## Contents

### Chapter 1  Introduction

1.1  Importance of Interaction
1.2  Importance of Material Behavior
1.2.1  Linear Elastic Behavior
1.2.2  Inelastic Behavior
1.2.3  Continuous Yield Behavior
1.2.4  Creep Behavior
1.2.5  Discontinuous Behavior
1.2.6  Material Parameters
1.3  Ranges of Applicability of Models
1.4  Computer Methods
1.5  Fluid Flow
1.6  Scope and Contents

### Chapter 2  Beam-Columns, Piles, and Walls: One-Dimensional Simulation

2.1  Introduction ... 11
2.2  Beams with Spring Soil Model ....... 11
2.2.1  Governing Equations for Beams with Winkler Model  11
2.2.2  Governing Equations for Flexible Beams ..................13
2.2.3  Solution .................. 14
2.3  Laterally Loaded (One-Dimensional) Pile 15
2.3.1  Coefficients A, B, C, D: Based on Boundary Conditions
2.3.2  Pile of Infinite Length
2.3.4  Moment at Top
2.3.5  Pile Fixed against Rotation at Top
2.3.6  Example 2.1: Analytical Solution for Load at Top of Pile with Overhang
2.3.7  Example 2.2: Long Pile Loaded at Top with No Rotation
2.4  Numerical Solutions
2.4.1  Finite Difference Method
2.4.1.1  First-Order Derivative: Central Difference
2.4.1.2  Second Derivative
2.4.1.3  Boundary Conditions
2.4.2  Example 2.3: Finite Difference Method: Long Pile Restrained against Rotation at Top 35
2.5  Finite Element Method: One-Dimensional Simulation
2.5.1  One-Dimensional Finite Element Method
2.5.2  Details of Finite Element Method
2.5.2.1  Bending Behavior
2.5.2.2  Axial Behavior
2.5.3  Boundary Conditions
2.5.3.1  Applied Forces
2.6  Soil Behavior: Resistance–Displacement Representation
2.6.1  One-Dimensional Response
2.6.2  Representation and Curves
2.6.3  Simulation of Curves ..50
2.6.4  Determination of p y –v (p–y) Curves .. 51
2.6.4.1  Ultimate Soil Resistance .....52
2.6.4.2  Ultimate Soil Resistance for Clays .............52
2.6.4.3  Curves for Yielding Behavior .............55
2.6.4.4  Curves for Stiff Clay ..56
2.6.4.5  Curves for Sands ...57
2.6.5  Curves for Cyclic Behavior ..59
2.6.6  Ramberg–Osgood Model (R–O) for Representation of p y –v Curves .....60
2.7  One-Dimensional Simulation of Retaining Structures ...........60
2.7.1  Calculations for Soil Modulus, E s  62
2.7.1.1  Terzaghi Method .62
2.7.2  Nonlinear Soil Response ....62
2.7.2.1  Ultimate Soil Resistance .....62
2.7.2.2  p y –v Curves .........63
2.8.1  Boundary Conditions .........66
2.8.2  Tip Behavior ..........67
2.8.3  Soil Resistance Curves at Tip .......68
2.8.4  Finite Difference Method for Axially Loaded Piles .... 68
2.8.5  Nonlinear Axial Response .69
2.8.6  Procedure for Developing Curves ..............69
2.8.6.1  Steps for Construction of Curves .69
2.9  Torsional Load on Piles ......70
2.9.1  Finite Difference Method for Torsionally Loaded Pile............72
2.9.2  Finite Element Method for Torsionally Loaded Pile ....................73
2.9.3  Design Quantities .. 74
2.10  Examples ....... 74
2.10.1  Example 2.4: p y –v Curves for Normally Consolidated Clay . 74
2.10.2  Example 2.5: Laterally Loaded Pile in Stiff Clay ...... 81
2.10.2.1  Development of p y –v Curves .83
2.10.3  Example 2.6: p y –v Curves for Cohesionless Soil .......88
2.10.4  Simulation of p y –v Curve by Using Ramberg Osgood Model .......92
2.10.5  Example 2.7: Axially Loaded Pile: Curves ..........95
2.10.5.2  Parameter, m ..... 101
2.10.5.3  Back Prediction for Curve ................ 102
2.10.5.4  Tip Resistance ... 102
2.10.6  Example 2.8: Laterally Loaded Pile—A Field Problem ...............104
2.10.6.1  Linear Analysis .104
2.10.6.2  Incremental Nonlinear Analysis ............... 105
2.10.8  Example 2.10: Tie-Back Sheet Pile Wall by One-Dimensional Simulation ... 108
2.10.9  Example 2.11: Hyperbolic Simulation for p y –v Curves ................. 110
2.10.10 Example 2.12: p y –v Curves from 3-D Finite Element Model .... 115
2.10.10.1 Construction of p y –v Curves  117
Problems .................120
References ..............134

### Chapter 3  Two- and Three-Dimensional Finite Element Static Formulations and Two-Dimensional Applications

3.1  Introduction . 139
3.2  Finite Element Formulations ......... 139
3.2.1  Element Equations ............ 144
3.2.2  Numerical Integration ...... 146
3.2.3  Assemblage or Global Equation . 146
3.2.4  Solution of Global Equations ..... 148
3.2.5  Solved Quantities  148
3.3  Nonlinear Behavior .......... 148
3.4  Sequential Construction ... 149
3.4.1  Dewatering .......... 151
3.4.2  Embankment ....... 152
3.4.2.1  Simulation of Embankment . 152
3.4.3  Excavation ...........154
3.4.3.1  Installation of Support Systems ................ 155
3.4.3.2  Superstructure ... 156
3.5  Examples ..... 156
3.5.1  Example 3.1: Footings on Clay ... 156
3.5.2  Example 3.2: Footing on Sand ... 160
3.5.3  Example 3.3: Finite Element Analysis of Axially Loaded Piles ........ 164
3.5.3.1  Finite Element Analysis .... 165
3.5.3.2  Results .. 167
3.5.4  Example 3.4: Two-Dimensional Analysis of Piles Using Hrennikoff Method  173
3.5.5  Example 3.5: Model Retaining Wall—Active Earth Pressure ..... 177
3.5.5.1  Finite Element Analysis .... 179
3.5.5.2  Validations ........ 180
3.5.6  Example 3.6: Gravity Retaining Wall . 181
3.5.6.1  Interface Behavior ...... 183
3.5.6.2  Earth Pressure System  183
3.5.7  Example 3.7: U-Frame, Port Allen Lock
3.5.7.1  Finite Element Analysis .... 186
3.5.7.2  Material Modeling ...... 189
3.5.7.3  Results .. 189
3.5.8  Example 3.8: Columbia Lock and Pile Foundations ....189
3.5.8.1  Constitutive Models .... 191
3.5.8.2  Two-Dimensional Approximation ............197
3.5.9  Example 3.9: Underground Works: Powerhouse Cavern .................202
3.5.9.1  Validations ........205
3.5.9.2  DSC Modeling of Rocks ...206
3.5.9.3  Hydropower Project ....206
3.5.10  Example 3.10: Analysis of Creeping Slopes ............. 215
3.5.11  Example 3.11: Twin Tunnel Interaction .................... 219
3.5.12  Example 3.12: Field Behavior of Reinforced Earth Retaining Wall .......225
3.5.12.1  Description of Wall .....225
3.5.12.2  Numerical Modeling ...227
3.5.12.3  Construction Simulation ...228
3.5.12.4  Constitutive Models ....228
3.5.12.5  Testing and Parameters .....230
3.5.12.6  Predictions of Field Measurements ..........230
Problems .................235
References ..............237

### Chapter 4  Three-Dimensional Applications

4.1  Introduction .243
4.2  Multicomponent Procedure ...........244
4.2.1  Pile as Beam-Column ......245
4.2.2  Pile Cap as Plate Bending 247
4.2.2.1  In-Plane Response ......247
4.2.3  Assemblage or Global Equations ..... 251
4.2.4  Torsion ................. 251
4.2.5  Representation of Soil ......252
4.2.6  Stress Transfer .....252
4.3  Examples ..... 253
4.3.1  Example 4.1: Deep Beam . 253
4.3.2  Example 4.2: Slab on Elastic Foundation .................254
4.3.3  Example 4.3: Raft Foundation ....257
4.3.4  Example 4.4: Mat Foundation and Frame System ...258
4.3.5  Example 4.5: Three-Dimensional Analysis of Pile Groups: Extended Hrennikoff Method
4.3.6  Example 4.6: Model Cap–Pile Group–Soil Problem: Approximate 3-D Analysis ..268
4.3.7  Example 4.7: Model Cap–Pile Group–Soil Problem—Full 3-D Analysis .....273
4.3.7.1  Properties of Materials .....273
4.3.7.2  Interface Element ........ 275
4.3.8  Example 4.8: Laterally Loaded Piles—3-D Analysis ............... 276
4.3.8.1  Finite Element Analysis ....277
4.3.8.2  Results ..280
4.3.9  Example 4.9: Anchor–Soil System ...280
4.3.9.1  Constitutive Models for Sand and Interfaces .......... 281
4.3.10  Example 4.10: Three-Dimensional Analysis of Pavements: Cracking and Failure .....283
4.3.11  Example 4.11: Analysis for Railroad Track Support Structures
4.3.11.1  Nonlinear Analyses
4.3.12  Example 4.12: Analysis of Buried Pipeline with Elbows
4.3.13  Example 4.13: Laterally Loaded Tool (Pile) in Soil with Material and Geometric Nonlinearities ....297
4.3.13.1  Constitutive Laws .......302
4.3.13.2  Validation ..........304
4.3.14  Example 4.14: Three-Dimensional Slope .................307
4.3.14.1  Results ..309

### Chapter 5  Flow through Porous Media: Seepage

5.1  Introduction .323
5.2  Governing Differential Equation  ..323
5.2.1  Boundary Conditions .......324
5.3  Numerical Methods ..........326
5.3.1  Finite Difference Method .327
5.3.1.2  Time-Dependent Free Surface Flow
5.3.1.3  Implicit Procedure ......330
5.3.1.4  Alternating Direction Explicit Procedure (ADEP) ......330
5.3.2  Example 5.1: Transient Free Surface in River Banks ................... 336
5.4  Finite Element Method ..... 338
5.4.1  Confined Steady-State Seepage  .. 339
5.4.1.1  Velocities and Quantity of Flow ...............340
5.4.2  Example 5.2: Steady Confined Seepage in Foundation of Dam ........... 341
5.4.3  Steady Unconfined or Free Surface Seepage  ...........345
5.4.3.1  Variable Mesh Method .....346
5.4.4  Unsteady or Transient Free Surface Seepage ...........349
5.4.5  Example 5.3: Steady Free Surface Seepage in Homogeneous Dam by VM Method 350
5.4.6  Example 5.4: Steady Free Surface Seepage in Zoned Dam by VM Method ....... 351
5.4.7  Example 5.5: Steady Free Surface Seepage in Dam with Core and Shell by VM Method
5.4.8  Example 5.6: Steady Confined/Unconfined Seepage through Cofferdam and Berm
5.4.8.1  Initial Free Surface ..... 357
5.5  Invariant Mesh or Fixed Domain Methods ... 357
5.5.1  Residual Flow Procedure . 358
5.5.1.1  Finite Element Method .....360
5.5.1.2  Time Integration .........362
5.5.1.3  Assemblage Global Equations ..................363
5.5.1.4  Residual Flow Procedure ..363
5.5.1.5  Surface of Seepage .....365
5.6  Applications: Invariant Mesh Using RFP 367
5.6.1  Example 5.7: Steady Free Surface in Zoned Dam .....367
5.6.2  Example 5.8: Transient Seepage in River Banks......367
5.6.3  Example 5.9: Comparisons between RFP and VI Methods ...............369
5.6.4  Example 5.10: Three-Dimensional Seepage ............ 370
5.6.5  Example 5.11: Combined Stress, Seepage, and Stability Analysis  373
5.6.6  Example 5.12: Field Analysis of Seepage in River Banks .........383
5.6.7  Example 5.13: Transient Three-Dimensional Flow ..... 385
5.6.8  Example 5.14: Three-Dimensional Flow under Rapid Drawdown .390
5.6.9  Example 5.15: Saturated–Unsaturated Seepage .......392
Problems .................397
Appendix A ............398
One-Dimensional Unconfined Seepage  ...398
Finite Element Method .....398
References ..............405

### Chapter 6  Flow through Porous Deformable Media: One-Dimensional Consolidation

6.1  Introduction .409
6.2  One-Dimensional Consolidation ...409
6.2.1  Review of One-Dimensional Consolidation .............409
6.2.2  Governing Differential Equations .... 410
6.2.2.1  Boundary Conditions .. 411
6.2.3  Stress–Strain Behavior ..... 412
6.2.3.1  Boundary Conditions .. 413
6.3  Nonlinear Stress–Strain Behavior . 414
6.3.1  Procedure 1: Nonlinear Analysis ..... 414
6.3.2  Procedure 2: Nonlinear Analysis ..... 416
6.3.2.1  Settlement ......... 416
6.3.3  Alternative Consolidation Equation . 416
6.3.3.1  Pervious Boundary ..... 417
6.3.3.2  Impervious Boundary at 2H  417
6.4  Numerical Methods .......... 418
6.4.1  Finite Difference Method . 418
6.4.1.1  FD Scheme No. 1: Simple Explicit ........... 418
6.4.1.2  FD Scheme No. 2: Implicit, Crank–Nicholson Scheme....... 419
6.4.1.3  FD Scheme No. 3: Another Implicit Scheme . 419
6.4.1.4  FD Scheme No. 4A: Special Explicit Scheme . 419
6.4.1.5  FD Scheme No. 4B: Special Explicit ........420
6.4.2  Finite Element Method .....420
6.4.2.1  Solution in Time .........423
6.4.2.2  Assemblage Equations 425
6.4.2.3  Boundary Conditions or Constraints ........425xiv Contents
6.4.2.4  Solution in Time .........426
6.4.2.5  Material Parameters ....426
6.5  Examples .....426
6.5.1  Example 6.1: Layered Soil—Numerical Solutions by Various Schemes .........426
6.5.2  Example 6.2: Two-Layered System ..428
6.5.3  Example 6.3: Test Embankment on Soft Clay ..........429
6.5.4  Example 6.4: Consolidation for Layer Thickness Increases with Time ......... 432
6.5.5  Example 6.5: Nonlinear Analysis ..... 432
6.5.6  Example 6.6: Strain-Based Analysis of Consolidation in Layered Clay ... 436
6.5.6.1  Numerical Example ....442
6.5.7  Example 6.7: Comparison of Uncoupled and Coupled Solutions 442
6.5.7.1  Uncoupled Solution .....443
6.5.7.2  Coupled Solution.........445
6.5.7.3  Numerical Example ....446
References ..............448

### Chapter 7  Coupled Flow through Porous Media: Dynamics and Consolidation

7.1  Introduction . 451
7.2  Governing Differential Equations . 451
7.2.1  Porosity ................ 451
7.2.2  Constitutive Laws 454
7.2.2.1  Volumetric Behavior ... 455
7.3  Dynamic Equations of Equilibrium ........456
7.4  Finite Element Formulation ........... 457
7.4.1  Time Integration: Dynamic Analysis ..460
7.4.1.1  Newmark Method .......460
7.4.2.1  Parameters ........466
7.5  Special Cases: Consolidation and Dynamics-Dry Problem ..468
7.5.1  Consolidation.......468
7.5.1.1  Dynamics-Dry Problem .... 470
7.5.2  Liquefaction ......... 471
7.6  Applications . 474
7.6.1  Example 7.1: Dynamic Pile Load Tests: Coupled Behavior .............. 474
7.6.1.1  Simulation of Phases ... 478
7.6.2  Example 7.2: Dynamic Analysis of Pile-Centrifuge Test including Liquefaction
7.6.2.1  Comparison between Predictions and Test Data ...........488
7.6.3  Example 7.3: Structure–Soil Problem Tested Using Centrifuge . 491
7.6.3.1  Material Properties .....493
7.6.3.2  Results ..497
7.6.4  Example 7.4: Cyclic and Liquefaction Response in Shake Table Test ...........498
7.6.4.1  Results ..500
7.6.5  Example 7.5: Dynamic and Consolidation Response of Mine Tailing Dam . 501
7.6.5.1  Material Properties .....509
7.6.5.2  Finite Element Analysis .... 510
7.6.5.3  Dynamic Analysis ...... 511
7.6.5.4  Earthquake Analysis ... 511
7.6.5.5  Design Quantities ....... 513
7.6.5.6  Liquefaction ...... 514
7.6.5.7  Results .. 514
7.6.5.8  Validation for Flow Quantity .................... 515
7.6.5.9  Q x  across a–b–c–d (Figure 7.40) .............. 516
7.6.6  Example 7.6: Soil–Structure Interaction: Effect of Interface Response ....... 517
7.6.6.1  Comparisons ..... 518
7.6.7  Example 7.7: Dynamic Analysis of Simple Block .... 521
7.6.8  Example 7.8: Dynamic Structure–Foundation Analysis ............... 523
7.6.8.1  Results ..528
7.6.9  Example 7.9: Consolidation of Layered Varved Clay Foundation .. 530
7.6.9.1  Material Properties ..... 530
7.6.9.2  Field Measurements .... 534
7.6.9.3  Finite Element Analysis .... 534
7.6.10  Example 7.10: Axisymmetric Consolidation ............ 536
7.6.10.1  Details of Boundary Conditions ............... 537
7.6.10.2  Results .. 539
7.6.11  Example 7.11: Two-Dimensional Nonlinear Consolidation.......540
7.6.11.1  Results ..540
7.6.12  Example 7.12: Subsidence Due to Consolidation .....542
7.6.12.1  Linear Analysis: Set 1 .543
7.6.12.2  Nonlinear Analysis .....545
7.6.13  Example 7.13: Three-Dimensional Consolidation ....545

### Appendix 1: Constitutive Models, Parameters, and Determination

A1.1  Introduction  557
A1.2  Elasticity Models ............. 557
A1.2.1  Limitations ......... 558
A1.2.2  Nonlinear Elasticity ........560
A1.2.3  Stress–Strain Behavior by Hyperbola ....................560
A1.2.4  Parameter Determination for Hyperbolic Model....560
A1.2.4.1  Poisson’s Ratio  561
A1.3  Normal Behavior .............563
A1.4  Hyperbolic Model for Interfaces/Joints ..563
A1.5  Ramberg–Osgood Model 566
A1.6  Variable Moduli Models .. 567
A1.7  Conventional Plasticity .... 567
A1.7.1  von Mises ...........568
A1.7.1.1  Compression Test
A1.7.2  Plane Strain ........ 570
A1.7.3  Mohr–Coulomb Model ... 570
A1.8  Continuous Yield Plasticity: Critical State Model ............... 571
A1.8.1  Cap Model.......... 574
A1.8.2  Limitations of Critical State and Cap Models ........ 576
A1.9  Hierarchical Single Surface Plasticity .... 576
A1.9.1  Nonassociated Behavior
A1.9.2  Parameters ......... 578
A1.9.2.1  Elasticity ......... 578
A1.9.2.2  Plasticity ......... 578
A1.9.2.3  Transition Parameter: n .. 579
A1.9.2.4  Yield Function 580
A1.9.2.5  Cohesive Intercept .... 581
A1.9.2.6  Nonassociative Parameter
A1.10  Creep Models .................. 581
A1.10.1 Yield Function ... 583
A1.11  Disturbed State Concept Models ..584
A1.11.1 DSC Equations...586
A1.11.2 Disturbance ........587
A1.11.3 DSC Model for Interface or Joint ...589
A1.12  Summary ....594
A1.12.1 Parameters for Soils, Rocks, and Interfaces/Joints .594
Appendix 2: Computer Software or Codes ..597
A2.1  Introduction 597
A2.2  List 1: Finite Element Software System: DSC Software ......597
A2.3  List 2: Commercial Codes ............598

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