulting nodal flow is then given by Eq. 4-6. This relation has a stable and monotonic solution if the timestep is lower than a critical value as expressed by Eq. 4-7.  Q  At  =  pold  Mkk  nV <  1 K  [4-6]  [4-7]  Mu  where: Mu: the permeability stffness sum over the four zones of the diagonal terms corresponding to  the selected node; K,c bulk modulus of fluid (water); V element volume; n. porosity;  ________________________  Chapter 4: Modeling ofInjection Flow and Void Redistribution  91  FLAC uses this timestep for flow computations with applying a factor of safety of 1.25. In the  same fashion, the critical mechanical timestep of a given model (of i x j zones) is determined by FLAG which is controlled by element size and compression wave velocity, 1’,  =  to assure  that no physical (mechanical) effects are transferred during the time interval in one cycle of numerical calculation. A safety factor of 2 is used in this case. Finally, FLAC uses the lowest critical timestep determined for the two types of computations for a given domain (of i x  j  zones), as expressed by Eq. 4-8 and Eq. 4-9,  respectively for mechanical and flow calculations (see Itasca, 2005 for details):  A  mm  .  Mech.  K4 I I Ksi + + G  —  4  —  At FIoM  =  2 1 .i(Ax.)n mm miniI  /XtFLAC  where  =  min(ixtMech  /itMech, /itplow  and  [4-9]  f  FLAC  ,  ,,,) 0 At,  /ItFLAC  [4-10]  are critical mechanical timestep, critical flow timestep and the  timestep used by FLA C respectively, and other parameters are as follows: zlXmin:  represents element minimum length (which is controlled by A, element area as  G: shear modulus; p. unit density. It may be seen that the timestep is controlled by size of the smallest element in the model  and also, it decreases with an increase in compression wave velocity (denominator in Eq. 4-8 for AtM)  and/or an increase in permeability and/or fluid bulk modulus, 1 K (denominator in Eq. 4-9  for 0 AtFl ) .  Chapter 4. Modeling ofInjection Flow and Void Redistribution  92  Starting from a state of mechanical equilibrium, a coupled stress-flow (hydro-mechanical) static simulation in FLA C involves a series of steps. Each step includes one or more flow steps (flow loop), followed by enough mechanical steps (mechanical loop) to maintain quasi-static equilibrium. The increment of pore fluid/water pressure due to fluid flow is evaluated in theflow loop; the contribution from volumetric strain is evaluated in the mechanical loop as a zone value which is then distributed to the nodes. The total stress correction due to pore water pressure change arising from mechanical volumetric strain is performed in the mechanical loop, and from that arising from fluid flow in the flow loop. The total value of the pore water pressure is used to evaluate effective stresses and detect failure in plastic materials. In this context, the pore water pressure field may originate from different sources, e.g., a flow analysis or a coupled stress-flow (hydro-mechanical) simulation (Itasca, 2000). Two FLA C executable codes are provided in two versions: a single-precision version and a double-precision version. The single-precision version is more efficient for most analyses and runs approximately 1.5 to 2 times faster than the double-precision version that also requires about 3 times more computer RAM (Random Access Memory). The double-precision version provides more accurate solutions for cases in which (Itasca, 2000): 1. The accumulated value of a variable after many thousands of time steps is much larger than the incremental change in the variable (e.g., an accumulated value for displacement in a flow failure). 2. Model grids contain many zones with coordinates that are large compared to typical zone dimensions. 3. The third situation at which double-precision is recommended is related to flow computations. There is a limit to the amount by which fluid modulus may be reduced, and instability results when too much fluid enters or leaves a zone in one timestep. An upper limit also exists to the fluid modulus. In this case, the amount of fluid exchanged with a zone in one timestep can be below the resolution of the computer arithmetic in single-precision (accuracy limit is around six decimal digits in single-precision, whereas, it is 15 digits for double- precision). However, computation speed in the double-precision mode is much slower compared to that of single-precision. All analyses discussed in this thesis were carried out in “Flow-on” and ‘single-precision modes, unless otherwise stated.  Chapter 4: Modeling ofInjection Flow and Void Redistribution 4.3  Stress-Strain Model for Sands  —  93  Principles of the UBCSAND Constitutive Model  Plasticity models are formulated along the lines of classical continuum mechanics, and a stress increment is specified by a strain increment. Therefore, the stress-strain relationship is incremental in form, and the total strain increment is separated into elastic and plastic strain increments (Hill, 1950). In addition, zones of elastic and plastic behavior are assumed to be separated by a boundary called a yield surface (or yield locus or loading surface). A classical plasticity model consists of four distinct components: (1) yield surface, (2) flow rule, (3) hardening rule (4) hardening parameter, which control stress-strain relationship. Yield surfaces are defined exclusively in stress space, and define the size of the elastic region. Any stress probe pushing outwards of the yield surface will cause plastic strains (known as loading process). The flow rule determines the directions of plastic shear and volumetric strain increments (plastic strain vectors). It could be associated (yield surface  plastic potential) or non-associated. The  hardening rule specifies the manner in which the elastic region evolves as yielding takes place (Prager, 1955). Two types of hardening are possible: i.e., isotropic (proportional expansion of yield surface in all directions) and kinematic (moving of the yield surface without change in orientation, size, or shape of the elastic region). The two types can also be combined and are known as mixed hardening. The hardening parameter is a scalar quantity used to record the plastic deformation history developed during the loading process. The stress-strain curve,  generally nonlinear, describes the response of soil to loading. The majority of classical plasticity models can be categorized into two types: (extended) Mohr-Coulomb model types and Critical-State model types (Puebla, 1999). More advanced models also exist: e.g., bounding surface models (Dafalias & Popov, 1975), multi-yield or nestedsurfaces models (e.g., Prevost, 1985), advanced general-plasticity models (e.g., Pastor Zienkiewicz Mark III, Pastor, et al., 1990), multi-mechanism models (e.g., Matsuoka & Sasakibara, 1978), and multi-laminate models (e.g., Pande & Pietruszezak, 1982). More discussion on constitutive models used for sands and liquefaction analysis can be found in the literature (e.g., Dafalias, 1994; Puebla, 1999; and Park, 2005, among others). In any case, the complicated models require more soil parameters that are not readily available in most cases and as a result they become less applicable for engineering purposes. The UBCSAND constitutive model, as a Mohr-Coulomb type stress-strain model, is an elastic-plastic model proposed by Byrne, et al. (1995), and further developed by Beaty and Byrne  Chapter 4. Modeling ofInjection Flow and Void Redistribution  94  (1998) and Puebla (1999). The model has been successfully used in analyzing the CANLEX liquefaction embankments (Puebla, et al., 1997) and for predicting the failure of the Mochikoshi tailings dam (Seid-Karbasi & Byrne, 2004b). It has been validated against dynamic centrifuge test data (e.g., Byrne, et al., 2004) and has also been used to examine re-liquefaction effects (Seid-Karbasi, et al., 2005). The key aspects of the model are summarized as: •  Yield loci are lines of constant stress ratio  •  Theflow rule relating the plastic strain increment directions is non-associated (see Fig. 43a) and leads to a plastic potential defined in tenns of dilation angle.  •  Sand dilation property is accounted for, based on the Rowe (1962) dilatancy theory.  •  Hardening rule is a kinematic type.  •  Hardening parameter is plastic shear strain.  •  The model is a co-axial constitutive model (i.e., coincidence of the directions of principal stresses with plastic strain increments). This is a widely-used assumption in plasticity models.  •  The model in this version is developed for 2D-condition and captures sand behavior under simple-shear test loading that better mimics the ground response to earthquake excitation.  •  The elastic and plastic shear strains take place simultaneously (no strain threshold is assumed in the model).  (ij  r/ a’), as shown in Fig. 4-3.  The prime features of the model properties are briefly described in the following section (see Puebla, 1999 for more details).  4.3.1  Elastic Properties  The elastic component of response is assumed to be isotropic and specified by a shear modulus, Ge, and a bulk modulus, K, as follows: G =kJ-  [4-11]  Chapter 4: Modeling ofInjection Flow and Void Redistribution  95  T  o’, d6j’  (a)  (b)  Fig. 4.3: Principles of UBCSAND model (a) moving yield loci and plastic strain increment vectors, (b) dilation and contraction regions. [4-12]  where k is an elastic shear modulus number; Pa is atmospheric pressure; o’  =  (o’  +  o’) /2;  e  is an elastic exponent usually assumed to be approximately 0.5; a depends on elastic Poisson ratio, ,u, and ranges from 2/3 to 4/3 (p controls K and G ratio as: p  3-2 =  2(3+1))•  Small-strain  drained Poisson ‘s ratio for granular soils commonly varies from 0 to 0.2 (Hardin & Drnevich, 1972). Recent investigations (e.g., Burland, 1989; Tatsuoka & Shibuya, 1992; and Lehane & Cosgrove, 2000) using advanced techniques (i.e., local strain measurements with special internal high-resolution instrumentation) have confirmed that the value of drained p ranges from 0.1 to 0.2 for all types of geomaterials at low strain levels, increasing to larger values as failure states are approached (Mayne, 2007).  4.3.2  Plastic Properties  The plastic shear strain increment d3I is related to stress ratio, dij, where  i  =  r/  J’,  as  shown in Fig. 4-4, and can be expressed as Eq. 4-24. Thus, under a constant shear stress, reduction in effective mean stress (due to mechanical or flow factors) results in plastic shear/volumetric strains.  Chapter 4. Modeling ofInjection Flow and Void Redistribution  96  =[[th]  dy  [4-13]  where G’ is the plastic shear modulus, given by a hyperbolic function which is a common form to express the stress-strain curve for granular materials (e.g., Kondner & Zelasko, 1963, Duncan & Chang, 1970; and Matsuoka & Nakai, 1977) as:  = Gf  G  1 --R 11 1—-  L S,flp  /‘  where Gf  =  [4-14]  J  .F  is the maximum plastic shear modulus (at  i  0),  a  k: plastic shear modulus number, n: plastic shear modulus exponent, ij  the stress ratio at failure and equals sin q where p is the peak friction angle, and 1  R failure ratio (= : 1 ij,), which is the ratio of the stress ratio at failure to that at the ultimate state. It is determined based on best-fit hyperbola, and generally ranges from 0.5 to 1.0.  ’j in turn is related to G and the relative density of the sand. The associated increment of plastic 5 G volumetric strain,  is related to the increment of plastic shear strain, dy  through the flow  rule as follows:  de°  = dy°.(sinq,  —)  [4-15]  where q,, is the friction angle at constant volume (considered equal to phase transformation,  qi,).  From Fig. 4-3, at low stress ratios, significant shear-induced plastic compaction is occurring (where plastic potential vectors slope to the right), while no compaction is predicted at stress ratios corresponding to ‘p (where the plastic potential vector is vertical). For stress ratios greater than pt,,, shear-induced plastic expansion or dilation is predicted as shown in Fig. 4-3b (where the plastic potential vectors slope to the left).  Chapter 4. Modeling ofInjection Flow and Void Redistribution  97  0  -a C,)  Plastic shear strain,  Fig. 4-4: Plastic shear strain increment and shear modulus.  This simple flow rule is in close agreement with the characteristic behavior of sand observed in drained laboratory element testing (discussed in Chapter 2). The response of sand is controlled by the skeleton behavior outlined above. The presence of a fluid (air-water mixture) in the pores of the sand acts as a volumetric constraint on the skeleton if drainage is fully or partially curtailed. This constraint causes the pore water pressure rise that can lead to liquefaction. Provided that the skeleton or drained behavior is appropriately modeled under monotonic and cyclic loading conditions, and that the stiffness of the pore fluid and drainage are accounted for, the liquefaction response can be predicted. Therefore, basically the model parameters should be determined based on laboratory drained tests. This model is incorporated in the computer code FLAC. As mentioned before, the program models the soil mass as a collection of grid zones or elements and solves the coupled stress-flow problem using an explicit time-stepping approach. The program has a number of built-in stress-strain models, including an elastic-plastic Mohr-Coulomb model, and UBCSAND is a variation of this model, in which friction and dilation angles are varied to incorporate the yield loci and flow rule described earlier. Drainage conditions are built into FLAC, and drained, undrained, or coupled stress-flow conditions are specified by the user. For practical purposes, the key elastic and plastic sand parameters can be expressed in terms of relative density, Dr or normalized Standard Penetration Test values, . 60 Initial ) 1 (N estimates of these parameters have been approximated from published data and model  Chapter 4: Modeling ofInjection Flow and Void Redistribution  98  calibrations. The response of sand elements under monotonic and cyclic loading can then be predicted and the results compared with laboratory data. In this way, the model can be made to match the observed response over the range of relative density or (N 60 values. The model has ) 1 also been calibrated to reproduce the NCEER 97 (Youd, et al., 2001) triggering chart (Byrne, 2003) which, in turn, is based on field experience during past earthquakes arid is expressed in tenns of the Standard Penetration Test resistance value, . 60 The model properties for ) 1 (N obtaining such agreement are therefore expressed in temis of (N,) . 60  4.3.3  Model Prediction of Laboratory Element Tests  The model was applied to simulate cyclic simple shear tests under undrained conditions. Fig. 4-5 shows model predictions along with test results on (air-pluviated) Fraser River sand. The test had an initial vertical consolidation stress cr’  100 kPa and Dr  =  40%. The results in terms  of stress-strain, stress path, and excess pore water pressure ratio, R compare reasonably well with the laboratory data. A comparison of model prediction with test results, in terms of required number of cycles to trigger liquefaction for different cyclic stress ratios, CSR, is shown in Fig. 45d and shows good agreement. 15  15  —  (a) io  (b)  Prediction  10  V  --  -.  -5  V  -10  -10 —  -15  -15 -15  -5  -10  5 0 rain (%)  10  15  0  25  Test data  75  50  100  125  Effective Vertical ress (kpa)  (c)  (d)  0.2  0.8  0.15 0.6  0.4  30.1  0.2  0.05  0  0  Predictio 0  2  4 No. of Cycles  6  8  0  5  10  15  No. of Cycles  Fig. 4-5; Comparison of predicted and measured response for Fraser River sand, (a) stress-strain, CSR = 0.1, (b) stress path, (c) R vs. No. of cycles for liquefaction: R 0.95, (d) CSR vs. No. of cycles for liquefaction (test data from Sriskandakumar, 2004).  20  99  Chapter 4: Modeling ofInjection Flow and Void Redistribution  The model was also used to predict the effect of both undrained and partial drainage as observed in triaxial monotonic tests. The partial drainage involved injecting the sample with water to expand its volume as it was sheared. The injection causes a drastic reduction in soil strength. In the numerical model, the same volumetric expansion was applied and the predicted results were compared to the test results shown in Fig. 4-6a to Fig. 4-6c (predictions and tests shown with solid and dotted lines, respectively). The test results conducted on Fraser River sand (Dr  =  82%) are presented in terms of stress-strain, volumetric strain vs. mean effective stress, and  stress path (Eliadorani, 2000). From Fig. 4-5, the predictions are in remarkably good agreement with the measured data. The above simulations illustrate that the model can generate the appropriate pore water pressures and stress-strain response to undrained loading as well as account for the effect of volumetric expansion caused by inflow of water into an element.  100 (a)  Undrained. dc.Jdt 1  =  0  *  Test Prediction  50  -1  Partially drained. dis 1  J 0 0  1  2 Axial strain,  si  (%)  3  4  3  4  :1 0  2  1  Axial strain,  si  (%)  200  (c)  150  Undrained, dnjdsi  =  0  Partially draine  100  50 LdsvIdcl1 b  V 0  50  100 (‘ + O’3)/2  150 (kpa)  200  250  Fig. 4-6: Prediction of soil element response in undrained and partially drained (inflow) triaxial tests for Fraser River sand, Dr = 82%: (a) stress-strain, (b) volumetric strain, and (c) stress paths (modified from Atigh & Byrne, 2004).  Chapter 4. Modeling oflnjection Flow and Void Redistribution  4.4  100  Soil Profile Used in the Analyses  The soil profile used throughout this study is a 1 Om thick deposit representing a sloping ground with 10 inclination (1.7% slope), with water level at ground surface, as shown in Fig. 4-7. It comprises a loose sand deposit resting on an impermeable base. The effect of a low permeability layer within the loose sand at a depth of 4m is examined. Fraser River sand, with relative density Dr  =  40 % is considered to represent the loose sand. Material properties are listed  in Table 4-1, where Pd, n, and k are material dry density, porosity, and permeability respectively. The UBCSAND model was applied to the loose sand layer with an equivalent UBCSAND model 60 value of 6.2 (see Table 4-lb for corresponding model properties). The low permeability silt ) 1 (N  layer barrier is simulated with a Mohr-Coulomb model with friction angle, q =300 and permeability, k =1000 times lower than that of the loose layer. Its stiffness in terms of bulk modulus and shear modulus was modeled as 1 e4 kPa and 0.5e4 kPa, respectively. It is not considered to generate excess pore water pressure. Input base motion, in terms of an acceleration time history, is shown in Fig. 4-8. It is a harmonic (sinusoid) excitation applied at the base of the soil layer, which ramps up to 2.5 rn/s 2 within is and dies out in 2s, and lasts for 7s in total. Analyses were conducted for two cases: 1. Case I: Sloping ground without low permeability sub-layer 2. Case II: Sloping ground with low permeability sub-layer 4.5  Analyses and Results To model the free field condition, a mesh with 9 x 22 zones (as illustrated in Fig. 4-9) was  used. Material types are recognized with different permeability values as shown in the figure. The nodes on the left and right boundaries were linked so as to force the soil column to deform as a shear beam. The earthquake motion was applied as a time history of acceleration at the base of the mesh.  Chapter 4: Modeling ofInjection Flow and Void Redistribution  101  Loose Layer  -  4m Low Permeability Layer 3 Loose Layer c-I C  E C  0 e  -lOm  -1  U U  -3  Firm Impervious Ground  0  1  2  3  4  Time (s)  Fig. 4-7 Soil profile used in the analyses.  5  Porosity  Loose sand layer Silt barrier  ) 3 (kglm  (n)  UBCSAND 60 ) 1 (N  (mis)  1500  0.448  6.2  8.81e-4  1500  0.448  ----  k  8.81e-7  Table 4-ib: Properties associated with UBCSAND model applied to sand layer. Model parameter Elastic shear modulus number,  Sand layer  K  Elastic shear modulus exponent,  797 0.5  lie  Elastic bulk modulus coefficient, a (B  =  .Ge) 8 a  0.7  K  115  Plastic shear modulus exponent, np  0.4  Peak friction angle, qt(deg.)  33.6  Constant-volume friction angle, q (deg.)  33.0  Failure ratio, Rf  0.94  Plastic shear modulus number,  Factor of an isotropy, F  7  8  Fig. 4-8 Acceleration time history for base input motion.  Table 4-la: Materials properties used in the analyses. Material  6  1.0  Chapter 4: Modeling ofInjection Flow and Void Redistribution  (a) case I  102  (b) case II  Material: Silt barrier Loose sand  10 9 8 7 6 5  Element:  :  (1,6)  0  -1  0  1  2  3  4(m)  Fig. 4-9: Analyses meshes used in the two cases with different materials types, (a) case j, profile without low permeability sub-layer, (b) case IL profile with low permeability sub-layer.  4.5.1  Sloping Ground without Barrier, Case I  As the benchmark condition, a sloping ground condition with  10  inclination was analyzed  without a low permeability layer. The results, in terms of time histories of excess pore water pressure ratio, R for selected depths, are shown in Fig. 4-10 (for position of the points refer to Fig. 4-9). The predicted patterns of excess pore water pressure indicate that essentially high excess pore water pressures build up within the soil profile during the strong shaking. Small dilation spikes, e.g., for element [1,3] are seen when R 1 and are less pronounced in the upper parts as a result of upward inflow. Excess pore water pressures dissipate somewhat more rapidly at depth, e.g., R at lOs is 55% and 75% for element [1,3] and [1,13], respectively. A similar trend has been observed in a number of centrifuge tests conducted for level and sloping grounds (e.g., Taboada & Dobry, 1993a; 1993b; 1998; Sharp, et al., 2003a, Phillips, et  aL, 2004).  Chapter 4: Modeling oflnjection Flow and Void Redistribution  103  1 0.8 0.6 0.4 0.2 0 (m  10  I 0.8  9  0.6  8  0.4  7  0.2  6  0  5  Ill’ liii Jill liii Ill, liii L.. liii 1.L.L li1ll 4Z4i.L.. LLL1M  0  5  10  15  20  [UlIll  11111 4jJf[j:  25 4  tLUii  DiIation  1  •I  3  III [11 Jul11  08 2  I lLi  0.2  1  II LIII  0  LII I I [I. I  —1  0 0  5  10  15  20  25  -1  0  1  2  3  4(m  lure (s)  Fig. 4-10: Excess pore water pressure ratio vs. time at selected points with increasing depth (case 1).  Ru  Fig. 4-11: Deformation pattern of soil profile without barrier, case I (with max. lateral displacement of 0.95m after 14 s).  Fig. 4-11 shows the predicted deformed mesh distortion occurring at the base and tapering off towards the surface resulting in a maximum displacement of 0.95m at the top surface. Fig. 4-12 shows isochrones of lateral displacement and excess pore water pressure at certain time intervals. It indicates that displacement gradually increases from the surface smoothly over time. It also shows that excess pore water pressure increases progressively along the soil profile while the motion is ramping up. This predicted pattern compares well with reported dynamic centrifuge data (e.g., Sharp, et al., 2003a). The authors modeled a lOm uniform submerged liquefiable layer in a 50g field  Chapter 4: Modeling ofInjection Flow and Void Redistribution  104  using a viscous pore fluid 50-times more viscous than water. Fig. 4-13 shows the model configuration in the model scale with 2° inclination. The applied acceleration is not horizontal but parallel to the base of the model, thus also forming an angle of 2° with the horizontal. Accounting for the effects of the weight of the rings and the different hydrostatic pressures at both sides of the box caused by the water level being horizontal, the equivalent prototype slope angle being modeled becomes  cfie1d  =  5.16° (Taboada, 1995). As shown in Fig. 4-13b, the model was shaken  with 22 cycles of harmonic motion with PGA Nevada Sand 120, air pluviated at Dr  =  0. 2 3g at 2 Hz. The soil used in the tests was  45%. Fig. 4-13c and Fig. 4-13d show measured profiles  of lateral displacement and excess pore water pressure, respectively, at different time intervals for the tested model. The majority of lateral displacements occurs after that excess pore water pressure approaches its high value (typically, R  0  0.9).  0  -  3.6s  5.9s  Is  2  2  4 3:  E  1)  3:  ID  I  6  8  8  (b)  (a)  10 0  0.2  0.4 0.6 x-dis (m)  10  0.8 0  20  40 60 Ue(kPa)  80  100  Fig. 4-12: Isochrones at certain time intervals for (a) lateral displacement, (b) excess pore water pressure (case I).  ___  Chapter 4: Modeling ofInjection Flow and Void Redistribution  105  50g  (c)  (a) Model Units  0  L9 U  •P7  --Af15  •P8  L7  •P5  -AH4  •P6  L6  •P3  --AH3  ‘p4  L4  •p1  -EAH2  •P2  L3 L2  20  2  8  Li  10 0  Input Motion  20 40 60 Lateral disp. (cm)  (d)  (b)  0.2 0.1 0.0 -0.1 .< -0.2  I  .0.3 5  0  10  15  20  Time (sec)  (e)  ‘lEa -mr  -._-.  10 0  20  40 60 Ue (kPa)  go  -4.l  Fig. 4-13: Centrifuge model of a lOm infinite slope, (a) model configuration (model scale), (b) base motion, (c) & (d) isochrones of measured lateral displacement and excess pore water pressure at different time intervals, (e) acceleration time history measured at 2.5m depth with AH4 (modified from Sharp & Dobry, 2002 and Sharp, et al., 2003a, with permission from ASCE).  Fig. 4-14 shows the time histories of predicted volumetric strain at different depths of the soil profile. As may be seen all volumetric strains are essent