Fractured Rock Hydraulics

Introduction Fractured rock hydraulics Scope 1. Fundamentals 1.1 Basic concepts 1.1.1 Pseudo-continuity 1.1.2 Observation scale 1.1.3 Description at different scales 1.1.4 Representative elementary volume 1.1.5 Hydraulic variables 1.1.5.1 Introduction 1.1.5.2 Specific discharge 1.1.5.3 Hydraulic gradient 1.1.6 Hydraulic conductivity 1.1.6.1 Introduction 1.1.6.2 Fractures and conduits 1.2 Governing equations 1.2.1 Preliminaries 1.2.2 Energy conservation principle: Darcy's law 1.2.3 Mass conservation principle: continuity equation 3 1.2.3.1 General equation 1.2.3.2 Dupuit's approximation 1.2.4 Boundary and initial conditions 1.2.4.1 Main boundary types 1.2.4.2 Submerged boundaries 1.2.4.3 Impervious boundaries 1.2.4.4 Seepage boundaries 1.2.4.5 Unconfined groundwater-air interface 1.3 Addenda to Chapter 1 1.3.1 Addendum 1.1: Effective velocity and specific discharge 1.3.2 Addendum 1.2: Hydrodynamic gradient 1.3.3 Addendum 1.3: Hydraulic conductivity for randomly fractured subsystems 1.3.4 Addendum 1.4: Energy conservation principle 1.3.5 Addendum 1.5: Mass conservation principle 2. Approximate solutions 2.1 Overview 2.2 Differential operators 2.3 Uniqueness of solutions 2.4 Approximate solution errors 2.5 Approximation methods 2.5.1 Preliminaries 2.5.2 Collocation method 2.5.3 Least squares method 2.5.4 Galerkin's method 2.5.4.1 Orthogonality 2.5.4.2 Galerkin's approach 2.5.4.3 "Weak solutions" 2.5.4.4 Variational notation 2.5.5 Time-dependent solutions 2.6 Addenda to Chapter 2 2.6.1 Addendum 2.1: Classification of second order linear partial differential equations 2.6.2 Addendum 2.2: Minimisation of the sum of the squared residuals 2.6.3 Addendum 2.3: Minimisation of the sum of the squared residuals transformed by the differential operators DV and DN 2.6.4 Addendum 2.4: The concept of "orthogonality" 3. Data analysis 3.1 Preliminaries 3.2 Analysing geological features 3.3 Handling of hydraulic head data 3.3.1 Variation in time 3.3.2 Variation in space 3.4 Handling of flow rate data 3.5 Handling of hydraulic conductivity data 3.5.1 Preliminaries 3.6 Hydraulic transmissivity and connectivity 3.6.1 Preliminaries 3.6.2 Hydraulic conductivity appraisal 3.6.2.1 Hydraulic tests at "core sample" scale 3.6.2.2 Hydraulic tests at "borehole integral core" scale 3.6.2.3 Hydraulic tests at "cluster of boreholes" scale 3.6.2.4 Hydraulic tests at "aquifer" scale 3.6.3 Hydraulic connectivity appraisal 3.6.3.1 Dynamic correlations of WT time series 3.6.3.2 Filtering WT contour maps 3.7 Modelling hydrogeological systems 3.7.1 Concepts 3.7.2 Guidelines to conceptual models 4. Finite differences 4.1 Preliminaries 4.2 Finite difference basics 4.2.1 Difference equations 4.2.2 Finite differences 4.2.3 Difference equations for steady-state systems 4.2.4 Difference equations for unsteady-state systems 4.2.5 Difference equations for boundary conditions 4.2.6 Simultaneous difference equations 4.2.6.1 Preliminaries 4.2.6.2 Gauss-Seidel iterative routine 4.2.6.3 Crank-Nicholson iterative routine 4.3 Finite differences algorithms for fractured rock masses 4.3.1 Preliminaries 4.3.2 Steady-state solutions 4.3.2.1 Dupuit's approximation 4.3.2.2 3D algorithms 4.3.3 Transient solutions Subject Index