About the authors |
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xiii | |
Acknowledgments |
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xvii | |
Foreword |
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xix | |
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1 | (40) |
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1.1 Who should read this book? |
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1 | (1) |
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1.2 How to use this book? |
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1 | (1) |
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1.3 Continuous vs. discontinuous deformation |
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2 | (6) |
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8 | (1) |
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1.5 Three decades of DDA research and development |
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9 | (1) |
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9 | (1) |
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10 | (2) |
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1.7.1 Block system kinematics |
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10 | (1) |
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1.7.2 Complete first order displacement approximation |
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11 | (1) |
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1.7.3 Equilibrium, dynamics and energy consumption |
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11 | (1) |
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11 | (1) |
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12 | (1) |
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1.8 Some limitations of the original DDA |
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12 | (3) |
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15 | (2) |
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1.10 Higher order displacement function |
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17 | (2) |
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1.11 Coupling DDA with other numerical methods |
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19 | (4) |
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1.11.1 Coupling DDA with FEM |
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19 | (2) |
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1.11.2 Coupling DDA with BEM |
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21 | (1) |
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1.11.3 Coupling DDA with NMM |
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22 | (1) |
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1.12 Improved contact algorithms |
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23 | (3) |
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1.13 Incorporation of viscous damping |
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26 | (1) |
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1.14 Improved friction law for discontinuities |
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27 | (2) |
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1.15 Gravity turn on and sequential excavation |
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29 | (1) |
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1.16 Dynamic wave propagation and blasting |
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30 | (3) |
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33 | (1) |
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1.18 Improved rockbolt element |
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33 | (1) |
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34 | (3) |
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1.19.1 Historical overview |
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34 | (1) |
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1.19.2 Modelling particulate media with DDA |
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35 | (2) |
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1.20 Pore pressure and fluid flow |
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37 | (3) |
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1.20.1 Historical overview |
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37 | (2) |
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1.20.2 Coupling DDA and fluid flow |
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39 | (1) |
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1.21 Current development of 3-D DDA |
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40 | (1) |
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2 Theory of the discontinuous deformation analysis (DDA) |
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41 | (32) |
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2.1 Governing equations and displacement approximation |
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41 | (4) |
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2.1.1 Governing equations |
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41 | (1) |
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2.1.2 Displacement approximation of a single block |
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42 | (3) |
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2.2 Formulation of matrices for each single block |
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45 | (9) |
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2.2.1 Sub-matrices of elastic strains |
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45 | (1) |
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2.2.2 Sub-matrices of initial stress |
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46 | (1) |
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2.2.3 Sub-matrices of point loading |
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47 | (1) |
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2.2.4 Sub-matrices of line loading |
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47 | (1) |
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2.2.5 Sub-matrices of body force |
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48 | (1) |
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2.2.6 Sub-matrices of bolting connection |
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49 | (2) |
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2.2.7 Sub-matrices of inertia force |
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51 | (1) |
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2.2.8 Sub-matrices of displacement constraints at a point |
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52 | (1) |
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2.2.9 Sub-matrices of displacement constraints in a direction |
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53 | (1) |
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2.3 Interactions between blocks |
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54 | (14) |
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55 | (2) |
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2.3.2 Contact constraint enforcement |
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57 | (1) |
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2.3.3 Open-close iterations |
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58 | (2) |
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2.3.4 Formulation of contact matrices |
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60 | (8) |
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2.4 Time integration scheme and governing equations for blocky systems |
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68 | (2) |
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2.5 Simplex integration for 2-D DDA |
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70 | (1) |
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71 | (2) |
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3 Theory of the discontinuous deformation analysis in three dimensions |
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73 | (30) |
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3.1 Block displacement approximation and global equilibrium equation |
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73 | (4) |
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3.1.1 Displacement weight function |
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73 | (3) |
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3.1.2 Global equilibrium equation |
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76 | (1) |
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3.2 Formulation of matrices for single block |
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77 | (11) |
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3.2.1 Sub-matrices of elastic strain |
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77 | (1) |
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3.2.2 Sub-matrices of initial stress |
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78 | (1) |
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3.2.3 Sub-matrices of point loading |
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79 | (1) |
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3.2.4 Sub-matrices of line loading |
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79 | (1) |
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3.2.5 Sub-matrices of surface loading |
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80 | (1) |
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3.2.6 Sub-matrices of body force |
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81 | (1) |
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3.2.7 Sub-matrices of bolting connection |
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82 | (2) |
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3.2.8 Sub-matrices of inertia force |
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84 | (1) |
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3.2.9 Sub-matrices of displacement constraints in a direction |
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85 | (1) |
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3.2.10 Sub-matrices of fixed point |
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86 | (2) |
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3.3 Interactions among blocks |
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88 | (10) |
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3.3.1 Contact detection and types |
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88 | (1) |
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3.3.2 Contact state and open-close iteration |
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88 | (3) |
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3.3.3 Formulation of contact matrices |
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91 | (7) |
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3.4 Simplex integration for 3D DDA |
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98 | (3) |
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101 | (2) |
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4 Geological input parameters for realistic DDA modeling |
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103 | (28) |
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103 | (1) |
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4.2 Realistic representation of rock mass structure |
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103 | (25) |
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4.2.1 Number of joint sets |
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107 | (2) |
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4.2.2 Types of joint sets |
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109 | (4) |
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4.2.3 Joint set orientation |
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113 | (6) |
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4.2.4 Joint set spacing and bias correction |
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119 | (2) |
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4.2.5 Joint set dispersion |
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121 | (2) |
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123 | (1) |
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4.2.7 Rock bridges and realistic mesh generation |
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124 | (4) |
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4.3 Mechanical input parameters for forward modeling |
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128 | (3) |
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4.3.1 Intact rock elements |
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128 | (1) |
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4.3.2 Shear strength of the discontinuities |
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129 | (2) |
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131 | (36) |
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131 | (1) |
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132 | (11) |
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133 | (4) |
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137 | (6) |
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143 | (3) |
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5.4 Block response to cyclic motion of frictional interface |
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146 | (8) |
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147 | (1) |
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148 | (6) |
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5.5 Dynamic rocking of slender blocks |
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154 | (3) |
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5.6 Wave propagation phenomena |
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157 | (10) |
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157 | (4) |
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5.6.2 Shear wave propagation |
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161 | (4) |
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5.6.3 Concluding remarks regarding wave propagation accuracy |
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165 | (2) |
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6 Underground excavations |
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167 | (32) |
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167 | (1) |
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6.2 Shallow underground excavations |
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167 | (15) |
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168 | (3) |
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171 | (6) |
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177 | (5) |
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6.3 Deep underground excavations |
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182 | (17) |
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6.3.1 Boundary conditions |
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182 | (2) |
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6.3.2 Excavation damage zone |
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184 | (3) |
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187 | (3) |
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190 | (9) |
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199 | (34) |
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199 | (2) |
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7.2 Rotational failure modes |
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201 | (12) |
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201 | (6) |
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207 | (3) |
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210 | (3) |
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7.3 Dynamic rock slope stability analysis |
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213 | (12) |
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7.3.1 First introduction of time dependent accelerations to DDA |
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213 | (1) |
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214 | (2) |
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7.3.3 Consideration of local site effects |
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216 | (5) |
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7.3.4 Application to single plane sliding |
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221 | (4) |
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7.4 Rock bolt reinforcement |
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225 | (8) |
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8 Shi's new contact theory |
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233 | (128) |
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233 | (2) |
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8.2 Geometric representations of angles and blocks |
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235 | (11) |
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8.2.1 Discontinuous computations |
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235 | (1) |
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8.2.2 Related mathematical symbols |
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235 | (2) |
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8.2.3 Algebraic operations of blocks |
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237 | (1) |
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8.2.4 Representation of solid angles |
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237 | (3) |
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8.2.5 Inequality equations of angles |
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240 | (2) |
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8.2.6 Representation of blocks |
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242 | (2) |
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8.2.7 Structure of blocks |
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244 | (1) |
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8.2.8 Inequality equations of blocks |
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245 | (1) |
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8.3 Definition of the entrance block |
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246 | (12) |
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8.3.1 Relations of two blocks |
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246 | (3) |
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8.3.2 Definition of entrance block |
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249 | (1) |
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8.3.3 Entrance block and parallel movement |
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249 | (1) |
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8.3.4 Entrance block of a block and a point |
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249 | (1) |
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8.3.5 The entrance block of a block and a ball |
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249 | (2) |
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8.3.6 The entrance ball between two balls |
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251 | (2) |
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8.3.7 Theorem of separation |
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253 | (1) |
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8.3.8 Theorem of entrance |
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253 | (1) |
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8.3.9 Theorem of distance |
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253 | (1) |
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254 | (3) |
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8.3.11 Examples of the entrance block |
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257 | (1) |
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8.4 Basic theorems of entrance block |
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258 | (5) |
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8.4.1 Theorem of uniqueness |
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258 | (1) |
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8.4.2 Theorem of finite covers of entrance blocks |
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258 | (1) |
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8.4.3 Theorem of including |
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259 | (1) |
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260 | (1) |
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8.4.5 Theorem of symmetry |
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260 | (1) |
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261 | (1) |
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8.4.7 Theorem of removability |
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262 | (1) |
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8.4.8 Theorem of inner points |
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262 | (1) |
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8.4.9 Theorem of convex blocks |
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262 | (1) |
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8.5 Boundaries of the entrance solid angles of 2D solid angles |
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263 | (10) |
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8.5.1 Local entrance solid angle of 2D blocks |
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264 | (1) |
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8.5.2 Existence of entrance solid angle boundary of 2D solid angles |
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264 | (2) |
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8.5.3 Contact surface of 2D solid angles |
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266 | (1) |
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8.5.4 Entrance of boundary vector to vector of 2D solid angles |
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266 | (1) |
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8.5.5 Contact vectors of angle to angle contact |
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267 | (2) |
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8.5.6 Finite covers of 2D parallel vector to vector entrance |
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269 | (3) |
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8.5.7 Contact vectors of 2D entrance solid angle |
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272 | (1) |
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8.6 Contact vectors of 2D solid angles |
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273 | (14) |
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8.6.1 Contact vectors of a 2D convex solid angle and a 2D concave solid angle |
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273 | (2) |
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8.6.2 Contact vectors of 2D convex solid angles |
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275 | (5) |
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8.6.3 Entrance solid angle of 2D round corner convex solid angle and concave solid angle |
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280 | (4) |
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8.6.4 Entrance round corner solid angle of 2D round corner convex solid angles |
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284 | (3) |
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8.7 Boundaries of an entrance block of 2D blocks |
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287 | (7) |
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8.7.1 Entrance of 2D block inner points |
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287 | (1) |
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8.7.2 Entrance of 2D edge to edges |
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287 | (2) |
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8.7.3 Contact edges of 2D block to block contact |
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289 | (2) |
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8.7.4 Finite covers of 2D parallel edge to edge entrance |
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291 | (2) |
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8.7.5 Contact edges of 2D entrance block |
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293 | (1) |
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8.8 Contact edges of 2D blocks |
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294 | (12) |
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8.8.1 Contact edges of 2D convex blocks |
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294 | (4) |
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8.8.2 Contact edges of 2D general blocks |
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298 | (1) |
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8.8.3 Applications of the theory of contact in 2D DDA |
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299 | (4) |
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8.8.4 Applications of the new theory of contact in 2D NMM |
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303 | (3) |
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8.9 Boundaries of entrance solid angle of 3D solid angles |
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306 | (22) |
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8.9.1 Local entrance angle of 3D angles |
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307 | (1) |
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8.9.2 Existence of entrance solid angle boundary of 3D solid angles |
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307 | (2) |
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8.9.3 Entrance of 3D solid angle inner points |
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309 | (1) |
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8.9.4 Entrance of boundary solid angle to angle of 3D solid angles |
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309 | (1) |
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8.9.5 Entrance of boundary angle to vector of 3D solid angles |
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310 | (3) |
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8.9.6 Contact solid angle of 3D vertex to boundary angle contact |
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313 | (2) |
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8.9.7 Contact solid angle of 3D boundary vector to vector contact |
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315 | (2) |
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8.9.8 Finite covers of parallel boundary angle to vector entrance |
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317 | (6) |
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8.9.9 Finite covers of parallel boundary angle entrance |
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323 | (1) |
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8.9.10 Contact angles of 3D entrance solid angle |
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324 | (4) |
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8.10 Contact solid angles of 3D solid angles |
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328 | (12) |
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8.10.1 Contact plane of a 3D solid angle and half space |
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328 | (1) |
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8.10.2 Contact plane of two 3D convex solid edges |
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328 | (2) |
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8.10.3 Contact half-planes of a 3D concave solid edge and a 3D solid angle |
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330 | (2) |
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8.10.4 Contact half-planes of a 3D convex solid edge and a 3D solid angle |
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332 | (2) |
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8.10.5 Contact solid angles of two 3D convex solid angles |
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334 | (3) |
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8.10.6 Contact solid angles of two 3D general solid angles |
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337 | (3) |
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8.11 Boundaries of entrance block of 3D blocks |
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340 | (13) |
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8.11.1 Entrance of 3D block inner points |
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340 | (1) |
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8.11.2 Entrance of boundary polygons of 3D blocks |
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340 | (2) |
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8.11.3 Entrance of polygon to edge of 3D blocks |
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342 | (1) |
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8.11.4 Contact polygon of 3D vertex to polygon contact |
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343 | (2) |
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8.11.5 Contact polygon of 3D edge to edge contact |
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345 | (2) |
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8.11.6 Finite covers of parallel polygon to edge entrance |
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347 | (2) |
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8.11.7 Finite covers of parallel polygon entrance |
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349 | (3) |
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8.11.8 Contact polygons of 3D entrance blocks |
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352 | (1) |
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8.12 Contact polygons of 3D blocks |
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353 | (6) |
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8.12.1 Contact polygons of two 3D convex blocks |
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353 | (4) |
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8.12.2 Contact polygons of two general 3D blocks |
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357 | (2) |
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8.12.3 Simple examples of the new contact theory in 3D DDA |
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359 | (1) |
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359 | (2) |
References |
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361 | (20) |
Subject Index |
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381 | |