Mechanics of Natural Solids (eBook)

Title Page 2
Preface 5
Contents 7
Sand as an archetypical natural solid 9
The magic of sand 9
Sand as a model of other geomaterials 10
Sand as a model for rock 10
Sand as model of the earth mantle 16
Lava volcanoes - sand volcanoes 16
The mechanical behaviour of sand 19
The grain skeleton and its physics 19
Strain localisation and pattern formation 21
Experimental observations—Proportional loading 22
Other experimental evidence 24
Mathematical models 26
Barodesy 27
Plasticity theory without yield surfaces 32
References 33
The Physics of Granular Mechanics 35
Introduction 35
Granular State Variables 37
The Elastic Strain 37
Mass, Entropy and Granular Entropy 39
History Dependence and Fabric Anisotropy 41
Granular Solid Hydrodynamics (GSH) 41
Entropy Production 41
Conservation Laws 43
Validation of GSH 44
Granular Statics, Tg = T 45
Granular Dynamics, $T_{g} /neq T$ 48
Competing Concepts and Misconceptions 51
References 53
Are we there yet? Following the energy trail in cohesionless granular solids 55
Introduction 55
Experiments 57
Nonaffine deformation in granular shear 57
Granular friction and stick-slip 62
Theory 67
Characterization of force chains and their evolution 67
Modeling of force chain evolution 75
Implications for constitutive theory 81
Thermomicromechanics of a Cosserat Continuum 81
Constitutive model 84
Predictive Capabilities of Model Based on Force Chain Failure 85
Conclusion 87
References 88
Micromechanical alternatives to phenomenological hardening plasticity 92
Introduction 92
Kinematic hardening plasticity and micromechanical roots 94
Phenomenological analog model 94
Alternative analog model 95
The micromechanical interpretation of the second analog 97
Generalisation of the micromechanical analog 99
A one-dimensional model for random elasto-plastic material 99
The micromechanical interpretation 101
Discussion about the physics of kinematic hardening 102
Isotropic hardening: phenomenology and micromechanical origins 103
A brief review on breakage mechanics 103
General breakage models 106
Isotropic hardening via breakage model based on linear contact law 108
Isotropic hardening via breakage model based on non-linear contact law 109
Conclusions 110
References 110
Mechanisms of localized deformation in geomaterials: an experimental insight using full-field measurement techniques 112
Introduction 112
Digital Image Correlation 115
X-ray Computed Tomography 116
Example 1: localized deformation in a clay rock 119
Example 2: localized deformation in sand 125
Conclusions 128
References 129
Two-dimensional Distinct Element Method (DEM) modeling of tectonic fault growth in mechanically layered sequences 133
Introduction 133
Geometry of faults in layered sequences 134
Origin of fault dip refraction 136
Distinct Element Method 139
Particle Flow Code (PFC) 139
Faulting model materials and boundary conditions 141
Results 142
Fault localization 143
Fault growth 145
Impact of strength and confining pressure on fault zone structure 146
Impact of layering on fault dip 148
Summary and discussion 150
References 151
When geophysics met geomechanics: Imaging of geomechanical properties and processes using elastic waves 153
Introduction 153
Elastic wave propagation in deforming geomaterials 155
Wave equation 155
Sensitivity of elastic wave propagation to geomechanical properties and processes 156
Laboratory Scale 160
Stress sensitivity 161
Anisotropy, crack density tensors and damage 161
Full-field measurement of elastic properties: ultrasonic tomography 165
Reservoir Scale 169
Seismic anisotropy detection and mapping 170
Time-lapse seismic and monitoring of fluid-extraction induced reservoir deformation 171
Conclusions 176
References 177
Fracture of Ice and other Coulombic Materials 182
Introduction 182
Structure of Ice 183
Crystal Structure 183
Microstructure 184
Texture-Induced 2D Behavior 185
Brittle Compressive Failure 185
Failure Envelope and Failure Modes 186
Confinement-Strengthening and Frictional Sliding 188
Micromechanical Processes Underlying Coulombic Faulting 189
The Comb Crack Model of Coulombic Faulting 193
Application to Other Coulombic Materials 193
Ductile-to Brittle Transition 194
Competition Between Creep and Fracture 196
Micro-Mechanical Model of the Ductile-Brittle Transition 196
Application to Other Coulombic Materials 197
Coulombic vs. Plastic Faulting 198
Scale-Independent Fracture Physics: Fracture of the Arctic Sea Ice Cover 199
Summary 202
References 203
Experimental studies of the viscoplasticty of ice and snow 208
Introduction 208
Viscoplasticity of ice 209
Ice is a crystalline material 209
Dislocations in ice 210
Single crystal vs. Polycrystal 211
Experimental study of the heterogeneous deformation of ice 213
Observations under polarized light 213
Observations under X-ray radiation 217
Experimental study of the micromechanics of dry snow 221
Conclusion 224
References 225
Discontinuities in granular materials: Particle-level mechanisms 227
Introduction 227
Mineral dissolution and shear strain localization 228
Evolution of internal stresses 228
Shear localization 229
Deformation Field 230
Desiccation cracks in saturated fine-grained soils 233
Fundamental Mechanism – Fine Grained Soils 233
Initiation – Surface Features 234
Implications 235
Hydraulic fracture in granular materials 236
Invading and Host Fluids – Particle-Level Forces 236
Fracture Initiation and Propagation 236
Experimental Evidence 237
Discussion on Pore Size Distribution 238
Conclusions 239
References 240
Grain Crushing, Pore Collapse and Strain Localization in Porous Sandstone 242
Introduction 242
Phenomenology of Inelastic Compaction and Failure 243
Strain hardening and shear-enhanced compaction 243
Onset of compactive yield and evolution of the yield cap 245
Micromechanics of Grain Crushing and Pore Collapse 247
Onset of Compaction Localization and Propagation of Compaction Band 249
Bifurcation analysis and discrete element modeling of compaction bands 250
Stress conditions for the propagation of compaction bands 253
Discussion 254
References 255
Long term behaviour and size effects of coarse granular media 258
Introduction 258
Particle Breakage 260
Suction controlled experiments on rockfill 265
Modelling the behaviour of a rockfill embankment subjected to rainfall 268
Scale effects 277
Conclusions 283
References 283
Nature – A Very Clever Experimentalist 285
Introduction 285
What Do Experimentalists Provide? 286
Why Makes Nature So Clever? 291
Material Properties 291
Deformation Systems 294
Summary Remarks 296
References 297
Author Index 299