Table Of ContentFractured Rock Hydraulics
Fractured Rock Hydraulics
F.O. Franciss
Progeo–ConsultoriadeEngenhariaLtda,RiodeJaneiro,Brazil
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Table of Contents
About the author IX
Preface XI
Introduction 1
Fracturedrockhydraulics 1
Scope 2
Chapter1 Fundamentals 3
1.1 Basicconcepts 3
1.1.1 Pseudo-continuity 3
1.1.2 Observationscale 4
1.1.3 Descriptionatdifferentscales 8
1.1.4 Representativeelementaryvolume 8
1.1.5 Hydraulicvariables 8
1.1.5.1 Introduction 8
1.1.5.2 Specificdischarge 9
1.1.5.3 Hydraulicgradient 10
1.1.6 Hydraulicconductivity 17
1.1.6.1 Introduction 17
1.1.6.2 Fracturesandconduits 19
1.2 Governingequations 28
1.2.1 Preliminaries 28
1.2.2 Energyconservationprinciple:Darcy’slaw 28
1.2.3 Massconservationprinciple:continuityequation 30
1.2.3.1 Generalequation 30
1.2.3.2 Dupuit’sapproximation 31
1.2.4 Boundaryandinitialconditions 35
1.2.4.1 Mainboundarytypes 35
1.2.4.2 Submergedboundaries 36
1.2.4.3 Imperviousboundaries 36
1.2.4.4 Seepageboundaries 37
1.2.4.5 Unconfinedgroundwater-airinterface 37
VI Table of Contents
1.3 AddendatoChapter1 39
1.3.1 Addendum1.1:Effectivevelocityandspecificdischarge 39
1.3.2 Addendum1.2:Hydrodynamicgradient 40
1.3.3 Addendum1.3:Hydraulicconductivityforrandomly
fracturedsubsystems 41
1.3.4 Addendum1.4:Energyconservationprinciple 42
1.3.5 Addendum1.5:Massconservationprinciple 43
Chapter2 Approximatesolutions 47
2.1 Overview 47
2.2 Differentialoperators 48
2.3 Uniquenessofsolutions 53
2.4 Approximatesolutionerrors 53
2.5 Approximationmethods 59
2.5.1 Preliminaries 59
2.5.2 Collocationmethod 60
2.5.3 Leastsquaresmethod 65
2.5.4 Galerkin’smethod 71
2.5.4.1 Orthogonality 71
2.5.4.2 Galerkin’sapproach 71
2.5.4.3 “Weaksolutions’’ 76
2.5.4.4 Variationalnotation 77
2.5.5 Time-dependentsolutions 80
2.6 AddendatoChapter2 87
2.6.1 Addendum2.1:Classificationofsecondorderlinear
partialdifferentialequations 87
2.6.2 Addendum2.2:Minimisationofthesumofthesquaredresiduals 88
2.6.3 Addendum2.3:Minimisationofthesumofthesquared
residualstransformedbythedifferentialoperatorsD andD 89
V N
2.6.4 Addendum2.4:Theconceptof“orthogonality’’ 89
Chapter3 Dataanalysis 91
3.1 Preliminaries 91
3.2 Analysinggeologicalfeatures 91
3.3 Handlingofhydraulicheaddata 91
3.3.1 Variationintime 93
3.3.2 Variationinspace 96
3.4 Handlingofflowratedata 105
3.5 Handlingofhydraulicconductivitydata 107
3.5.1 Preliminaries 107
3.6 Hydraulictransmissivityandconnectivity 108
3.6.1 Preliminaries 108
3.6.2 Hydraulicconductivityappraisal 108
3.6.2.1 Hydraulictestsat“coresample’’scale 109
3.6.2.2 Hydraulictestsat“boreholeintegralcore’’scale 109
3.6.2.3 Hydraulictestsat“clusterofboreholes’’scale 112
3.6.2.4 Hydraulictestsat“aquifer’’scale 115
Table of Contents VII
3.6.3 Hydraulicconnectivityappraisal 119
3.6.3.1 DynamiccorrelationsofWTtimeseries 119
3.6.3.2 FilteringWTcontourmaps 119
3.7 Modellinghydrogeologicalsystems 120
3.7.1 Concepts 120
3.7.2 Guidelinestoconceptualmodels 121
Chapter4 Finitedifferences 125
4.1 Preliminaries 125
4.2 Finitedifferencebasics 125
4.2.1 Differenceequations 125
4.2.2 Finitedifferences 126
4.2.3 Differenceequationsforsteady-statesystems 128
4.2.4 Differenceequationsforunsteady-statesystems 131
4.2.5 Differenceequationsforboundaryconditions 133
4.2.6 Simultaneousdifferenceequations 134
4.2.6.1 Preliminaries 134
4.2.6.2 Gauss-Seideliterativeroutine 134
4.2.6.3 Crank-Nicholsoniterativeroutine 140
4.3 Finitedifferencesalgorithmsforfracturedrockmasses 143
4.3.1 Preliminaries 143
4.3.2 Steady-statesolutions 144
4.3.2.1 Dupuit’sapproximation 144
4.3.2.2 3Dalgorithms 158
4.3.3 Transientsolutions 174
SubjectIndex 177
About the author
Born in 1935, Fernando Olavo Franciss grew up in Rio de
Janeiro and was educated as a civil engineer in the Pontifi-
calCatholicUniversityofRiodeJaneiro,Brazil.Hestarted
his professional career in 1959 by his education in applied
geologybythelateanddistinguishedProf.ReynoldBarbier
at the Institut Dolomieu of the University of Grenoble,
France. Ten years later, in 1970, he obtained his doctoral
degreefromthesameuniversity.Aleadingrockengineer,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
reservoirengineering. From1964to1980, heworkedasapart-timeprofessoratthe
PontificalCatholicUniversityofRiodeJaneiro.Until1991heworkedatSondotecnica,
a reputed Brazilian consulting bureau, and since then as an independent consultant.
Manynowwell-knownBrazilianexpertsincivil,earthandwaterengineeringstarted
their professional careers closely working with Prof. Franciss, a fact that pleases him
verymuch.
During his career, Dr. Franciss has had the chance to devote part of his time to
an investigation of the hydraulics of fractured rocks related to civil works, mining,
oil and gas storage caverns and the interactions of hydrothermal resources with dam
reservoirs.Hehasaccordinglydevelopedatensorapproachtodescribethehydraulic
propertiesoffracturedrocksanduniquefinitedifferencematrix-algorithmstomodel
thehydraulicandhydrothermalbehaviourofrandomlyfracturedrockmasses.
HeismemberoftheBrazilianSocietyforSoilMechanicsandGeotechnicalEngineer-
ing, 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 co-authored contribution with
Manoel Rocha on rock mass permeability in Structural and Geotechnical Mechanics
byW.J.Hall,ed.(PrenticeHall,NewJersey,1976).
