Finite Element Analysis in Geotechnical Engineering Application

Contents

Preface xi

Authorship xvi

Acknowledgements xvi

1. Obtaining geotechnical parameters 1

1.1 Synopsis 1

1.2 Introduction 1

1.3 Laboratory tests 2

1.3.1 Introduction 2

1.3.2 Oedometer test 3

1.3.3 Triaxial test 6

1.3.4 True triaxial test 11

1.3.5 Direct shear test 12

1.3.6 Simple shear test 14

1.3.7 Ring shear test 15

1.3.8 Hollow cylinder test 16

1.3.9 Directional shear cell 20

1.3.10 Geophysical techniques 20

1.3.11 Permeameters 22

1.4 In-situ tests 23

1.4.1 Introduction 23

1.4.2 Standard penetration test (SPT) 23

1.4.3 Cone penetration test (CPT) 27

1.4.4 Pressuremeter testing 30

1.4.5 The plate loading test 32

1.4.6 Pumping tests 35

1.5 Summary

35

2. Tunnels 38

2.1 Synopsis 38

2.2 Introduction 38

2.3 Tunnel construction 39

2.3.1 Introduction 39

2.3.2 Open faced shield tunnelling 40

2.3.3 Tunnel Boring Machines (TBM), including slurry

shields and Earth Pressure Balance (EPB) tunnelling 40

2.3.4 The sprayed concrete lining (SCL) method 41

2.3.5 Ground response to tunnel construction 41

2.4 Simulation of the construction process 43

2.4.1 Introduction 43

2.4.2 Setting up the initial conditions 44

2.4.3 Important boundary conditions 45

2.4.4 Modelling tunnel excavation 45

2.4.5 Modelling the tunnel lining 48

2.5 Modelling time dependent behaviour 52

2.5.1 Introduction 52

2.5.2 Setting up the initial conditions 52

2.5.3 Hydraulic boundary conditions 54

2.5.4 Permeability models 55

2.5.5 A parametric study of the effect of permeable and

impermeable tunnel linings 57

2.6 Choice of soil model 59

2.6.1 Introduction 59

2.6.2 Results from a parametric study 59

2.6.3 Devices for improving the surface settlement

prediction 60

2.7 Interaction analysis 63

2.7.1 The influence of building stiffness on tunnel-induced

ground movements 63

2.7.2 The Treasury building – a case study 66

2.7.3 Twin runnel interaction 70

2.8 Summary 72

3. Earth retaining structures 74

3.1 Synopsis 74

3.2 Introduction 74

3.3 Types of retaining structure 75

3.3.1 Introduction 75

3.3.2 Gravity walls 75

3.3.3 Reinforced/anchored earth wall 76

3.3.4 Embedded walls 76

3.4 General considerations 77

3.4.1 Introduction 77

3.4.2 Symmetry 77

3.4.3 Geometry of the finite element model 79

3.4.4 Support systems 82

3.4.5 Choice of constitutive models 84

3.4.5.1 Structural components 84

3.4.5.2 Soil 85

3.4.6 Initial ground conditions 88

3.4.6.1 General 88

3.4.6.2 ‘Greenfield’ conditions 88

3.4.6.3 Modified initial soil stresses 89

3.4.7 Construction method and programme 91

3.4.7.1 General 91

3.4.7.2 Construction method 91

3.4.7.3 Time related movements 92

3.4.7.4 Ground water control 93

3.5 Gravity walls 93

3.5.1 Introduction 93

3.5.2 Earth pressure due to compaction 94

3.5.3 Finite element analysis 95

3.6 Reinforced earth walls 96

3.6.1 Introduction 96

3.6.2 Finite element analysis 99

3.7 Embedded walls 103

3.7.1 Introduction 103

3.7.2 Installation effects 104

3.7.2.1 General 104

3.7.2.2 Field measurements 104

3.7.2.3 Analysis 105

3.7.2.4 Comments 106

3.7.3 Modelling of walls 107

3.7.3.1 Element type 107

3.7.3.2 Wall stiffness 109

3.7.3.3 Interface behaviour 111

3.7.3.4 Wall permeability 111

3.7.4 Support systems 112

3.7.4.1 Introduction 112

3.7.4.2 Support stiffness 112

3.7.4.3 Connection details 113

3.7.4.4 Active support systems 114

3.7.4.5 Berms 115

3.7.4.6 Ground anchors 115

3.7.4.7 Relieving slabs 116

3.7.5 Long term behaviour and post construction effects 118

3.7.6 Adjacent structures 119

3.8 Summary 122

Appendix III.1 123

4. Cut slopes 125

4.1 Synopsis 125

4.2 Introduction 125

4.3 ‘Non-softening’ analyses 126

4.3.1 Introduction 126

4.3.2 Cut slopes in stiff ‘non-softening’ clay 127

4.3.2.1 Introduction 127

4.3.2.2 Soil parameters 127

4.3.2.3 Finite element analyses 127

4.3.2.4 Results of analyses 128

4.3.3 Cut slopes in soft clay 131

4.3.3.1 Introduction 131

4.3.3.2 Soil parameters 132

4.3.3.3 Finite element analyses 136

4.3.3.4 Results of analyses 138

4.4 Progressive failure 141

4.5 ‘Softening’ analyses 145

4.5.1 Introduction 145

4.5.2 Choice of constitutive model 146

4.5.3 Implications for convergence 147

4.5.4 Cut slopes in London Clay 147

4.5.4.1 Introduction 147

4.5.4.2 Soil parameters 148

4.5.4.3 Finite element analyses 150

4.5.4.4 Results of a typical analysis 150

4.5.4.5 Effect of coefficient of earth

pressure at rest 153

4.5.4.6 Effect of surface boundary suction 155

4.5.4.7 Effect of slope geometry 155

4.5.4.8 Effect of surface cracking 156

4.5.4.9 Effect of subsequent changes to slope

geometry 158

4.5.4.10 Further discussion 160

4.6 Construction of cut slope under water 162

4.7 Summary 163

5. Embankments 166

5.1 Synopsis 166

5.2 Introduction 166

5.3 Finite element analysis of rockfill dams 167

5.3.1 Introduction 167

5.3.2 Typical stress paths 167

5.3.3 Choice of constitutive models 168

5.3.3.1 Linear elastic analysis 169

5.3.3.2 ‘Power law’ models 169

5.3.3.3 Hyperbolic model 170

5.3.3.4 K-G model 171

5.3.3.5 Elasto-plastic models 171

5.3.4 Layered analysis, stiffness of the simulated layer

and compaction stresses 173

5.3.5 Example: Analysis of Roadford dam 175

5.3.5.1 Introduction 175

5.3.5.2 Material parameters 175

5.3.5.3 Finite element analysis 177

5.3.5.4 Comparison with observations 179

5.3.6 Example: Analysis of old puddle clay core dams 180

5.3.6.1 Introduction 180

5.3.6.2 Dale Dyke dam 181

5.3.6.3 Ramsden dam 183

5.4 Finite element analysis of earth embankments 185

5.4.1 Introduction 185

5.4.2 Modelling of earthfill 186

5.4.3 Example: Road embankments on London Clay 186

5.4.3.1 Introduction 186

5.4.3.2 Material properties 187

5.4.3.3 Finite element analyis 188

5.4.4 Example: Failure of Carsington embankment 189

5.4.4.1 Introduction 189

5.4.4.2 Material parameters and soil model used 190

5.4.4.3 Finite element analysis 191

5.4.4.4 Original Carsington section 191

5.4.4.5 Effect of the core geometry on

progressive failure 192

5.4.4.6 Effect of berm in improving the stability 193

5.5 Finite element analysis of embankments on soft clay 194

5.5.1 Introduction 194

5.5.2 Typical soil conditions 195

5.5.3 Choice of constitutive model 196

5.5.4 Modelling soil reinforcement 198

5.5.5 Example: Effect of a surface crust 198

5.5.5.1 Introduction 198

5.5.5.2 Soil conditions 198

5.5.5.3 Finite element analysis 199

5.5.5.4 Results 200

5.5.6 Example: Effect of reinforcement 200

5.5.6.1 Introduction 200

5.5.6.2 Soil conditions 201

5.5.6.3 Results 201

5.5.7 Example: Staged construction 202

5.5.7.1 Introduction 202

5.5.7.2 Soil conditions 203

5.5.7.3 Finite element analysis 204

5.5.7.4 Results 205

5.5.8 Example: Effect of anisotropic soil behaviour 206

5.5.8.1 Introduction 206

5.5.8.2 Geometry 206

5.5.8.3 Soil conditions 207

5.5.8.4 Finite element analysis 207

5.5.8.5 Results 208

5.6 Summary 211

6. Shallow foundations 214

6.1 Synopsis 214

6.2 Introduction 214

6.3 Foundation types 215

6.3.1 Surface foundations 215

6.3.2 Shallow foundations 215

6.4 Choice of soil model 215

6.5 Finite element analysis of surface foundations 216

6.5.1 Introduction 216

6.5.2 Flexible foundations 218

6.5.3 Rigid foundations 218

6.5.4 Examples of vertical loading 219

6.5.4.1 Introduction 219

6.5.4.2 Strip footings on undrained clay 219

6.5.4.3 Effect of footing shape on the bearing

capacity of undrained clay 223

6.5.4.4 Strip footings on weightless drained soil 225

6.5.4.5 Strip footings on a drained soil 227

6.5.4.6 Circular footings on a weightless drained

soil 230

6.5.4.7 Circular footings on a drained soil 232

6.5.5 Undrained bearing capacity of non-homogeneous

clay 233

6.5.5.1 Introduction 233

6.5.5.2 Constitutive model 234

6.5.5.3 Geometry and boundary conditions 236

6.5.5.4 Failure mechanisms 236

6.5.6 Undrained bearing capacity of pre-loaded strip

foundations on clay 238

6.5.6.1 Introduction 238

6.5.6.2 Constitutive model 239

6.5.6.3 Geometry and boundary conditions 240

6.5.6.4 Results of the analyses 240

6.5.6.5 Concluding remarks 243

6.5.7 Effect of anisotropic strength on bearing capacity 243

6.5.7.1 Introduction 243

6.5.7.2 Soil behaviour 244

6.5.7.3 Behaviour of strip footings 246

6.5.7.4 Behaviour of circular footings 247

6.6 Finite element analysis of shallow foundations 248

6.6.1 Introduction 248

6.6.2 Effect of foundation depth on undrained bearing

capacity 248

6.6.3 Example: The leaning Tower of Pisa 252

6.6.3.1 Introduction 252

6.6.3.2 Details of the Tower and ground profile 253

6.6.3.3 History of construction 254

6.6.3.4 History of tilting 255

6.6.3.5 The motion of the Tower foundations 256

6.6.3.6 Stability of tall towers 256

6.6.3.7 Soil properties 259

6.6.3.8 Finite element analysis 263

6.6.3.9 Simulation of the history of inclination 265

6.6.3.10 Temporary counterweight 267

6.6.3.11 Observed behaviour during application

of the counterweight 269

6.6.3.12 Permanent stabilisation of the Tower 271

6.6.3.13 Soil extraction 271

6.6.3.14 The response of the Tower to

soil extraction 275

6.6.3.15 Comments 276

6.7 Summary 278

7. Deep foundations 280

7.1 Synopsis 280

7.2 Introduction 280

7.3 Single piles 282

7.3.1 Introduction 282

7.3.2 Vertical loading 282

7.3.3 Lateral loading 287

7.4 Pile group behaviour 289

7.4.1 Introduction 289

7.4.2 Analysis of a pile group 291

7.4.3 Superposition 291

7.4.3.1 Simple superposition 292

7.4.3.2 Pile displacements with depth 293

7.4.4 Load distribution within a pile group 294

7.4.4.1 Obtaining an initial trial division of the

applied loads 296

7.4.4.2 Evaluating pile head displacements 297

7.4.4.3 Checking the rigid pile cap criterion 297

7.4.5 Pile group design 298

7.4.5.1 Matrix formulation of the pile group

response 298

7.4.5.2 Superposition of loads 299

7.4.5.3 Evaluating the solution displacements

and rotations 302

7.4.6 Magnus 304

7.4.6.1 Introduction 304

7.4.6.2 Soil properties and initial conditions 304

7.4.6.3 Finite element analyses 308

7.4.6.4 Design of Magnus foundations 309

7.4.6.5 Environmental loading 314

7.5 Bucket foundations 317

7.5.1 Introduction 317

7.5.2 Geometry 318

7.5.3 Finite element analysis 318

7.5.4 Modelling of the interface between top cap and soil 320

7.5.5 Isotropic study 321

7.5.5.1 Soil conditions 321

7.5.5.2 Parametric studies 322

7.5.5.3 Results 322

7.5.6 Anisotropic study 326

7.5.6.1 Introduction 326

7.5.6.2 Results 326

7.5.7 Suction anchors 327

7.5.7.1 Introduction 327

7.5.7.2 Geometry 327

7.5.7.3 Results 329

7.6 Summary 329

8. Benchmarking 332

8.1 Synopsis 332

8.2 Definitions 332

8.3 Introduction 333

8.4 Causes of errors in computer calculations 334

8.5 Consequences of errors 335

8.6 Developers and users 336

8.6.1 Developers 336

8.6.2 Users 337

8.7 Techniques used to check computer calculations 339

8.8 Benchmarking 339

8.8.1 General 339

8.8.2 Standard benchmarks 340

8.8.3 Non-standard benchmarks 341

8.9 The INTERCLAY II project 341

8.10 Examples of benchmark problems – Part I 342

8.10.1 General 342

8.10.2 Example 1: Analyses of an ideal triaxial test 343

8.10.3 Example 2: Analysis of a thick cylinder 344

8.10.4 Example 3: Analyses of an advancing tunnel

heading 346

8.10.5 Example 4: Analysis of a shallow waste disposal 348

8.10.6 Example 5: Simplified analysis of a shallow waste 351

8.11 Examples of benchmark problems – Part II

(German Society for Geotechnics benchmarking exercise) 353

8.11.1 Background 353

8.11.2 Example 6: Construction of a tunnel 353

8.11.3 Example 7: Deep excavation 355

8.11.4 General comments 356

8.12 Summary 357

Appendix VIII. 1 Specification for Example 1: Analyses of an

idealised triaxial test 358

VIII. 1.1 Geometry 358

VIII. 1.2 Material properties and initial stress conditions 358

VIII.1.3 Loading conditions 358

Appendix VIII.2 Specification for Example 2: Analysis of a thick

cylinder 358

VIII.2.1 Geometry 358

VIII.2.2 Material properties 358

VIII.2.3 Loading conditions 359

Appendix VIII.3 Specification for Example 3: Analysis of an

advancing tunnel heading 359

VIII.3.1 Geometry 359

VIII.3.2 Material properties 359

VIII.3.3 Loading conditions 359

Appendix VIII.4 Specification for Example 4: Analysis of a shallow

waste disposal 360

VIII.4.1 Geometry 360

VIII.4.2 Material properties 360

VIII.4.3 Loading conditions 361

Appendix VIII.5 Specification for Example 5: Simplified analysis

of a shallow waste disposal 361

VIII.5.1 Geometry 361

VIII.5.2 Material properties 361

VIII.5.3 Loading conditions 361

VIII.5.4 Additional boundary conditions 362

Appendix VIII.6 Specification for Example 6: Construction of a tunnel 362

VIII.6.1 Geometry 362

VIII.6.2 Material properties 362

Appendix V11I.7 Specification for Example 7: Deep excavation 362

VIII.7.1 Geometry 362

VIII.7.2 Material properties 362

VIII.7.3 Construction stages 363

9. Restrictions and pitfalls 364

9.1 Synopsis 364

9.2 Introduction 364

9.3 Discretisation errors 365

9.4 Numerical stability of zero thickness interface elements 368

9.4.1 Introduction 368

9.4.2 Basic theory 368

9.4.3 Ill-conditioning 370

9.4.4 Steep stress gradients 373

9.5 Modelling of structural members in plane strain analysis 376

9.5.1 Walls 376

9.5.2 Piles 377

9.5.3 Ground anchors 378

9.5.4 Structural members in coupled analyses 380

9.5.5 Structural connections 380

9.5.6 Segmental tunnel linings 381

9.6 Use of the Mohr-Coulomb model for undrained analysis 382

9.7 Influence of the shape of the yield and plastic potential

surfaces in the deviatoric plane 384

9.8 Using critical state models in undrained analysis 386

9.9 Construction problems 387

9.10 Removal of prescribed degrees of freedom 388

9.11 Modelling underdrainage 389

9.12 Summary 394

References 396

List of symbols 410

Index 415