Fractured Rock Hydraulics  book cover
1st Edition

Fractured Rock Hydraulics

ISBN 9781138112759
Published August 23, 2018 by CRC Press
188 Pages 163 B/W Illustrations

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Book Description

Uniquely devoted to hard and fractured rock hydraulics, this advanced-level introduction provides tools to solve practical engineering problems. Chapter I covers the fundamentals of fractured rock hydraulics under a tensor approach. Chapter II presents some key concepts about approximate solutions. Chapter III discuss a few data analysis techniques applied to groundwater modeling. Chapter IV presents unique 3D finite difference algorithms to simulate practical problems concerning the hydraulic behavior of saturated, heterogeneous and randomly fractured rock masses without restriction to the geometry and properties of their discontinuities. Supported by examples, cases, illustrations and references, this book is intended for professionals and researchers in hydrogeology, engineering geology, petroleum reservoir, rock and hydraulic engineering. Its explanatory nature allows its use as a textbook for advanced students.

Table of Contents


  • 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
  • Introduction
  • Specific discharge
  • Hydraulic gradient
  • 1.1.6 Hydraulic conductivity
  • Introduction
  • 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
  • General equation
  • Dupuit’s approximation
  • 1.2.4 Boundary and initial conditions
  • Main boundary types
  • Submerged boundaries
  • Impervious boundaries
  • Seepage boundaries
  • 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
  • Orthogonality
  • Galerkin’s approach
  • "Weak solutions’’
  • 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
  • Hydraulic tests at "core sample’’ scale
  • Hydraulic tests at "borehole integral core’’ scale
  • Hydraulic tests at "cluster of boreholes’’ scale
  • Hydraulic tests at "aquifer’’ scale
  • 3.6.3 Hydraulic connectivity appraisal
  • Dynamic correlations of WT time series
  • 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
  • Preliminaries
  • Gauss-Seidel iterative routine
  • Crank-Nicholson iterative routine
  • 4.3 Finite differences algorithms for fractured rock masses
  • 4.3.1 Preliminaries
  • 4.3.2 Steady-state solutions
  • Dupuit’s approximation
  • 3D algorithms
  • 4.3.3 Transient solutions

Subject Index

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Born in 1935, Fernando Olavo Franciss grew up in Rio de Janeiro and was educated as a Civil Engineer in the Pontifical Catholic University of Rio de Janeiro, Brazil. He started his professional career in 1959 by being educated on applied geology by the late and distinguished Prof. Reynold Barbier at the Institut Dolomieu of the University of Grenoble, France. Ten years later, in 1970, he obtained his doctoral degree from the same university. A leading rock engineer, he has gathered a lifetime of international experience in civil engineering practice, often while crossing with other fields such as engineering geology, underground mining and oil reservoir engineering. From 1964 to 1980, he worked as a part time professor at the Pontifical Catholic University of Rio de Janeiro. Until 1991 he worked at Sondotecnica, a reputed Brazilian Consulting Bureau, and since then as an independent consultant. Many now well-known Brazilian experts in civil, earth and water engineering start their professional career closely working with Prof. Franciss, a fact that pleased him very much.

During his career, Dr. Franciss has had the chance to devote part of his time to investigate the hydraulics of fractured rocks related to civil works, mining, oil and gas storage caverns and interactions of hydrothermal resources with dam reservoirs. He has accordingly developed a tensor approach to describe the hydraulic properties of fractured rocks and unique finite difference matrix-algorithms to model the hydraulic and hydrothermal behavior of randomly fractured rock masses.

He is member of the Brazilian Society for Soil Mechanics and Geotechnical Engineering, the Brazilian Society for Engineering and Environmental Geology, the National Academy of Engineering and the International Society for Rock Mechanics. He has won a number of prestigious awards in Brazil, and has written several papers and a number of books: "Soil and Rock Hydraulics" (Balkema, Rotterdam, 1985), "Weak Rock Tunnelling" (Balkema, Rotterdam, 1994) and a part co-authored with Manoel Rocha on Rock Mass Permeability in ‘Structural and Geotechnical Mechanics’ by W.J. Hall, Ed. (Prentice Hall, New Jersey, 1976).


“This book is a joy to read because of its extreme clarity, which is further enhanced by the clear layout and the frequent addition of explanatory examples.”
“I strongly recommend this book to everyone who is involved with fractured rock hydraulics — whether as student, teacher, researcher or engineer.”
John A Hudson
Emeritus Professor, Imperial College, UK
President, International Society for Rock Mechanics