About the author |
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xi | |
Acknowledgments |
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xiii | |
Preface |
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xv | |
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1 | (10) |
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1 | (1) |
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1 | (1) |
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1 | (3) |
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1.3.1 Addition and subtraction |
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1 | (1) |
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2 | (1) |
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2 | (1) |
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2 | (1) |
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1.3.5 Coordinate systems and base vectors |
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3 | (1) |
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1.3.6 Vector operations on a Cartesian coordinate system |
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3 | (1) |
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4 | (3) |
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1.4.1 Definition of tensors of rank n |
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4 | (2) |
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6 | (1) |
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1.5 Matrix representation of tensors |
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7 | (1) |
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1.5.1 Matrix representation of vectors |
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7 | (1) |
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1.5.2 Matrix representation of tensors |
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7 | (1) |
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1.6 Coordinate transformation |
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8 | (1) |
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1.7 Derivation of tensorial quantities |
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9 | (2) |
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1.7.1 Derivative of a scalar function |
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9 | (1) |
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9 | (1) |
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9 | (1) |
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1.7.4 Gradient of a vector: second-order tensor |
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9 | (1) |
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1.7.5 Divergence of a tensor (second-order tensor) |
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10 | (1) |
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10 | (1) |
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11 | (7) |
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2.1 Definition of a stress vector |
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11 | (1) |
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11 | (1) |
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2.3 Relationship between a stress vector and a stress tensor: Cauchy's law |
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12 | (2) |
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2.4 Stress transformation |
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14 | (1) |
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2.5 Principal stresses and stress invariants |
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15 | (1) |
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2.6 Geometrical representation of stress tensor on the Mohr circle for the 2D condition |
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15 | (3) |
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17 | (1) |
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18 | (8) |
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18 | (1) |
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3.2 Derivation of a strain tensor using the Lagrangian description |
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19 | (2) |
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3.3 Derivation of a train tensor using the Eulerian description |
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21 | (2) |
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3.4 Relationship between the small strain theory and the finite strain theory |
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23 | (1) |
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3.5 Geometrical interpretations of a strain tensor |
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23 | (3) |
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3.5.1 Uniaxial deformation |
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23 | (1) |
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3.5.2 Simple shear deformation |
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24 | (1) |
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25 | (1) |
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4 Fundamental conservation laws |
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26 | (17) |
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4.1 Fundamental conservation laws for one-dimensional cases |
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26 | (9) |
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4.1.1 Mass conservation law |
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26 | (1) |
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4.1.2 Momentum conservation law |
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27 | (1) |
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4.1.3 Energy conservation laws |
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28 | (2) |
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4.1.4 Fundamental governing equations for coupled hydro-mechanical phenomena |
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30 | (5) |
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4.2 Multi-dimensional conservation laws |
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35 | (1) |
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4.2.1 Mass conservation laws for seepage and diffusion phenomena |
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35 | (1) |
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4.2.2 Momentum conservation law |
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36 | (1) |
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4.2.3 Angular momentum conservation law |
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36 | (1) |
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4.2.4 Energy conservation law |
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36 | (1) |
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4.3 Derivation of governing equations in the integral form |
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36 | (7) |
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4.3.1 Mass conservation law |
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36 | (2) |
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4.3.2 Momentum conservation law |
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38 | (1) |
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4.3.3 Angular momentum conservation law |
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39 | (1) |
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4.3.4 Energy conservation law |
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40 | (1) |
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41 | (2) |
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43 | (37) |
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5.1 One dimensional (1D) constitutive laws |
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43 | (14) |
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5.1.1 1D linear constitutive laws |
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43 | (6) |
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5.1.2 1D non-linear constitutive laws for solids |
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49 | (8) |
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5.2 Multi-dimensional constitutive laws |
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57 | (2) |
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57 | (1) |
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57 | (1) |
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57 | (1) |
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58 | (1) |
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58 | (1) |
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5.2.6 Kelvin--Voigt's law |
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58 | (1) |
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58 | (1) |
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5.3 Non-linear behavior (elasto-plasticity and elasto-visco-plasticity) for solids |
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59 | (11) |
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59 | (3) |
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5.3.2 Elasto-visco-plasticity |
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62 | (3) |
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5.3.3 Yield/failure criteria |
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65 | (5) |
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5.4 Equivalent models for discontinua |
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70 | (10) |
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5.4.1 Equivalent elastic compliance model (Singh's model) |
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71 | (2) |
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5.4.2 Crack tensor model (CTM) |
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73 | (1) |
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73 | (1) |
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5.4.4 Microstructure models |
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74 | (2) |
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5.4.5 Homogenization technique |
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76 | (1) |
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77 | (3) |
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80 | (41) |
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6.1 Laboratory tests on mechanical properties |
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80 | (21) |
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6.1.1 Uniaxial compression tests |
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81 | (1) |
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6.1.2 Direct and indirect tensile strength tests (Brazilian tests) |
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82 | (3) |
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6.1.3 Triaxial compression tests |
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85 | (1) |
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6.1.4 Post-failure behavior in uniaxial and triaxial compression tests |
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85 | (4) |
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89 | (4) |
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93 | (4) |
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6.1.7 Experimental techniques for creep tests |
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97 | (4) |
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6.2 Thermal properties of rocks and their measurements |
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101 | (6) |
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6.3 Tests far seepage parameters |
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107 | (7) |
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108 | (1) |
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6.3.2 Transient pulse test method |
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109 | (5) |
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6.4 Tests far diffusion parameters |
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114 | (7) |
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118 | (3) |
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7 Methods for exact (closed-form) solutions |
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121 | (71) |
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121 | (1) |
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7.1.1 Intuitive function methods |
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121 | (1) |
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7.1.2 Solution by separating variables |
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121 | (1) |
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7.1.3 Complex variable method |
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122 | (1) |
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7.2 Closed-form solutions for solids |
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122 | (40) |
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7.2.1 Visco-elastic rock sample subjected to uniaxial loading |
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122 | (5) |
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7.2.2 Visco-elastic layer on an incline |
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127 | (5) |
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7.2.3 One-dimensional bar embedded in rock |
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132 | (2) |
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7.2.4 Circular cavity in the elastic rock under a far-field hydrostatic stress |
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134 | (3) |
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7.2.5 Unified analytical solutions for circular/spherical cavity in an elasto-plastic rock |
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137 | (16) |
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7.2.6 Foundations-bearing capacity |
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153 | (2) |
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7.2.7 Two-dimensional closed-form solution methods |
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155 | (6) |
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7.2.8 Three-dimensional closed-form solutions |
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161 | (1) |
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7.3 Closed-form solutions for fluid flow through porous rocks |
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162 | (15) |
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7.3.1 Some considerations on the Darcy law for rocks and discontinuities |
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162 | (5) |
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7.3.2 Permeability tests based on a steady-state flow |
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167 | (2) |
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7.3.3 Permeability tests based on a non-steady-state flow (transient flow tests) |
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169 | (8) |
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7.4 Temperature distribution in the vicinity of geological active faults |
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177 | (3) |
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7.5 Closed-form solutions for diffusion problems |
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180 | (6) |
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7.5.1 Drying testing procedure |
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180 | (5) |
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7.5.2 Saturation testing technique |
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185 | (1) |
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7.6 Evaluation of creep-like deformation of semi-infinite soft rock layer |
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186 | (6) |
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188 | (4) |
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8 Methods for approximate solutions |
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192 | (58) |
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8.1 Comparison of exact and approximate solutions |
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192 | (6) |
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8.1.1 Exact (closed-form) solution |
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193 | (1) |
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8.1.2 Finite difference method |
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193 | (1) |
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8.1.3 Finite element method |
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194 | (3) |
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197 | (1) |
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8.2 ID hyperbolic problem: equation of motion |
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198 | (5) |
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8.2.1 Weak form formulation |
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199 | (1) |
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199 | (3) |
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202 | (1) |
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8.2.4 ID parabolic problem: creep problem |
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202 | (1) |
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8.2.5 ID elliptic problem: static problem |
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202 | (1) |
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8.2.6 Computational examples |
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203 | (1) |
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8.3 Parabolic problems: heat flow, seepage and diffusion |
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203 | (6) |
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203 | (1) |
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204 | (1) |
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8.3.3 Weak form formulation |
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205 | (1) |
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205 | (2) |
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8.3.5 Steady-state problem |
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207 | (1) |
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208 | (1) |
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8.3.7 Example 1: simulation of a solid body with heat generation |
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208 | (1) |
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8.3.8 Example 2: simulation of a diffusion problem |
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208 | (1) |
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8.4 FEM for ID pseudo-coupled parabolic problems: heat flow and thermal stress; swelling and swelling pressure |
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209 | (9) |
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209 | (1) |
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8.4.2 Governing equations |
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210 | (1) |
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8.4.3 Coupling of heat and stress fields |
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211 | (1) |
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8.4.4 Weak form formulation |
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212 | (1) |
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213 | (3) |
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216 | (1) |
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8.4.7 Example: simulation of heat generation and associated thermal stress |
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216 | (2) |
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8.5 Hydro-mechanical coupling: seepage and effective stress problem |
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218 | (8) |
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218 | (1) |
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8.5.2 Governing equations |
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218 | (1) |
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8.5.3 Weak form formulation |
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219 | (1) |
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220 | (4) |
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224 | (1) |
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8.5.6 Example: simulation of settlement under sudden loading |
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225 | (1) |
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8.6 Biot problem: coupled dynamic response of porous media |
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226 | (7) |
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226 | (1) |
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8.6.2 Governing equations |
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226 | (1) |
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8.6.3 Weak form formulation |
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227 | (1) |
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228 | (4) |
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232 | (1) |
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8.6.6 Example: simulation of dynamic response of saturated porous media |
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233 | (1) |
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8.7 Introduction of boundary conditions in a simultaneous equation system |
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233 | (3) |
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233 | (2) |
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8.7.2 Actual implementation and solution of Eq. (8.216b) |
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235 | (1) |
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8.8 Rayleigh damping and its implementation |
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236 | (1) |
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236 | (1) |
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8.10 Multi-dimensional situations |
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236 | (6) |
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237 | (4) |
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8.10.2 Numerical integration |
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241 | (1) |
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8.11 Special numerical methods for media having discontinuities |
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242 | (8) |
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8.11.1 No-tension finite element method |
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242 | (1) |
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8.11.2 Pseudo discontinuum finite element method |
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243 | (1) |
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8.11.3 Smeared crack element |
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243 | (1) |
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8.11.4 Finite element method with joint or interface element (FEM-J) |
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244 | (1) |
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8.11.5 Discrete finite element method (DFEM) |
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245 | (1) |
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8.11.6 Displacement discontinuity method (DDM) |
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246 | (1) |
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8.11.7 Discrete element method (DEM) |
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246 | (2) |
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8.11.8 Discontinuous deformation analysis method (DDA) |
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248 | (1) |
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248 | (2) |
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9 Applications of approximate methods in geo-engineering problems |
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250 | (53) |
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9.1 Applications in continuum |
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250 | (29) |
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9.1.1 The stress state of earth and earth's crust |
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250 | (2) |
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9.1.2 Evaluation of the tunnel face effect |
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252 | (2) |
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9.1.3 Three-dimensional simulation of the excavation of a railway tunnel supported with forepoles, rockbolts, shotcrete and steel ribs |
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254 | (3) |
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9.1.4 Effect of bolting pattern in underground excavations |
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257 | (1) |
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9.1.5 Numerical studies on the indentation (impression) experiment |
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257 | (4) |
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9.1.6 The evaluation of the long-term response of an underground cavern |
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261 | (1) |
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9.1.7 Long-term stability of the Derinkuyu underground city, Cappadocia, Turkey |
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262 | (3) |
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9.1.8 Stability analyses of Tomb of Pharaoh Amenophis III, Luxor, Egypt |
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265 | (1) |
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9.1.9 Dynamic response of a large underground cavern |
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265 | (1) |
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9.1.10 Response and stability of abandoned room and pillar mine under static and earthquake loading |
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266 | (5) |
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9.1.11 Modal analyses of shafts at the Horonobe Underground Laboratory |
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271 | (1) |
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9.1.12 Temperature and stress distributions around an underground opening |
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272 | (1) |
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9.1.13 Water-head variations in rock mass around an underground cavern |
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273 | (1) |
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9.1.14 Breakout formation in boreholes in sedimentary rocks due to moisture loss |
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274 | (5) |
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9.2 Applications in discontinuum |
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279 | (24) |
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9.2.1 Earthquake fault rupture simulation |
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279 | (3) |
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9.2.2 Pseudo-dynamic analyses on the interaction of structures and earthquake faults |
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282 | (1) |
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9.2.3 Dynamic stability conditions of a single rock block |
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282 | (2) |
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9.2.4 Stability of a slope against planar sliding |
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284 | (1) |
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9.2.5 Stability of rock slope against columnar toppling |
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285 | (1) |
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9.2.6 Stability of rock slope against flexural toppling and its stabilization |
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286 | (2) |
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9.2.7 Retrofitting of unlined tunnels |
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288 | (2) |
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9.2.8 Analysis of backfilling of abandoned mines |
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290 | (4) |
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9.2.9 Simulation of creep-like deformation of the Babadag landslide by DFEM |
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294 | (2) |
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9.2.10 Simulation of creep-like deformation of a rock block at the Nakagusuku Castle |
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296 | (3) |
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299 | (4) |
Appendix 1 Gauss divergence theorem |
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303 | (2) |
Appendix 2 Geometrical interpretation of the Taylor expansion |
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305 | (1) |
Appendix 3 Reynolds transport theorem |
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306 | (1) |
Appendix 4 The Gauss elimination method and its implementation |
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307 | (3) |
Appendix 5 Constitutive modeling of discontinuities and interfaces |
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310 | (4) |
Appendix 6 Thin band element for modeling discontinuities and interfaces in numerical analyses |
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314 | (7) |
Index |
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321 | |