Fractured Rock Hydraulics

Fractured Rock Hydraulics......Page 2
Table of Contents......Page 4
About the author......Page 7
Preface......Page 8
Fractured rock hydraulics......Page 10
Scope......Page 11
1.1.1 Pseudo-continuity......Page 12
1.1.2 Observation scale......Page 13
1.1.5.1 Introduction......Page 17
1.1.5.2 Specific discharge......Page 18
1.1.5.3 Hydraulic gradient......Page 19
1.1.6.1 Introduction......Page 26
1.1.6.2 Fractures and conduits......Page 28
1.2.2 Energy conservation principle: Darcy’s law......Page 37
1.2.3.1 General equation......Page 39
1.2.3.2.1 UNCONFINED GROUNDWATER......Page 40
1.2.3.2.2 CONFINED GROUNDWATER......Page 42
1.2.4.1 Main boundary types......Page 44
1.2.4.3 Impervious boundaries......Page 45
1.2.4.5 Unconfined groundwater-air interface......Page 46
1.3.1 Addendum 1.1: Effective velocity and specific discharge......Page 48
1.3.2 Addendum 1.2: Hydrodynamic gradient......Page 49
1.3.3 Addendum 1.3: Hydraulic conductivity for randomly fractured subsystems......Page 50
1.3.4 Addendum 1.4: Energy conservation principle......Page 51
1.3.5 Addendum 1.5: Mass conservation principle......Page 52
References......Page 54
2.1 Overview......Page 55
2.2 Differential operators......Page 56
2.4 Approximate solution errors......Page 61
2.5.1 Preliminaries......Page 67
2.5.2 Collocation method......Page 68
2.5.3 Least squares method......Page 73
2.5.4.2 Galerkin’s approach......Page 79
2.5.4.3 “Weak solutions"......Page 84
2.5.4.4 Variational notation......Page 85
2.5.5 Time-dependent solutions......Page 88
2.6.1 Addendum 2.1: Classification of second order linear partial differential equations......Page 95
2.6.2 Addendum 2.2: Minimisation of the sum of the squared residuals......Page 96
2.6.4 Addendum 2.4: The concept of “orthogonality’’......Page 97
References......Page 98
3.3 Handling of hydraulic head data......Page 99
3.3.1 Variation in time......Page 101
3.3.2 Variation in space......Page 104
3.4 Handling of flow rate data......Page 113
3.5.1 Preliminaries......Page 115
3.6.2 Hydraulic conductivity appraisal......Page 116
3.6.2.2 Hydraulic tests at "borehole integral core" scale......Page 117
3.6.2.3 Hydraulic tests at "cluster of boreholes" scale......Page 120
3.6.2.4 Hydraulic tests at “aquifer" scale......Page 123
3.6.3.2 Filtering WT contour maps......Page 127
3.7.1 Concepts......Page 128
3.7.2 Guidelines to conceptual models......Page 129
References......Page 130
4.2.1 Difference equations......Page 132
4.2.2 Finite differences......Page 133
4.2.3 Difference equations for steady-state systems......Page 135
4.2.4 Difference equations for unsteady-state systems......Page 138
4.2.5 Difference equations for boundary conditions......Page 140
4.2.6.2 Gauss-Seidel iterative routine......Page 141
4.2.6.3 Crank-Nicholson iterative routine......Page 147
4.3.1 Preliminaries......Page 150
4.3.2.1.1 UNCONFINED FLOW......Page 151
4.3.2.1.2 CONFINED FLOW......Page 163
4.3.2.2 3D algorithms......Page 165
4.3.3 Transient solutions......Page 181
References......Page 182