土木 地质岩土工程专业毕业英文翻译原文和译文.docx

土木 地质岩土工程专业毕业英文翻译原文和译文.docx

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土木地质岩土工程专业毕业英文翻译原文和译文

FailurePropertiesofFracturedRockMassesasAnisotropic

HomogenizedMedia

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,attentionisprimarilyfocusedontheformulationofrealisticmodelsfordescribingthejointbehavior.

Sincethepreviouslymentioneddirectapproachisbecominghighlycomplex,andthennumericallyuntractable,assoonasaverylargenumberofblocksisinvolved,itseemsadvisabletolookforalternativemethodssuchasthosederivedfromtheconceptofhomogenization.Actually,suchaconceptisalreadypartiallyconveyedinanempiricalfashionbythefamousHoekandBrown’scriterion（HoekandBrown1980;Hoek1983）.Itstemsfromtheintuitiveideathatfromamacroscopicpointofview,arockmassintersectedbyaregularnetworkofjointsurfaces,maybeperceivedasahomogeneouscontinuum.Furthermore,owingtotheexistenceofjointpreferentialorientations,oneshouldexpectsuchahomogenizedmaterialtoexhibitanisotropicproperties.

Theobjectiveofthepresentpaperistoderivearigorousformulationforthefailurecriterionofajointedrockmassasahomogenizedmedium,fromtheknowledgeofthejointsandrockmaterialrespectivecriteria.Intheparticularsituationwheretwomutuallyorthogonaljointsetsareconsidered,aclosed-formexpressionisobtained,givingclearevidenceoftherelatedstrengthanisotropy.Acomparisonisperformedonanillustrativeexamplebetweentheresultsproducedbythehomogenizationmethod,makinguseofthepreviouslydeterminedcriterion,andthoseobtainedbymeansofacomputercodebasedonthedistinctelementmethod.Itisshownthat,whilebothmethodsleadtoalmostidenticalresultsforadenselyfracturedrockmass,a‘‘size’’or‘‘scaleeffect’’isobservedinthecaseofalimitednumberofjoints.Thesecondpartofthepaperisthendevotedtoproposingamethodwhichattemptstocapturesuchascaleeffect,whilestilltakingadvantageofahomogenizationtechnique.ThisisachievedbyresortingtoamicropolarorCosseratcontinuumdescriptionofthefracturedrockmass,throughthederivationofageneralizedmacroscopicfailureconditionexpressedintermsofstressesandcouplestresses.Theimplementationofthismodelisfinallyillustratedonasimpleexample,showinghowitmayactuallyaccountforsuchascaleeffect.

ProblemStatementandPrincipleofHomogenizationApproach

Theproblemunderconsiderationisthatofafoundation（bridgepierorabutment）restinguponafracturedbedrock（Fig.1）,whosebearing

capacityneedstobeevaluatedfromtheknowledgeofthestrengthcapacitiesoftherockmatrixandthejointinterfaces.ThefailureconditionoftheformerwillbeexpressedthroughtheclassicalMohr-Coulombconditionexpressedbymeansofthecohesion

andthefrictionangle

.Notethattensilestresseswillbecountedpositivethroughoutthepaper.

Likewise,thejointswillbemodeledasplaneinterfaces（representedbylinesinthefigure’splane）.Theirstrengthpropertiesaredescribedbymeansofaconditioninvolvingthestressvectorofcomponents（σ,τ）actingatanypointofthoseinterfaces

Accordingtotheyielddesign（orlimitanalysis）reasoning,theabovestructurewillremainsafeunderagivenverticalloadQ（forceperunitlengthalongtheOzaxis）,ifonecanexhibitthroughouttherockmassastressdistributionwhichsatisfiestheequilibriumequationsalongwiththestressboundaryconditions,whilecomplyingwiththestrengthrequirementexpressedatanypointofthestructure.

ThisproblemamountstoevaluatingtheultimateloadQ﹢beyondwhichfailurewilloccur,orequivalentlywithinwhichitsstabilityisensured.Duetothestrongheterogeneityofthejointedrockmass,insurmountabledifficultiesarelikelytoarisewhentryingtoimplementtheabovereasoningdirectly.Asregards,forinstance,thecasewherethestrengthpropertiesofthejointsareconsiderablylowerthanthoseoftherockmatrix,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）.Itwillnowbeexplicitlyformulatedintheparticularsituationoftwomutuallyorthogonalsetsofjointsunderplanestrainconditions.ReferringtoanorthonormalframeO

whoseaxesareplacedalongthejointsdirections,andintroducingthefollowingchangeofstressvariables:

suchamacroscopicfailureconditionsimplybecomes

whereitwillbeassumedthat

Aconvenientrepresentationofthemacroscopiccriterionistodrawthestrengthenveloperelatingtoanorientedfacetofthehomogenizedmaterial,whoseunitnormalnIisinclinedbyanangleawithrespecttothejointdirection.Denotingby

and

thenormalandshearcomponentsofthestressvectoractinguponsuchafacet,itispossibletodetermineforanyvalueofathesetofadmissiblestresses（

）deducedfromconditions（3）expressedintermsof（

）.ThecorrespondingdomainhasbeendrawninFig.2intheparticularcasewhere

.

Twocommentsareworthbeingmade:

1.ThedecreaseinstrengthofarockmaterialduetothepresenceofjointsisclearlyillustratedbyFig.2.Theusualstrengthenvelopecorrespondingtotherockmatrixfailureconditionis‘‘truncated’’bytwoorthogonalsemilinesassoonascondition

isfulfilled.

2.Themacroscopicanisotropyisalsoquiteapparent,sinceforinstancethestrengthenvelopedrawninFig.2isdependentonthefacetorientationa.Theusualnotionofintrinsiccurveshouldthereforebediscarded,butalsotheconceptsofanisotropiccohesionandfrictionangleastentativelyintroducedbyJaeger（1960）,orMcLamoreandGray（1967）.

NorcansuchananisotropybeproperlydescribedbymeansofcriteriabasedonanextensionoftheclassicalMohr-Coulombconditionusingtheconceptofanisotropytensor（BoehlerandSawczuk1977;Nova1980;AllirotandBochler1981）.

ApplicationtoStabilityofJointedRockExcavation

Theclosed-formexpression（3）obtainedforthemacroscopicfailurecondition,makesitthenpossibletoperformthefailuredesignofanystructurebuiltinsuchamaterial,suchastheexcavationshowninFig.3,

wherehandβdenotetheexcavationheightandtheslopeangle,respectively.Sincenosurchargeisappliedtothestructure,thespecificweightγoftheconstituentmaterialwillobviouslyconstitutethesoleloadingparameterofthesystem.Assessingthestabilityofthisstructurewillamounttoevaluatingthemaximumpossibleheighth+beyondwhichfailurewilloccur.Astandarddimensionalanalysisofthisproblemshowsthatthiscriticalheightmaybeputintheform

whereθ=jointorientationandK+=nondimensionalfactorgoverningthestabilityoftheexcavation.Upper-boundestimatesofthisfactorwillnowbedeterminedbymeansoftheyielddesignkinematicapproach,usingtwokindsoffailuremechanismsshowninFig.4.

RotationalFailureMechanism[Fig.4（a）]

Thefirstclassoffailuremechanismsconsideredintheanalysisisadirecttranspositionofthoseusuallyemployedforhomogeneousandisotropicsoilorrockslopes.InsuchamechanismavolumeofhomogenizedjointedrockmassisrotatingaboutapointΩwithanangularvelocityω.Thecurveseparatingthisvolumefromtherestofthestructurewhichiskeptmot