Preface ...................................................... xiii
Acknowledgements ............................................... xv
About the authors ............................................ xvii
List of figures ............................................... xix
List of tables ............................................. xxxvii
Explanatory notes ........................................... xxxix
1 Introduction ................................................. I
1.1 The purpose of this book ................................ 1
1.2 Why do things break? .................................... 1
1.3 Rock failure in geological and recent history ........... 2
1.4 Rock failure in present day engineering ................. 5
1.5 The nature of rock—a natural material ................... 7
1.5.1 Discontinuities .................................. 7
1.5.2 Inhomogeneity .................................... 7
1.5.3 Anisotropy ....................................... 8
1.5.4 Inelasticity .................................... 10
1.6 Numerical modelling of rock failure .................... 10
1.7 The content of this book ............................... 11
2 Rock failure in uniaxial tension ............................ 13
2.1 Introduction ........................................... 13
2.2 Specimen simulation .................................... 15
2.3 Numerical simulation results for the uniaxial tension
case ................................................... 16
2.4 Further studies of simulated rock failure in uniaxial
tension ................................................ 22
3 Rock failure in indirect tension ............................ 29
3.1 Generating a tensile stress through compressive
loading ................................................ 29
3.2 Establishing the numerical simulation model for
indirect tensile strength tests ........................ 30
3.3 Numerical simulations of rock failure in indirect
tensile strength tests ................................. 32
3.3.1 The disc test ................................... 32
3.3.1.1 Stress distribution in the discs ....... 32
3.3.1.2 Effect of the material properties of
the load-bearing strip on the disc
test ................................... 35
3.3.1.3 Effect of load-bearing strip width on
disc test .............................. 36
3.3.1.4 Effect of specimen size on the disc
test ................................... 40
3.3.2 The plate test .................................. 41
3.3.3 The ring test ................................... 42
3.3.3.1 Stress distribution along the loading
diameter for ring specimens ............ 43
3.3.3.2 Effect of hole diameter on the failure
pattern of ring specimens .............. 44
3.3.3.3 Effect of hole diameter on the ring
test indirect tensile strength ......... 49
4 Rock failure in uniaxial compression ........................ 55
4.1 Introduction ........................................... 55
4.2 Numerical illustrations of rock failure in uniaxial
compression ............................................ 58
4.2.1 Model description ............................... 58
4.2.2 Numerical simulation results .................... 59
4.2.3 Summary of the numerical simulation
observations .................................... 65
4.2.3.1 The complete stress-strain curve ....... 65
4.2.3.2 Acoustic emission (AE) events and
their locations ........................ 67
4.2.3.3 Stress distribution and failure-
induced stress redistribution .......... 68
4.3 Rock failure modes in uniaxial compression ............. 69
4.4 Factors affecting rock failure behaviour ............... 72
4.4.1 Model description ............................... 73
4.4.2 Effect of end constraint in terms of the
Young's modulus of the loading platens .......... 73
4.4.3 Effect of height to width ratio (slenderness)
of the specimen ................................. 78
4.4.4 Class I and Class II curves in uniaxial
compression ..................................... 82
4.4.5 The size effect ................................. 85
5 Confinement and shear ....................................... 89
5.1 The effect of confinement .............................. 89
5.2 Acoustic emission during shearing ...................... 95
5.3 Biaxial loading ........................................ 97
6 Effect of heterogeneity on rock failure .................... 101
6.1 Introduction .......................................... 101
6.2 Heterogeneity-induced stress fluctuations ............. 102
6.2.1 Discs subjected to diametral loading ........... 102
6.2.2 Rock blocks under hydrostatic stress ........... 103
6.3 Heterogeneity-related seismic patterns ................ 106
6.4 Influence of heterogeneity on crack propagation
modes ................................................. 109
6.4.1 Numerical specimen ............................. 109
6.4.2 Numerical results and discussion ............... 110
6.5 The influence of heterogeneity on the meso-scale ...... 114
6.5.1 Digital image based modelling method ........... 115
6.5.2 Numerical model based on the digital image ..... 115
6.5.3 Simulation results for uniaxial compression .... 117
6.5.4 Influence of interface strength ................ 118
7 The effect of rock anisotropy on rock failure .............. 121
7.1 Introduction .......................................... 121
7.2 Numerical models ...................................... 122
8 Loading, unloading and the Kaiser Effect ................... 129
8.1 Introduction .......................................... 129
8.2 Numerical simulation .................................. 130
9 Time dependency of rock failure ............................ 135
9.1 Introduction .......................................... 135
9.2 A constitutive model for the time-dependent behaviour
of rocks .............................................. 137
9.3 Illustrations of time-dependent micro-structural
damage ................................................ 138
9.3.1 The creep test ................................. 138
9.3.2 The relaxation test ............................ 141
9.4 Degradation of building stones with time .............. 144
10 Coalescence of fractures ................................... 147
10.1 Introduction .......................................... 147
10.2 Modelling of crack growth from crack-like flaws in
compression ........................................... 147
10.2.1 An angled crack-like flaw ...................... 148
10.2.2 Crack growth from an array of crack-like
flaws .......................................... 158
10.2.2.1 Wing crack growth from three flaw
arrays ................................ 158
10.2.2.2 Wing crack growth from randomly
distributed multi-flaws ............... 162
10.3 Crack growth from a pore-like flaw in compression ..... 165
10.3.1 Modelling crack growth from a single hole
in specimens under compression ................. 166
10.3.1.1 Crack growth from a single hole
in specimens of different width ....... 166
10.3.1.2 Crack growth from a single hole
with different diameters .............. 167
10.3.1.3 Modelling of crack growth from an
array of holes in a specimen under
compression ........................... 172
11 Dynamic loading of rock .................................... 181
11.1 Introduction .......................................... 181
11.2 The simulation models ................................. 183
11.3 Simulation demonstration .............................. 185
11.3.1 Influence of heterogeneity on stress wave
propagation .................................... 185
11.3.2 Influence of stress wave amplitude on the
fracture process and failure pattern ........... 186
12 Rock failure and water flow ................................ 189
12.1 Introduction .......................................... 189
12.2 Rock failure under hydraulic pressure ................. 190
12.3 Illustrations of fluid flow in heterogeneous
initially intact rock ................................. 193
12.3.1 Evolution of flow paths ....................... 196
12.4 Comparison with the rock degradation modelling
by Yuan and Harrison (2005) ........................... 200
12.5 Fluid flow in initially intact rock containing block
inhomogeneities ....................................... 203
13 Rock failure induced by thermal stress ..................... 209
13.1 Introduction .......................................... 209
13.2 Thermally-induced rock failure ........................ 210
13.3 Thermal cracking of a disc-ring model ................. 212
13.4 Thermal cracking in models containing irregularly
shaped inclusions ..................................... 215
14 Slope failure in rock masses ............................... 219
14.1 Introduction .......................................... 219
14.2 Strength reduction rule and determination of safety
factor ................................................ 220
14.3 A slope in a layered rock mass ........................ 223
14.4 A slope in a jointed rock mass ........................ 225
14.5 A slope in a jointed rock mass with differing joint
persistence ........................................... 228
15 The fracture process when cutting inhomogeneous rocks ...... 229
15.1 Introduction .......................................... 229
15.2 Modelling rock cutting and the failure mechanism ...... 229
15.2.1 Quasi-photoelastic fringe pattern .............. 230
15.2.2 Fracture pattern ............................... 231
15.2.3 The chipping process ........................... 233
15.3 The load-displacement response when cutting
inhomogeneous rock .................................... 234
15.4 The crushed zone during rock cutting .................. 236
16 Rock failure around tunnels in jointed rock ................ 237
16.1 Introduction .......................................... 237
16.2 Progressive failure around a tunnel in a jointed
rock mass ............................................. 238
16.2.1 Effect of dip angles on the stability of the
tunnel ......................................... 239
16.2.2 The effect of the lateral stress on the mode
of tunnel failure .............................. 243
16.2.3 Displacements at the tunnel periphery .......... 247
17 Rock failure induced by longwall coal mining ............... 249
17.1 Introduction .......................................... 249
17.2 Illustrations of longwall mining simulations .......... 250
17.3 The Daliuta coal mine in China ........................ 255
17.3.1 The strata failure process ..................... 256
17.3.2 Pillar stresses ................................ 258
18 Gas outbursts in coal mines ................................ 263
18.1 Introduction .......................................... 263
18.2 Outbursts induced by cross-cutting from rock to coal
seam .................................................. 266
18.3 Outburst as the working face approaches high methane
pressure in the coal seam ............................. 269
19 Particle breakage and comminution .......................... 273
19.1 Introduction .......................................... 273
19.2 Single particle breakage .............................. 274
19.2.1 Breakage of single particle under diametral
loading without confinement .................... 274
19.2.2 Breakage of single particle under diametral
loading with confinement ....................... 276
19.3 Multiple particle breakage ............................ 284
19.3.1 Fragmentation process of a rock particle
assemblage in a container ...................... 285
19.3.2 Force and displacement relation during the
breakage process ............................... 287
19.3.3 Energy considerations .......................... 290
19.3.4 Size distribution .............................. 292
19.3.5 Influence of particle shape .................... 293
20 3-D modelling and ‘turtle crack formation’ in rock ......... 297
20.1 Introduction .......................................... 297
20.2 The three-layer model ................................. 298
20.3 Fracture spacing measurements ......................... 303
21 Concluding remarks ......................................... 307
References and bibliography ................................... 309
Index ......................................................... 321
|
