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.Sineethelatterhavemuchpoorermechanicalcharacteristicsthantherockmaterial,theyplayadecisiveroleintheoverallbehaviorofrockstructures,whosedeformationaswellasfailurepatternsaremainlygovernedbythoseofthejoints.Itfollowsthat,fromageomechanicalengineeringstandpoint,designmethodsofstructuresinvolvingjointedrockmasses,mustabsolutelyaccountforsuch

‘‘weakness''surfaeesahalysis.

Themoststraightforwardwayofdealingwiththissituationistotreatthejointedrockmassasanassemblageofpiecesofintactrockmaterialinmutualinteractionthroughtheseparatingjointinterfaces.Manydesign-orientedmethodsrelatingtothiskindofapproachhavebeendevelopedinthepastdecades,amongthem,thewedlnown‘‘blocktheory,''whichattemptstoidentifypoten-

tiallyunstablelumpsofrockfromgeometricalandkinematicalconsiderations（GoodmanandShi1985;Warburton1987;Goodman1995）.Oneshouldalsoquotethewidelyuseddistinetelementmethod,originatingfromtheworksofCundallandcoauthors（CundallandStrack1979;Cundall1988）,whichmakesuseofanexplicit?

nite-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''isobservedinthecaseofa

joints.Thesecondpartofthepaperisthendevotedtoproposingamethodwhichattemptsto

capturesuchascaleeffect,whilestilltakingadvantageofahomogenizationtechnique.ThisisachievedbyresortingtoamicropolarorCosseratcontinuumdescriptionofthefracturedrockmass,throughthederivationofageneralizedmacroscopicfailureconditionexpressedintermsofstressesandcouplestresses.Theimplementationofthismodelis?

nallyillustratedonasimpleexample,showinghowitmayactuallyaccountforsuchascaleeffect.

ProblemStatementandPrincipleofHomogenizationApproach

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

Fig,1,Bearingcapacit>poffoundationonfracturedrockmass

capacityneedstobeevaluatedfromtheknowledgeofthestrengthcapacitiesoftherockmatrixandthejointinterfaces.ThefailureconditionoftheformerwillbeexpressedthroughtheclassicalMohr-CoulombconditionexpressedbymeansofthecohesionCmandthefrictionanglem.Notethattensilestresseswillbecountedpositivethroughoutthepaper.

Likewise,thejointswillbemodeledasplaneinterfaces（representedbylinesinthe?

gure'splane）.Theirstrengthpropertieiseadescribedbymeansofaconditioninvolvingthestressvectorofcomponents（c,t）actingatanypointofthoseinterfaces

F7（o-,t）=|t|+

Accordingtotheyielddesign（orlimitanalysis）reasoning,theabovestructurewillremainsafeunderagivenverticalloadQ（forceperunitlengthalongtheOzaxis）,ifonecanexhibitthroughouttherockmassastressdistributionwhichsatis?

estheequilibriumequationsalongwiththestressboundaryconditions,whilecomplyingwiththestrengthrequirementexpressedatanypointofthestructure.

+

ThisproblemamountstoevaluatingtheultimateloadQbeyondwhichfailurewilloccur,orequivalentlywithinwhichitsstabilityisensured.Duetothestrongheterogeneityofthejointedrockmass,insurmountabledif?

cultiesareilkelytoarisewhentryingtoimplementtheabovereasoningdirectly.Asregards,forinstanee,thecasewherethestrengthpropertiesofthejointsareconsiderablylowerthanthoseoftherockmatrix,theimplementationofa

kinematicapproachwouldrequiretheuseoffailuremechanismsinvolvingvelocityjumpsacrossthejoints,sincethelatterwouldconstitutepreferentialzonesfortheoccurreneeof

failure.Indeed,suchadirectapproachwhichisappliedinmostclassicaldesignmethods,isbecomingrapidlycomplexasthedensityofjointsincreases,thatisasthetypicaljointspacinglisbecomingsmallincomparisonwithacharacteristiclengthofthestructuresuchasthefoundationwidthB.

Insuchasituation,theuseofanalternativeapproachbasedontheideaofhomogenizationandrelatedconceptofmacroscopicequivalentcontinuumforthejointedrockmass,maybeappropriatefordealingwithsuchaproblem.Moredetailsaboutthistheory,appliedinthecontextofreinforcedsoilandrockmechanics,willbefoundin（deBuhanetal.1989;deBuhanandSalenc,on1990;Bernaudetal.1995）.

MacroscopicFailureConditionforJointedRockMass

Theformulationofthemacroscopicfailureconditionofajointedrockmassmaybeobtainedfromthesolutionofanauxiliaryyielddesignboundary-valueproblemattachedtoaunitrepresentativecellofjointedrock（BekaertandMaghous1996;Maghousetal.1998）.Itwillnowbeexplicitlyformulatedintheparticularsituationoftwomutuallyorthogonalsetsofjointsunderplanestrainconditions.ReferringtoanorthonormalframeO12whoseaxesareplacedalongthejointsdirections,andintroducingthefollowingchangeofstressvariables:

p=（（T]|+（T22）/\2,i?

=（（T22-O，i1）/\2,1=\2（T|2

（2）

（如

suchamacroscopicfailureconditionsimplybecomes

m

whereitwillbeassumedthat

15=5tan

Aconvenientrepresentationofthemacroscopiccriterionistodrawthestrengthenveloperelatingtoanorientedfacetofthehomogenizedmaterial,whoseunitnormalnIisinclinedbyanangleawithrespecttothejointdirection.Denotingby-nandnthenormalandshearcomponentsofthestressvectoractinguponsuchafacet,itispossibletodetermineforanyvalueofathesetofadmissiblestresses,n）deducedfromconditions（3）expressedintermsof（J,、,-12）.ThecorrespondingdomainhasbeendrawninFig.2intheparticularcasewhere乞m

Fig.2.Strengthenvelopeattachedcofaceiofhomogenizedmaterial

Twocommentsareworthbeingmade:

1.ThedecreaseinstrengthofarockmaterialduetothepresenceofjointsisclearlyillustratedbyFig.2.Theusualstrengthenvelopecorrespondingtotherockmatrixfailureconditionis‘‘truncatedytwoorthogonalsemilinesassoonasconditionHj：

Hmisful?

lled.

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

NorcansuchananisotropybeproperlydescribedbymeansofcriteriabasedonanextensionoftheclassicalMohr-Coulombconditionusingtheconceptofanisotropytensor（BoehlerandSawczuk1977;Nova1980;AllirotandBochler1981）.

ApplicationtoStabilityofJointedRockExcavation

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

Fig.3.Stabilityanalysisofjointedrockexcavation

wherehandBdenotetheexcavationheightandtheslopeangle,respectively.Sinceno

surchargeisappliedtothestructure,thespeci?

cweightyoftheconstituentmaterialwillobviouslyconstitutethesoleloadingparameterofthesystem.AssessingthestabilityofthisstructurewillamounttoevaluatingthemaximumpossibleheightFbeyondwhichfailurewilloccur.Astandarddimensionalanalysisofthisproblemshowsthatthiscriticalheightmaybeputintheform

where0=jointorientationandK+=nondimensionalfactorgoverningthestabilityoftheexcavation.Upper-boundestimatesofthisfactorwillnowbedeterminedbymeansoftheyielddesignkinemati