Fundamentals of Rock Mechanics

489 Pages·2006·3.64 MB·English

Fundamentals of Rock Mechanics
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Fundamentals of Rock Mechanics
Fourth Edition
J. C. Jaeger, N. G. W. Cook, and R. W. Zimmerman
Blackwell
Publishing
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©2007BlackwellPublishing
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Firsteditionpublished1969byMethuen
Reprintpublished1971byChapmanandHall
Secondeditionpublished1976byChapmanandHall
Thirdeditionpublished1979
Fourtheditionpublished2007byBlackwellPublishingLtd
12007
LibraryofCongressCataloging-in-PublicationData
Jaeger, J.C.(JohnConrad),1907-
Fundamentalsofrockmechanics–J.C.Jaeger,N.G.W.Cook,andR.W.Zimmerman.–4thed.
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Includesbibliographicalreferencesandindex.
ISBN-13:978-0-632-05759-7(pbk.:alk.paper)
ISBN-10:0-632-05759-9(pbk.:alk.paper)1.Rockmechanics.I.Cook,NevilleG.W.
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Contents
PrefacetotheFourthEdition ix
1 RockasaMaterial 1
1.1 Introduction 1
1.2 Jointsandfaults 2
1.3 Rock-formingminerals 4
1.4 Thefabricofrocks 6
1.5 Themechanicalnatureofrock 7
2 AnalysisofStressandStrain 9
2.1 Introduction 9
2.2 Definitionoftractionandstress 10
2.3 Analysisofstressintwodimensions 17
2.4 Graphicalrepresentationsofstressintwodimensions 23
2.5 Stressesinthreedimensions 27
2.6 Stresstransformationsinthreedimensions 32
2.7 Mohr’srepresentationofstressinthreedimensions 35
2.8 Stressinvariantsandstressdeviation 38
2.9 Displacementandstrain 41
2.10 Infinitesimalstrainintwodimensions 43
2.11 Infinitesimalstraininthreedimensions 49
2.12 Determinationofprincipalstressesorstrainsfrom
measurements 55
2.13 Compatibilityequations 56
2.14 Stressandstraininpolarandcylindricalcoordinates 57
2.15 Finitestrain 60
3 FrictiononRockSurfaces 65
3.1 Introduction 65
3.2 Amonton’slaw 66
3.3 Frictiononrocksurfaces 67
3.4 Stick–sliposcillations 70
3.5 Slidingonaplaneofweakness 73
3.6 Effectsoftimeandvelocity 76
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vi contents
4 DeformationandFailureofRock 80
4.1 Introduction 80
4.2 Thestress–straincurve 80
4.3 Effectsofconfiningstressandtemperature 85
4.4 Typesoffracture 87
4.5 Coulombfailurecriterion 90
4.6 Mohr’shypothesis 94
4.7 Effectsofporefluids 97
4.8 Failureundertrue-triaxialconditions 100
4.9 Theeffectofanisotropyonstrength 103
5 LinearElasticity 106
5.1 Introduction 106
5.2 Stress–strainrelationsforanisotropiclinearelastic
solid 107
5.3 Specialcases 111
5.4 Hooke’slawintermsofdeviatoricstressesandstrains 115
5.5 Equationsofstressequilibrium 116
5.6 Equationsofstressequilibriumincylindricalandspherical
coordinates 122
5.7 Airystressfunctions 126
5.8 Elasticstrainenergyandrelatedprinciples 128
5.9 Uniquenesstheoremforelasticityproblems 135
5.10 Stress–strainrelationsforanisotropicmaterials 137
6 LaboratoryTestingofRocks 145
6.1 Introduction 145
6.2 Hydrostatictests 146
6.3 Uniaxialcompression 148
6.4 Triaxialtests 150
6.5 Stabilityandstifftestingmachines 152
6.6 True-triaxialtests 157
6.7 Diametralcompressionofcylinders 158
6.8 Torsionofcircularcylinders 161
6.9 Bendingtests 162
6.10 Hollowcylinders 165
7 PoroelasticityandThermoelasticity 168
7.1 Introduction 168
7.2 Hydrostaticporoelasticity 169
7.3 Undrainedcompression 175
7.4 Constitutiveequationsofporoelasticity 178
7.5 Equationsofstressequilibriumandfluidflow 183
7.6 One-dimensionalconsolidation 189
7.7 Applicationsofporoelasticity 195
7.8 Thermoelasticity 197
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contents vii
8 StressesaroundCavitiesandExcavations 205
8.1 Introduction 205
8.2 Complexvariablemethodfortwo-dimensionalelasticity
problems 206
8.3 Homogeneousstateofstress 211
8.4 Pressurizedhollowcylinder 214
8.5 Circularholeinarockmasswithgivenfar-field
principalstresses 216
8.6 Stressesappliedtoacircularholeinaninfiniterockmass 221
8.7 Stressesappliedtothesurfaceofasolidcylinder 225
8.8 Inclusionsinaninfiniteregion 228
8.9 Ellipticalholeinaninfiniterockmass 231
8.10 Stressesnearacracktip 237
8.11 Nearlyrectangularhole 242
8.12 Sphericalcavities 244
8.13 Penny-shapedcracks 247
8.14 Interactionsbetweennearbycavities 250
9 InelasticBehavior 252
9.1 Introduction 252
9.2 Plasticityandyield 252
9.3 Elastic–plastichollowcylinder 255
9.4 Circularholeinanelastic–brittle–plasticrockmass 257
9.5 Perfectlyplasticbehavior 260
9.6 Flowbetweenflatsurfaces 263
9.7 Flowrulesandhardening 266
9.8 Creep 268
9.9 Simplerheologicalmodels 271
9.10 Theoryofviscoelasticity 276
9.11 Somesimpleviscoelasticproblems 279
10 MicromechanicalModels 281
10.1 Introduction 281
10.2 Effectivemoduliofheterogeneousrocks 281
10.3 Effectofporesoncompressibility 284
10.4 Crackclosureandelasticnonlinearity 292
10.5 Effectivemediumtheories 295
10.6 Slidingcrackfrictionandhysteresis 301
10.7 GriffithcracksandtheGriffithlocus 307
10.8 Linearelasticfracturemechanics 311
10.9 Griffiththeoryoffailure 314
11 WavePropagationinRocks 321
11.1 Introduction 321
11.2 One-dimensionalelasticwavepropagation 322
11.3 Harmonicwavesandgroupvelocity 327
11.4 Elasticwavesinunboundedmedia 332
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viii contents
11.5 Reflectionandrefractionofwavesataninterface 337
11.6 Surfaceandinterfacewaves 343
11.7 Transientwaves 347
11.8 Effectsoffluidsaturation 353
11.9 Attenuation 355
11.10 Inelasticwaves 360
12 HydromechanicalBehaviorofFractures 365
12.1 Introduction 365
12.2 Geometryofrockfractures 365
12.3 Normalstiffnessofrockfractures 369
12.4 Behaviorofrockfracturesundershear 375
12.5 Hydraulictransmissivityofrockfractures 377
12.6 Coupledhydromechanicalbehavior 386
12.7 Seismicresponseofrockfractures 388
12.8 Fracturedrockmasses 394
13 StateofStressUnderground 399
13.1 Introduction 399
13.2 Simplemodelsforthestateofstressinthesubsurface 400
13.3 Measuredvaluesofsubsurfacestresses 403
13.4 Surfaceloadsonahalf-space:two-dimensionaltheory 404
13.5 Surfaceloadsonahalf-space:three-dimensionaltheory 408
13.6 Hydraulicfracturing 411
13.7 Otherstress-measurementmethods 415
14 GeologicalApplications 419
14.1 Introduction 419
14.2 Stressesandfaulting 419
14.3 Overthrustfaultingandslidingundergravity 423
14.4 Stressesaroundfaults 425
14.5 Mechanicsofintrusion 428
14.6 Beammodelsforcrustalfolding 431
14.7 Earthquakemechanics 434
References 439
Index 469
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Preface to the Fourth Edition
When the first edition of this book appeared in 1969, rock mechanics had
only recently begun to emerge as a distinct and identifiable scientific subject.
It coalesced from several strands, including classical continuum mechanics,
engineering and structural geology, and mining engineering. The two senior
authors of Fundamentals of Rock Mechanics were perhaps uniquely qualified to
play seminal roles in bringing about this emergence. John Jaeger had by that
timealreadyenjoyedalonganddistinguishedcareerasarguablythepreeminent
applied mathematician of the English-speaking world, and was the coauthor,
withH.S.Carslaw,ofoneofthetrueclassicsofthescientificliterature,Conduc-
tionofHeatinSolids.NevilleCookwasatthattimebarely30yearsold,butwas
alreadythedirectorofresearchattheSouthAfricanChamberofMines,andwell
onhiswaytobecomingacknowledgedastheleadingandmostbrilliantfigurein
thisnewfieldofrockmechanics.
The earlier editions of this book played a large role in establishing an iden-
tity for the field of rock mechanics and in defining what are now accepted to
be the “fundamentals” of the field. These fundamentals consist firstly of the
classicaltopicsofsolidmechanics–stressandstrain, linearelasticity, plasticity,
viscoelasticity,andelasticwavepropagation.Butrocksaremuchmorecomplex
than are most of the traditional engineering materials for which the classical
mechanics theories were intended to apply. Hence, a book entitled Fundamen-
tals of Rock Mechanics must also treat certain topics that are either unique to
rocks,oratanyratewhichassumegreatimportanceforrocks,suchasfriction
alongroughsurfaces,degradationandfailureundercompressiveloads,coupling
betweenmechanicaldeformationandfluidflow,theeffectofcracksandporeson
mechanicaldeformation,and,perhapsmostimportantly,theeffectoffractures
andjointsonlarge-scalerockbehavior.
Rockmechanics,thusdefined,formsacornerstoneofseveralfieldsofscience
andengineering–fromstructuralgeologyandtectonophysics,tomining,civil,
andpetroleumengineering.Asearchofcitationsinscientificjournalsshowsthat
previouseditionsofthisbookhavefoundanaudiencethatencompassesnotonly
theseareas,butalsoincludesmaterialscientistsandceramicists,forexample.It
ishopedthatthisneweditionwillcontinuetobefoundusefulbysuchavariety
ofresearchers,students,andpractitioners.
Theextenttowhichthedifferentchaptersofthiseditionareneworexpanded
varies considerably, but aside from the brief, introductory Chapter 1, all have
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