综合知识（第二版）

Contents
Chapter 1  Introduction 1
1.1  Research background and significances 1
1.2  Numerical investigations for damage and fracture in rock considering multiphysical fields coupling 2
1.3  Research aims and contents of the book 4
1.3.1  Research aims 4
1.3.2  Research contents 5
References 6
Chapter 2  Finite element algorithm for continuum damage evolution of rock considering hydro-mechanical coupling 9
2.1  Introduction 9
2.2  Assignment of petrophysical heterogeneity 11
2.3  Governing equations with hydro-mechanical coupling 13
2.4  Continuum damage evolution 14
2.5  Finite element analysis strategy 16
2.6  Results and discussion 16
2.6.1  Finite element model of heterogeneous rock 17
2.6.2  Rock damage analysis under different conditions 18
2.6.3  Effective stress analysis by hydro-mechanical coupling influence 21
2.7  Conclusions 22
References 23
Chapter 3  Finite element analysis for continuum damage evolution and wellbore stability of transversely isotropic rock considering hydro-mechanical coupling 25
3.1  Introduction 25
3.2  Finite element analysis strategy 29
3.3  Finite element solution 30
3.3.1  Constitutive equation 30
3.3.2  Finite element formulation 31
3.3.3  Finite element model and adaptive mesh refinement for wellbore stability analysis 32
3.4  Damage tensor calculation 36
3.4.1  Damage tensor 37
3.4.2  Stress and permeability with damage 38
3.5  Wellbore stability analysis 39
3.6  Results and discussion 40
3.6.1  Pore pressure and stress analysis of rock surrounding wellbore 40
3.6.2  Instability analysis of wellbore failure region 42
3.6.3  Collapse and fracture pressure computation 44
3.7  Conclusions 48
References 48
Chapter 4  Finite element analysis for continuum damage evolution and inclined wellbore stability of transversely isotropic rock considering hydro-mechanical-chemical coupling 52
4.1  Introduction 52
4.2  Transverse isotropy and hydration characterization 55
4.2.1  Constitutive equation 55
4.2.2  Hydration effect 57
4.3  Finite element analysis strategy 59
4.4  Finite element solution 60
4.4.1  Finite element formulation 60
4.4.2  Finite element model and adaptive mesh refinement for wellbore stability analysis 61
4.5  Damage tensor calculation 62
4.5.1  Damage tensor 62
4.5.2  Stress and permeability with damage 64
4.6  Wellbore stability analysis based on weak plane strength criterion 64
4.7  Results and discussion 65
4.7.1  Pore pressure and stress analysis of rock surrounding wellbore with hydro-mechanical-chemical coupling 66
4.7.2  Petrophysical heterogeneity and chemically active effect analysis 68
4.7.3  Time-dependent collapse and fracture pressure computation 72
4.8  Conclusions 73
Appendix: Coordinate systems and stresses transformation 74
References 77
Chapter 5  Adaptive finite element algorithm for damage detection of non-uniform Euler-Bernoulli beams with multiple cracks based on natural frequencies 80
5.1  Introduction 80
5.2  Adaptive approach for damage detection of cracked beams 84
5.2.1  Formulation and analogy of cracked beams 84
5.2.2  Stop criterion 86
5.2.3  Analysis strategy 87
5.3  Adaptive analysis 88
5.3.1  Finite element solution 88
5.3.2  Error estimation and mesh refinement 89
5.4  Newton-Raphson iteration 92
5.5  Damage refinement 94
5.6  Algorithms 94
5.7  Results and discussion 96
5.7.1  Free vibration problems 97
5.7.2  Damage detection problems 103
5.8  Conclusions 109
References 110
Chapter 6  Adaptive finite element-discrete element analysis for the multistage hydrofracturing in naturally fractured reservoirs considering hydro-mechanical coupling 113
6.1  Introduction 113
6.2  Adaptive finite element-discrete element method for hydraulic fracturing 118
6.2.1  Governing equations 118
6.2.2  Numerical discretization 122
6.2.3  Fracture propagation and local remeshing methods 123
6.3  Numerical models and procedure 124
6.3.1  Fracturing models in perforated horizontal wellbore 124
6.3.2  Discrete fracture network models for naturally fractured reservoir 126
6.3.3  Global procedure for hydraulic fracturing 127
6.4  Results and discussion 128
6.4