土木工程岩土工程裂隙岩体毕业论文中英文资料对照外文翻译文献综述.docx
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土木工程岩土工程裂隙岩体毕业论文中英文资料对照外文翻译文献综述.docx
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中英文资料对照外文翻译文献综述
FailurePropertiesofFracturedRockMassesasAnisotropicHomogenizedMedia
Introduction
Itiscommonlyacknowledgedthatrockmassesalwaysdisplaydiscontinuoussurfacesofvarioussizesandorientations,usuallyreferredtoasfracturesorjoints.Sincethelatterhavemuchpoorermechanicalcharacteristicsthantherockmaterial,theyplayadecisiveroleintheoverallbehaviorofrockstructures,whosedeformationaswellasfailurepatternsaremainlygovernedbythoseofthejoints.Itfollowsthat,fromageomechanicalengineeringstandpoint,designmethodsofstructuresinvolvingjointedrockmasses,mustabsolutelyaccountforsuch‘‘weakness’’surfacesintheiranalysis.
Themoststraightforwardwayofdealingwiththissituationistotreatthejointedrockmassasanassemblageofpiecesofintactrockmaterialinmutualinteractionthroughtheseparatingjointinterfaces.Manydesign-orientedmethodsrelatingtothiskindofapproachhavebeendevelopedinthepastdecades,amongthem,thewell-known‘‘blocktheory,’’whichattemptstoidentifypoten-
tiallyunstablelumpsofrockfromgeometricalandkinematicalconsiderations(GoodmanandShi1985;Warburton1987;Goodman1995).Oneshouldalsoquotethewidelyuseddistinctelementmethod,originatingfromtheworksofCundallandcoauthors(CundallandStrack1979;Cundall1988),whichmakesuseofanexplicitfinite-differencenumericalschemeforcomputingthedisplacementsoftheblocksconsideredasrigidordeformablebodies.Inthiscontext,attentionisprimarilyfocusedontheformulationofrealisticmodels
fordescribingthejointbehavior.
Sincethepreviouslymentioneddirectapproachisbecominghighlycomplex,andthennumericallyuntractable,assoonasaverylargenumberofblocksisinvolved,itseemsadvisabletolookforalternativemethodssuchasthosederivedfromtheconceptofhomogenization.Actually,suchaconceptisalreadypartiallyconveyedinanempiricalfashionbythefamousHoekandBrown’scriterion(HoekandBrown1980;Hoek1983).Itstemsfromtheintuitiveideathatfromamacroscopicpointofview,arockmassintersectedbyaregularnetworkofjointsurfaces,maybeperceivedasahomogeneouscontinuum.Furthermore,owingtotheexistenceofjointpreferentialorientations,oneshouldexpectsuchahomogenizedmaterialtoexhibitanisotropicproperties.
Theobjectiveofthepresentpaperistoderivearigorousformulationforthefailurecriterionofajointedrockmassasahomogenizedmedium,fromtheknowledgeofthejointsandrockmaterialrespectivecriteria.Intheparticularsituationwheretwomutuallyorthogonaljointsetsareconsidered,aclosed-formexpressionisobtained,givingclearevidenceoftherelatedstrengthanisotropy.Acomparisonisperformedonanillustrativeexamplebetweentheresultsproducedbythehomogenizationmethod,makinguseofthepreviouslydetermined
14
criterion,andthoseobtainedbymeansofacomputercodebasedonthedistinctelementmethod.Itisshownthat,whilebothmethodsleadtoalmostidenticalresultsforadenselyfracturedrockmass,a‘‘size’’or‘‘scaleeffect’’isobservedinthecaseofalimitednumberofjoints.Thesecondpartofthepaperisthendevotedtoproposingamethodwhichattemptstocapturesuchascaleeffect,whilestilltakingadvantageofahomogenizationtechnique.ThisisachievedbyresortingtoamicropolarorCosseratcontinuumdescriptionofthefracturedrockmass,throughthederivationofageneralizedmacroscopicfailureconditionexpressedintermsofstressesandcouplestresses.Theimplementationofthismodelisfinallyillustratedonasimpleexample,showinghowitmayactuallyaccountforsuchascaleeffect.
ProblemStatementandPrincipleofHomogenizationApproach
Theproblemunderconsiderationisthatofafoundation(bridgepierorabutment)restinguponafracturedbedrock(Fig.1),whosebearing
capacityneedstobeevaluatedfromtheknowledgeofthestrengthcapacitiesoftherockmatrixandthejointinterfaces.Thefailureconditionoftheformerwillbeexpressedthrough
theclassicalMohr-CoulombconditionexpressedbymeansofthecohesionCm
andthe
frictionangle m.Notethattensilestresseswillbecountedpositivethroughoutthepaper.
Likewise,thejointswillbemodeledasplaneinterfaces(representedbylinesinthefigure’splane).Theirstrengthpropertiesaredescribedbymeansofaconditioninvolvingthestressvectorofcomponents(σ,τ)actingatanypointofthoseinterfaces
Accordingtotheyielddesign(orlimitanalysis)reasoning,theabovestructurewillremainsafeunderagivenverticalloadQ(forceperunitlengthalongtheOzaxis),ifonecanexhibitthroughouttherockmassastressdistributionwhichsatisfiestheequilibriumequationsalongwiththestressboundaryconditions,whilecomplyingwiththestrengthrequirementexpressedatanypointofthestructure.
ThisproblemamountstoevaluatingtheultimateloadQ﹢beyondwhichfailurewilloccur,orequivalentlywithinwhichitsstabilityisensured.Duetothestrongheterogeneityofthejointedrockmass,insurmountabledifficultiesarelikelytoarisewhentryingtoimplementtheabovereasoningdirectly.Asregards,forinstance,thecasewherethestrengthpropertiesofthejointsareconsiderablylowerthanthoseofthe rockmatrix,theimplementationofakinematicapproachwouldrequiretheuseoffailuremechanismsinvolvingvelocityjumpsacrossthejoints,sincethelatterwouldconstitutepreferentialzonesfortheoccurrenceof
failure.Indeed,suchadirectapproachwhichisappliedinmostclassicaldesignmethods,isbecomingrapidlycomplexasthedensityofjointsincreases,thatisasthetypicaljointspacinglisbecomingsmallincomparisonwithacharacteristiclengthofthestructuresuchasthefoundationwidthB.
Insuchasituation,theuseofanalternativeapproachbasedontheideaofhomogenizationandrelatedconceptofmacroscopicequivalentcontinuumforthejointedrockmass,maybeappropriatefordealingwithsuchaproblem.Moredetailsaboutthistheory,appliedinthecontextofreinforcedsoilandrockmechanics,willbefoundin(deBuhanetal.1989;deBuhanandSalenc,on1990;Bernaudetal.1995).
MacroscopicFailureConditionforJointedRockMass
Theformulationofthemacroscopicfailureconditionofajointedrockmassmaybeobtainedfromthesolutionofanauxiliaryyielddesignboundary-valueproblemattachedtoaunitrepresentativecellofjointedrock(BekaertandMaghous1996;Maghousetal.1998).Itwillnowbeexplicitlyformulatedintheparticularsituationoftwomutuallyorthogonalsetsof
jointsunderplanestrainconditions.ReferringtoanorthonormalframeO
12whoseaxesare
placedalongthejointsdirections,andintroducingthefollowingchangeofstressvariables:
suchamacroscopicfailureconditionsimplybecomes
whereitwillbeassumedthat
Aconvenientrepresentationofthemacroscopiccriterionistodrawthestrengthenveloperelatingtoanorientedfacetofthehomogenizedmaterial,whoseunitnormalnIisinclinedby
anangleawithrespecttothejointdirection.Denotingby nand nthenormalandshearcomponentsofthestressvectoractinguponsuchafacet,itispossibletodetermineforanyvalueofathesetofadmissiblestresses( n, n)deducedfromconditions(3)expressedin
termsof(11,22, 12).ThecorrespondingdomainhasbeendrawninFig.2inthe
particularcasewhere m.
Twocommentsareworthbeingmade:
1.ThedecreaseinstrengthofarockmaterialduetothepresenceofjointsisclearlyillustratedbyFig.2.Theusualstrengthenvelopecorrespondingtotherockmatrixfailure
conditionis‘‘truncated’’bytwoorthogonalsemilinesassoonasconditionHj Hmis
fulfilled.
2.Themacroscopicanisotropyisalsoquiteapparent,sinceforinstancethestrengthenvelopedrawninFig.2isdependentonthefacetorientationa.Theusualnotionofintrinsiccurveshouldthereforebediscarded,butalsotheconceptsofanisotropiccohesionandfrictionangleastentativelyintroducedbyJaeger(1960),orMcLamoreandGray(1967).
NorcansuchananisotropybeproperlydescribedbymeansofcriteriabasedonanextensionoftheclassicalMohr-Coulombconditionusingtheconceptofanisotropytensor(BoehlerandSawczuk1977;Nova1980;AllirotandBochler1981).
ApplicationtoStabilityofJointedRockExcavation
Theclosed-formexpression(3)obtainedforthemacroscopicfailurecondition,makesitthenpossibletoperformthefailuredesignofanystructurebuiltinsuchamaterial,suchastheexcavationshowninFig.3,
wherehandβdenotetheexcavationheightandtheslopeangle,respectively.Sinceno
surchargeisappliedtothestructure,thespecificweightγoftheconstituentmaterialwillobviouslyconstitutethesoleloadingparameterofthesystem.Assessingthestabilityofthisstructurewillamounttoevaluatingthemaximumpossibleheighth+beyondwhichfailurewilloccur.Astandarddimensionalanalysisofthisproblemshowsthatthiscriticalheightmaybeputintheform
whereθ=jointorientationandK+=nondimensionalfactorgoverningthestabilityoftheexcavation.Upper-boundestimatesofthisfactorwillnowbedeterminedbymeansoftheyielddesignkinematicapproach,usingtwokindsoffailuremechanismsshowninFig.4.
RotationalFailureMechanism[Fig.4(a)]
Thefirstclassoffailuremechanismsconsideredintheanalysisisadirecttranspositionofthoseusuallyemployedforhomogeneousandisotropicsoilorrockslopes.Insuchamechanismavolumeofhomogenizedjointedrockmassisrotatingabout
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