Plasticity and geomechanics

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
1.1 Introduction......Page 15
1.2 Soil mechanics and continuum mechanics......Page 17
1.3 Sign conventions......Page 18
1.4 Deformation and strain......Page 19
1.5 Strain compatibility......Page 24
1.6 Forces and tractions......Page 25
1.7 The stress matrix......Page 26
1.8 Principal stresses......Page 28
1.9 Mohr circles......Page 30
1.10 The effective stress principle......Page 34
1.11 Equilibrium......Page 36
Exercises......Page 39
2.1 Introduction......Page 41
2.2 Hooke’s law......Page 42
2.3 Values for elastic constants......Page 45
2.4 Solution of problems in elasticity......Page 47
2.5 Plane elasticity......Page 48
2.6 Indications of inelastic behaviour......Page 52
2.7 The oedometer test......Page 58
2.8 The triaxial test......Page 60
Further reading......Page 63
Exercises......Page 64
3.1 Introduction......Page 66
3.2 Principal stress space......Page 67
3.3 Yield surfaces for metals......Page 72
3.4 The Coulomb yield criterion......Page 74
3.5 Modifications to Coulomb’s criterion......Page 79
3.6 The Cambridge models......Page 82
3.7 Two-dimensional yield loci......Page 86
3.8 Example – plane strain......Page 89
Further Reading......Page 93
Exercises......Page 94
4.1 Introduction......Page 97
4.2 Normality......Page 98
4.3 Associated flow rules......Page 104
4.4 Example – plane strain......Page 106
4.5 Non-associated flow......Page 108
4.6 A loading criterion......Page 109
4.7 A complete stress–strain relationship......Page 111
4.8 The pressuremeter problem......Page 113
Further reading......Page 120
Exercises......Page 121
5.1 Introduction......Page 123
5.2 The theorems......Page 124
5.3 Discontinuities of stress and deformation......Page 126
5.4 A vertical cut......Page 130
5.5 Shallow foundation – lower bound......Page 134
5.6 Shallow foundation – upper bound......Page 141
5.7 Shallow foundation – discussion......Page 147
5.8 Retaining walls......Page 151
5.9 Arching......Page 155
5.10 Non-associated flow and the upper bound theorem......Page 158
Further reading......Page 162
Exercises......Page 163
6.1 Introduction......Page 166
6.2 Two-dimensional stress states......Page 167
6.3 Slip lines......Page 169
6.4 Slip line geometries......Page 171
6.5 Some simple problems......Page 174
6.6 Frictional materials......Page 183
6.7 Effects of gravity......Page 189
6.8 The velocity field......Page 191
Further reading......Page 196
Exercises......Page 197
7.1 Introduction......Page 199
7.2 Work hardening for metals......Page 201
7.3 Cam Clay......Page 204
7.4 Beyond Cam Clay......Page 215
7.5 Last words......Page 225
Further reading......Page 226
Exercises......Page 227
Appendix A Non-Cartesian coordinate systems......Page 229
Further reading......Page 240
Appendix B Mohr circles......Page 242
Mohr circles in two dimensions......Page 248
Mohr circles in three dimensions......Page 250
Further reading......Page 253
Appendix C Principles of virtual work......Page 255
Further reading......Page 259
Appendix D Extremum principles......Page 260
Further reading......Page 267
Appendix E Drucker’s stability postulate......Page 269
Further reading......Page 271
Appendix F The associated flow rule......Page 273
Further reading......Page 275
Appendix G A uniqueness theorem for elastic–plastic deformation......Page 277
Further reading......Page 281
Appendix H Theorems of limit analysis......Page 283
Further reading......Page 289
Appendix I Limit analysis and limiting equilibrium......Page 291
Further reading......Page 292
Index......Page 293