Modelling of cohesive-frictional materials : proceedings of 2nd International Symposium on Continuous and Discontinuous Modelling of Cohesive-Frictional Materials, CDM 2004, Stuttgart, 27-28 September 2004

Cover......Page 1
Modelling of Cohesive-Frictional Materials......Page 4
Table of Contents......Page 6
Preface......Page 10
Granular materials & mechanics......Page 12
1  INTRODUCTION......Page 14
2.1  Rolling measure based on relative rotation......Page 15
2.3  Rolling measure based on the shift of the contact point on the particle surfaces......Page 16
3.1  Introductory remarks......Page 17
3.2  Definition of the rolling curl......Page 18
4.1  Comparison of the different definitions of contact rolling......Page 19
4.2  Spatial patterns of contact rolling......Page 20
REFERENCES......Page 22
2  HOW TO DEFINE GRANULAR MATERIALS......Page 24
3.1  Scalar parameters of internal state......Page 25
3.2  Internal variables describing the local geometrical anisotropy......Page 28
3.3  Internal variables describing the local distribution of contact forces......Page 33
4  INTERNAL VARIABLES IN GRANULAR MATERIALS USED AT THE GLOBAL LEVEL......Page 34
REFERENCES......Page 35
1  MICROMECHANICAL BACKGROUND: KINEMATICS AND STRESS......Page 38
1.1  Geometry and kinematics......Page 39
2  SUMMARY OF MAXIMUM-ENTROPY ESTIMATES......Page 41
3  CANONICAL FORMS AND VIRTUAL THERMODYNAMICS......Page 42
4  CONCLUSIONS......Page 44
REFERENCES......Page 45
1  INTRODUCTION......Page 46
2  AIMS......Page 47
3  GRADIENT AND MICROMORPHIC CONTINUA......Page 48
REFERENCES......Page 52
Discrete modeling......Page 54
1  INTRODUCTION......Page 56
2.1  Generation of polygons......Page 58
2.2  Contact forces......Page 59
2.3  Floppy boundary......Page 61
2.5  Molecular dynamics simulation......Page 63
3  BIAXIAL TEST......Page 65
4.1  Calculation of the incremental response......Page 69
4.2  Elastic response......Page 72
4.3  Plastic response......Page 74
ACKNOWLEDGEMENT......Page 76
REFERENCES......Page 77
1  INTRODUCTION......Page 80
2.1  Outline of the Model......Page 82
2.2  Discussion of Cohesion Modeling......Page 83
3.1  Basic idea......Page 84
3.2  Mohr-Coulomb plasticity model......Page 85
3.3  Numerical realization......Page 89
3.4  Numerical results......Page 90
3.4.1  Tension simulations......Page 91
3.4.2  Compression simulations......Page 93
3.5  Discussion of cohesion modeling......Page 94
4.1  Generation of a microstructure......Page 95
4.2.1  Compression simulations......Page 97
4.2.2  Tension simulations......Page 99
5  CONCLUSION......Page 100
REFERENCES......Page 101
1  INTRODUCTION......Page 104
2.1  Incremental contact force......Page 105
3  EQUILIBRIUM......Page 106
4  AVERAGES......Page 107
REFERENCES......Page 109
1  INTRODUCTION......Page 112
2.1  Particle distribution......Page 113
2.2  Beam lattice......Page 114
2.3  Fracture criterion......Page 115
3  NUMERICAL RESULTS......Page 116
4  DISCUSSION: PERCOLATION AND SCALING......Page 117
5  CONCLUSIONS......Page 118
REFERENCES......Page 119
1  INTRODUCTION......Page 120
2  MECHANICAL PROBLEM......Page 122
3  LATTICE MODEL FOR THE HYDRO-MECHANICAL PROBLEM......Page 124
4  EXPERIMENTAL DATA......Page 127
5  CLOSURE......Page 129
REFERENCES......Page 130
1  INTRODUCTION......Page 132
2  MAIN FEATURES OF THE DEM MODEL......Page 133
3  PROGRAM OF STRESS PROBING......Page 135
4  RESULTS AT THE MACROSCOPIC SCALE......Page 136
5  RESULTS AT THE MICRO SCALE......Page 139
REFERENCES......Page 144
Discontinuum vs. continuum......Page 146
1  INTRODUCTION......Page 148
2.2  Reference WTD test......Page 149
3  CONSTITUTIVE MODEL......Page 150
4  DISTINCT ELEMENT MODEL......Page 152
4.2  Oedometric tests on silica sand and cemented silica sand......Page 153
6  PROGRESSIVE SETTLEMENTS DUE TO MINE PILLAR DEGRADATION......Page 155
6.2  DEM analysis......Page 156
6.3  FEM and DEM results......Page 157
7  CONCLUSIONS......Page 158
REFERENCES......Page 159
1  INTRODUCTION......Page 160
2  MOLECULAR DYNAMIC SIMULATION......Page 161
3  HOMOGENISATION STRATEGY......Page 162
4  NUMERICAL EXAMPLE......Page 167
5  CONCLUSIONS......Page 169
REFERENCES......Page 170
1  INTRODUCTION......Page 172
2.1  Continuum-continuum scale transitions......Page 173
2.2  Continuum-discontinuum scale transitions......Page 175
3  CONTINUUM-DISCONTINUUM TRANSITION IN DAMAGING MASONRY WALLS......Page 176
3.2  Solution of the finite volume problem at the integration point level......Page 177
3.4  Summary of the solution strategy......Page 178
4  CONCLUSIONS......Page 180
REFERENCES......Page 181
1  INDUSTRIAL CONTEXT......Page 184
2  BASICS OF MULTISCALE MODELING......Page 185
2.2  Homogenization methods......Page 186
2.3  Experimental identification and verification......Page 187
3.1  Material representation......Page 188
3.2  Localization and homogenization......Page 189
3.3  Application......Page 190
4.2  Localization and homogenization......Page 192
4.3  Application......Page 194
5.1  Material representation......Page 196
5.3  Application......Page 198
6  LOW-TEMPERATURE CREEP OF BITUMINOUS MIXTURES......Page 199
6.1  Material representation......Page 200
6.2  Localization and homogenization......Page 201
6.4  Validation of upscaling scheme......Page 202
REFERENCES......Page 204
2  MICRO-MACRO TRANSITION FOR ONE CONTACT......Page 206
2.2  Small changes of the potential energy density......Page 207
2.4  The stiffness tensor from a static contact......Page 208
3.2  The Stress tensor......Page 209
4.2  Discrete particle model......Page 210
4.4.1  Density and volumetric strain......Page 211
4.4.2  Fabric tensor......Page 212
4.4.3  Stress tensor......Page 213
4.4.4  Stiffness tensor......Page 214
5  SUMMARY AND CONCLUSION......Page 215
REFERENCES......Page 216
Continous modelling......Page 218
1  INTRODUCTION......Page 220
3  CLASSICAL COUPLED PROBLEMS......Page 221
3.1.2 Mass balance equations......Page 222
3.3  Governing equations......Page 223
3.4  Linearized equations......Page 224
4.1  Monophasic medium......Page 225
5  COUPLED FINITE ELEMENT FORMULATION......Page 226
6  NUMERICAL APPLICATION OF LOCAL SECOND GRADIENT COUPLED MODEL......Page 227
7  CONCLUSIONS......Page 230
REFERENCES......Page 231
1   INTRODUCTION......Page 232
2.1  General formulation......Page 233
2.2 Plastic behaviour......Page 234
2.3  Hardening/softening rule for the pore collapse model......Page 235
3.1  Chemical effects on clay behaviour during wetting by a contaminant......Page 236
3.2  Chemical effects on biaxial response......Page 237
3.3  Chemical effects around an excavation in clay......Page 239
ACKNOWLEDGEMENTS......Page 241
REFERENCES......Page 242
1  INTRODUCTION......Page 244
2  FAILURE DOMAIN IN AXISYMMETRIC CONDITIONS......Page 246
3  SENSIBILITY ANALYSIS IN THE CASE OF AN ELASTO-PLASTIC MODEL......Page 250
3.1  A simple elasto-plastic hardening model: Plasol......Page 252
3.2  Sensibility analysis......Page 254
4  FLOW RULE IN THE CASE OF INCREMENTALLY NON-LINEAR RELATIONS......Page 255
REFERENCES......Page 257
1  INTRODUCTION......Page 260
2  TRANSIENT THERMAL ANALYSIS......Page 261
4  MECHANICAL STRAIN......Page 262
4.1.3  Tensile strength of concrete......Page 263
4.1.4 Concrete fracture energy......Page 264
5.2  Stress induced thermal strain—creep......Page 265
6.2  Pull-out of the headed stud anchor from a concrete block......Page 266
7  CONCLUSIONS......Page 270
REFERENCES......Page 271
1  INTRODUCTION......Page 274
2  STONE CHARACTERIZATION TESTS......Page 275
3.1  Test description and program......Page 276
3.2  Analysis of indentation results......Page 279
4.1  Consolidated mortar......Page 283
4.2  Artificially weathered marbles......Page 284
REFERENCES......Page 285
1  INTRODUCTION......Page 288
2.1  The velocity-pressure formulation and some further simplifications for the propagation phase......Page 289
2.1.1  Depth integrated models......Page 291
2.2  Some useful forms in computational soil mechanics: the u−pw formulation......Page 292
3  AN IMPROVEMENT OF THE GENERALIZED PLASTICITY MODEL FOR BONDED GEOMATERIALS......Page 294
4.1  Failure of an embankment on a collapsible soil under earthquake loading......Page 296
4.2  Simple fluid flow example......Page 299
4.3  Tip No. 7 flowslide at Aberfan (1966)......Page 301
REFERENCES......Page 303
1  INTRODUCTION......Page 306
2.1  Notation......Page 307
2.4  Energy balance—first principle......Page 308
2.5.3  Entropy variation—volume dissipation......Page 309
2.6.2  Second set: Nonlocality residual and Non-standard boundary conditions......Page 310
2.6.3  Third set: Evolution equations......Page 312
3.1  Full coupling......Page 313
4  CONCLUSION......Page 315
REFERENCES......Page 316
1  INTRODUCTION......Page 318
2  KINEMATICAL MODEL......Page 319
3.1  Fluid discharge......Page 320
4  FINITE ELEMENT SOLUTION......Page 321
5.1  One-dimensional piping......Page 323
5.2  Two-dimensional erosion around a wellbore......Page 326
REFERENCES......Page 329
Regularization......Page 332
1  INTRODUCTION......Page 334
2  BASIC EQUATIONS OF PLASTICITY AND DAMAGE MECHANICS......Page 335
3.1  Nonlocal hardening law......Page 336
3.2  Rate problem......Page 337
3.3  Localization analysis......Page 338
3.4  Examples......Page 341
4.1  Combined plastic-damage model......Page 343
4.3  Localization analysis......Page 344
4.4  Examples......Page 346
ACKNOWLEDGEMENT......Page 347
REFERENCES......Page 348
1  INTRODUCTION......Page 350
2  ADVANCED DISCRETIZATION CONCEPTS FOR CONCRETE FRACTURE......Page 351
2.1  The Strong Discontinuity Approach (SDA)......Page 352
2.2.1  Kinematics......Page 353
2.2.2  Enhanced displacement approximation......Page 354
3  CRACK GROWTH LAWS......Page 355
3.2  Linear elastic fracture mechanics......Page 356
4  COMPARATIVE NUMERICAL INVESTIGATION OF SDA AND X-FEM......Page 357
6  CONCLUSIONS......Page 360
REFERENCES......Page 362
2.1  Constitutive relationships......Page 364
2.2  Discontinuous interpolation......Page 366
2.3  Introduction of a discontinuity in the bulk material......Page 367
3.1  Concrete beam in four-point bending......Page 368
3.2  Composite compact-tension specimen......Page 370
3.4  Strip footing near a slope......Page 371
3.5  Steel fibre-reinforced concrete......Page 374
3.6  An illustration of a difficulty......Page 376
REFERENCES......Page 378
1  INTRODUCTION......Page 380
2.1  Plastic shear strain in primary loading......Page 381
2.2  Yield function for friction hardening......Page 382
2.4  Completion of the model......Page 383
3  ON THE BENCHMARK PROBLEMS......Page 384
3.1  The smooth passive wall......Page 386
3.2  The smooth active wall......Page 387
3.3  The rough passive wall......Page 388
4  CONCLUSIONS......Page 389
REFERENCES......Page 390
1  INTRODUCTION......Page 392
2  BASIC EQUATIONS......Page 393
3  CONSTITUTIVE RELATION FOR THE SLIP LINE......Page 394
5  ON THE DIRECTION OF A SLIP LINE......Page 396
6  ON THE USE OF THE DISPLACEMENT RATE GRADIENT......Page 398
7  AVERAGE ELEMENT GRADIENT VERSUS NON-LOCAL GRADIENT......Page 400
8  SLIP LINE TRACING ALGORITHM......Page 401
9  THE PASSIVE WALL PROBLEM......Page 402
REFERENCES......Page 404
APPENDIX ON EXTENDED FINITE ELEMENT METHOD (X-FEM)......Page 406
Localization & fracture......Page 408
2.1  Experimental evidence......Page 410
2.2  Theoretical background......Page 414
3.1  FEM code and constitutive law used......Page 415
4.1  Perfect-imperfect geometry......Page 416
4.2.3  Very fast loading......Page 417
4.2.4  Impervious boundaries: globally undrained case......Page 418
4.3  Delayed drainage......Page 419
REFERENCES......Page 420
2  PSAMMOID SAMPLES......Page 422
3  LARGE PSAMMOID BODIES......Page 425
4  PELOID SAMPLES......Page 427
5  LARGE-SIZE SHEAR LOCALIZATION WITH PELOIDS......Page 429
REFERENCES......Page 432
1  INTRODUCTION......Page 434
2  FRACTURE ENERGY PARAMETERS FOR CRACK PROPAGATION......Page 435
3.1  Plasticity models......Page 438
3.2  Verification of simulations......Page 439
4  EVOLUTION OF STRESS FIELDS DURING CRACK PROPAGATION......Page 440
5  CORRELATION BETWEEN STRESS FIELD AND FRACTURE ENERGY......Page 442
6  CONCLUSIONS......Page 444
REFERENCES......Page 445
1  INTRODUCTION......Page 446
2  FORMULATION OF THE MODEL......Page 447
3.1  Analytical considerations......Page 449
3.2  Simulations of slope failure by shear crack propagation......Page 450
4.1  Critical stress for slope failure......Page 452
4.3  Critical force for crack propagation......Page 453
4.4  Crack front elasticity and crack pinning: theory......Page 454
REFERENCES......Page 456
Author index......Page 458