文献及翻译-均质各向异性裂隙岩体的破坏特性

FAILUREPROPERTIESOFFRACTUREDROCKMASSESASANISOTROPICHOMOGENIZEDMEDIAINTRODUCTIONITISCOMMONLYACKNOWLEDGEDTHATROCKMASSESALWAYSDISPLAYDISCONTINUOUSSURFACESOFVARIOUSSIZESANDORIENTATIONS,USUALLYREFERREDTOASFRACTURESORJOINTSSINCETHELATTERHAVEMUCHPOORERMECHANICALCHARACTERISTICSTHANTHEROCKMATERIAL,THEYPLAYADECISIVEROLEINTHEOVERALLBEHAVIOROFROCKSTRUCTURES,WHOSEDEFORMATIONASWELLASFAILUREPATTERNSAREMAINLYGOVERNEDBYTHOSEOFTHEJOINTSITFOLLOWSTHAT,FROMAGEOMECHANICALENGINEERINGSTANDPOINT,DESIGNMETHODSOFSTRUCTURESINVOLVINGJOINTEDROCKMASSES,MUSTABSOLUTELYACCOUNTFORSUCHWEAKNESSSURFACESINTHEIRANALYSISTHEMOSTSTRAIGHTFORWARDWAYOFDEALINGWITHTHISSITUATIONISTOTREATTHEJOINTEDROCKMASSASANASSEMBLAGEOFPIECESOFINTACTROCKMATERIALINMUTUALINTERACTIONTHROUGHTHESEPARATINGJOINTINTERFACESMANYDESIGNORIENTEDMETHODSRELATINGTOTHISKINDOFAPPROACHHAVEBEENDEVELOPEDINTHEPASTDECADES,AMONGTHEM,THEWELLKNOWNBLOCKTHEORY,WHICHATTEMPTSTOIDENTIFYPOTENTIALLYUNSTABLELUMPSOFROCKFROMGEOMETRICALANDKINEMATICALCONSIDERATIONSGOODMANANDSHI1985WARBURTON1987GOODMAN1995ONESHOULDALSOQUOTETHEWIDELYUSEDDISTINCTELEMENTMETHOD,ORIGINATINGFROMTHEWORKSOFCUNDALLANDCOAUTHORSCUNDALLANDSTRACK1979CUNDALL1988,WHICHMAKESUSEOFANEXPLICITNITEDIFFERENCENUMERICALSCHEMEFORCOMPUTINGTHEDISPLACEMENTSOFTHEBLOCKSCONSIDEREDASRIGIDORDEFORMABLEBODIESINTHISCONTEXT,ATTENTIONISPRIMARILYFOCUSEDONTHEFORMULATIONOFREALISTICMODELSFORDESCRIBINGTHEJOINTBEHAVIORSINCETHEPREVIOUSLYMENTIONEDDIRECTAPPROACHISBECOMINGHIGHLYCOMPLEX,ANDTHENNUMERICALLYUNTRACTABLE,ASSOONASAVERYLARGENUMBEROFBLOCKSISINVOLVED,ITSEEMSADVISABLETOLOOKFORALTERNATIVEMETHODSSUCHASTHOSEDERIVEDFROMTHECONCEPTOFHOMOGENIZATIONACTUALLY,SUCHACONCEPTISALREADYPARTIALLYCONVEYEDINANEMPIRICALFASHIONBYTHEFAMOUSHOEKANDBROWNSCRITERIONHOEKANDBROWN1980HOEK1983ITSTEMSFROMTHEINTUITIVEIDEATHATFROMAMACROSCOPICPOINTOFVIEW,AROCKMASSINTERSECTEDBYAREGULARNETWORKOFJOINTSURFACES,MAYBEPERCEIVEDASAHOMOGENEOUSCONTINUUMFURTHERMORE,OWINGTOTHEEXISTENCEOFJOINTPREFERENTIALORIENTATIONS,ONESHOULDEXPECTSUCHAHOMOGENIZEDMATERIALTOEXHIBITANISOTROPICPROPERTIESTHEOBJECTIVEOFTHEPRESENTPAPERISTODERIVEARIGOROUSFORMULATIONFORTHEFAILURECRITERIONOFAJOINTEDROCKMASSASAHOMOGENIZEDMEDIUM,FROMTHEKNOWLEDGEOFTHEJOINTSANDROCKMATERIALRESPECTIVECRITERIAINTHEPARTICULARSITUATIONWHERETWOMUTUALLYORTHOGONALJOINTSETSARECONSIDERED,ACLOSEDFORMEXPRESSIONISOBTAINED,GIVINGCLEAREVIDENCEOFTHERELATEDSTRENGTHANISOTROPYACOMPARISONISPERFORMEDONANILLUSTRATIVEEXAMPLEBETWEENTHERESULTSPRODUCEDBYTHEHOMOGENIZATIONMETHOD,MAKINGUSEOFTHEPREVIOUSLYDETERMINEDCRITERION,ANDTHOSEOBTAINEDBYMEANSOFACOMPUTERCODEBASEDONTHEDISTINCTELEMENTMETHODITISSHOWNTHAT,WHILEBOTHMETHODSLEADTOALMOSTIDENTICALRESULTSFORADENSELYFRACTUREDROCKMASS,ASIZEORSCALEEFFECTISOBSERVEDINTHECASEOFALIMITEDNUMBEROFJOINTSTHESECONDPARTOFTHEPAPERISTHENDEVOTEDTOPROPOSINGAMETHODWHICHATTEMPTSTOCAPTURESUCHASCALEEFFECT,WHILESTILLTAKINGADVANTAGEOFAHOMOGENIZATIONTECHNIQUETHISISACHIEVEDBYRESORTINGTOAMICROPOLARORCOSSERATCONTINUUMDESCRIPTIONOFTHEFRACTUREDROCKMASS,THROUGHTHEDERIVATIONOFAGENERALIZEDMACROSCOPICFAILURECONDITIONEXPRESSEDINTERMSOFSTRESSESANDCOUPLESTRESSESTHEIMPLEMENTATIONOFTHISMODELISNALLYILLUSTRATEDONASIMPLEEXAMPLE,SHOWINGHOWITMAYACTUALLYACCOUNTFORSUCHASCALEEFFECTPROBLEMSTATEMENTANDPRINCIPLEOFHOMOGENIZATIONAPPROACHTHEPROBLEMUNDERCONSIDERATIONISTHATOFAFOUNDATIONBRIDGEPIERORABUTMENTRESTINGUPONAFRACTUREDBEDROCKFIG1,WHOSEBEARINGCAPACITYNEEDSTOBEEVALUATEDFROMTHEKNOWLEDGEOFTHESTRENGTHCAPACITIESOFTHEROCKMATRIXANDTHEJOINTINTERFACESTHEFAILURECONDITIONOFTHEFORMERWILLBEEXPRESSEDTHROUGHTHECLASSICALMOHRCOULOMBCONDITIONEXPRESSEDBYMEANSOFTHECOHESIONANDTHEFRICTIONANGLENOTETHATTENSILESTRESSESMCMWILLBECOUNTEDPOSITIVETHROUGHOUTTHEPAPERLIKEWISE,THEJOINTSWILLBEMODELEDASPLANEINTERFACESREPRESENTEDBYLINESINTHEGURESPLANETHEIRSTRENGTHPROPERTIESAREDESCRIBEDBYMEANSOFACONDITIONINVOLVINGTHESTRESSVECTOROFCOMPONENTS,ACTINGATANYPOINTOFTHOSEINTERFACESACCORDINGTOTHEYIELDDESIGNORLIMITANALYSISREASONING,THEABOVESTRUCTUREWILLREMAINSAFEUNDERAGIVENVERTICALLOADQFORCEPERUNITLENGTHALONGTHEOZAXIS,IFONECANEXHIBITTHROUGHOUTTHEROCKMASSASTRESSDISTRIBUTIONWHICHSATISESTHEEQUILIBRIUMEQUATIONSALONGWITHTHESTRESSBOUNDARYCONDITIONS,WHILECOMPLYINGWITHTHESTRENGTHREQUIREMENTEXPRESSEDATANYPOINTOFTHESTRUCTURETHISPROBLEMAMOUNTSTOEVALUATINGTHEULTIMATELOADQBEYONDWHICHFAILUREWILLOCCUR,OREQUIVALENTLYWITHINWHICHITSSTABILITYISENSUREDDUETOTHESTRONGHETEROGENEITYOFTHEJOINTEDROCKMASS,INSURMOUNTABLEDIFCULTIESARELIKELYTOARISEWHENTRYINGTOIMPLEMENTTHEABOVEREASONINGDIRECTLYASREGARDS,FORINSTANCE,THECASEWHERETHESTRENGTHPROPERTIESOFTHEJOINTSARECONSIDERABLYLOWERTHANTHOSEOFTHEROCKMATRIX,THEIMPLEMENTATIONOFAKINEMATICAPPROACHWOULDREQUIRETHEUSEOFFAILUREMECHANISMSINVOLVINGVELOCITYJUMPSACROSSTHEJOINTS,SINCETHELATTERWOULDCONSTITUTEPREFERENTIALZONESFORTHEOCCURRENCEOFFAILUREINDEED,SUCHADIRECTAPPROACHWHICHISAPPLIEDINMOSTCLASSICALDESIGNMETHODS,ISBECOMINGRAPIDLYCOMPLEXASTHEDENSITYOFJOINTSINCREASES,THATISASTHETYPICALJOINTSPACINGLISBECOMINGSMALLINCOMPARISONWITHACHARACTERISTICLENGTHOFTHESTRUCTURESUCHASTHEFOUNDATIONWIDTHBINSUCHASITUATION,THEUSEOFANALTERNATIVEAPPROACHBASEDONTHEIDEAOFHOMOGENIZATIONANDRELATEDCONCEPTOFMACROSCOPICEQUIVALENTCONTINUUMFORTHEJOINTEDROCKMASS,MAYBEAPPROPRIATEFORDEALINGWITHSUCHAPROBLEMMOREDETAILSABOUTTHISTHEORY,APPLIEDINTHECONTEXTOFREINFORCEDSOILANDROCKMECHANICS,WILLBEFOUNDINDEBUHANETAL1989DEBUHANANDSALENC,ON1990BERNAUDETAL1995MACROSCOPICFAILURECONDITIONFORJOINTEDROCKMASSTHEFORMULATIONOFTHEMACROSCOPICFAILURECONDITIONOFAJOINTEDROCKMASSMAYBEOBTAINEDFROMTHESOLUTIONOFANAUXILIARYYIELDDESIGNBOUNDARYVALUEPROBLEMATTACHEDTOAUNITREPRESENTATIVECELLOFJOINTEDROCKBEKAERTANDMAGHOUS1996MAGHOUSETAL1998ITWILLNOWBEEXPLICITLYFORMULATEDINTHEPARTICULARSITUATIONOFTWOMUTUALLYORTHOGONALSETSOFJOINTSUNDERPLANESTRAINCONDITIONSREFERRINGTOANORTHONORMALFRAMEOWHOSEAXESAREPLACED21ALONGTHEJOINTSDIRECTIONS,ANDINTRODUCINGTHEFOLLOWINGCHANGEOFSTRESSVARIABLESSUCHAMACROSCOPICFAILURECONDITIONSIMPLYBECOMESWHEREITWILLBEASSUMEDTHATACONVENIENTREPRESENTATIONOFTHEMACROSCOPICCRITERIONISTODRAWTHESTRENGTHENVELOPERELATINGTOANORIENTEDFACETOFTHEHOMOGENIZEDMATERIAL,WHOSEUNITNORMALNIISINCLINEDBYANANGLEAWITHRESPECTTOTHEJOINTDIRECTIONDENOTINGBYANDTHENORMALANDSHEARCOMPONENTSOFTHESTRESSVECTORACTINGUPONSUCHAFACET,ITISPOSSIBLETODETERMINEFORANYVALUEOFATHESETOFADMISSIBLESTRESSES,DEDUCEDFROMCONDITIONS3EXPRESSEDINTERMSOFN,THECORRESPONDINGDOMAINHASBEENDRAWNINFIG2INTHE1212PARTICULARCASEWHEREMTWOCOMMENTSAREWORTHBEINGMADE1THEDECREASEINSTRENGTHOFAROCKMATERIALDUETOTHEPRESENCEOFJOINTSISCLEARLYILLUSTRATEDBYFIG2THEUSUALSTRENGTHENVELOPECORRESPONDINGTOTHEROCKMATRIXFAILURECONDITIONISTRUNCATEDBYTWOORTHOGONALSEMILINESASSOONASCONDITIONISFULLLEDMJH2THEMACROSCOPICANISOTROPYISALSOQUITEAPPARENT,SINCEFORINSTANCETHESTRENGTHENVELOPEDRAWNINFIG2ISDEPENDENTONTHEFACETORIENTATIONATHEUSUALNOTIONOFINTRINSICCURVESHOULDTHEREFOREBEDISCARDED,BUTALSOTHECONCEPTSOFANISOTROPICCOHESIONANDFRICTIONANGLEASTENTATIVELYINTRODUCEDBYJAEGER1960,ORMCLAMOREANDGRAY1967NORCANSUCHANANISOTROPYBEPROPERLYDESCRIBEDBYMEANSOFCRITERIABASEDONANEXTENSIONOFTHECLASSICALMOHRCOULOMBCONDITIONUSINGTHECONCEPTOFANISOTROPYTENSORBOEHLERANDSAWCZUK1977NOVA1980ALLIROTANDBOCHLER1981APPLICATIONTOSTABILITYOFJOINTEDROCKEXCAVATIONTHECLOSEDFORMEXPRESSION3OBTAINEDFORTHEMACROSCOPICFAILURECONDITION,MAKESITTHENPOSSIBLETOPERFORMTHEFAILUREDESIGNOFANYSTRUCTUREBUILTINSUCHAMATERIAL,SUCHASTHEEXCAVATIONSHOWNINFIG3,WHEREHANDDENOTETHEEXCAVATIONHEIGHTANDTHESLOPEANGLE,RESPECTIVELYSINCENOSURCHARGEISAPPLIEDTOTHESTRUCTURE,THESPECICWEIGHTOFTHECONSTITUENTMATERIALWILLOBVIOUSLYCONSTITUTETHESOLELOADINGPARAMETEROFTHESYSTEMASSESSINGTHESTABILITYOFTHISSTRUCTUREWILLAMOUNTTOEVALUATINGTHEMAXIMUMPOSSIBLEHEIGHTHBEYONDWHICHFAILUREWILLOCCURASTANDARDDIMENSIONALANALYSISOFTHISPROBLEMSHOWSTHATTHISCRITICALHEIGHTMAYBEPUTINTHEFORMWHEREJOINTORIENTATIONANDKNONDIMENSIONALFACTORGOVERNINGTHESTABILITYOFTHEEXCAVATIONUPPERBOUNDESTIMATESOFTHISFACTORWILLNOWBEDETERMINEDBYMEANSOFTHEYIELDDESIGNKINEMATICAPPROACH,USINGTWOKINDSOFFAILUREMECHANISMSSHOWNINFIG4ROTATIONALFAILUREMECHANISMFIG4ATHERSTCLASSOFFAILUREMECHANISMSCONSIDEREDINTHEANALYSISISADIRECTTRANSPOSITIONOFTHOSEUSUALLYEMPLOYEDFORHOMOGENEOUSANDISOTROPICSOILORROCKSLOPESINSUCHAMECHANISMAVOLUMEOFHOMOGENIZEDJOINTEDROCKMASSISROTATINGABOUTAPOINTWITHANANGULARVELOCITYTHECURVESEPARATINGTHISVOLUMEFROMTHERESTOFTHESTRUCTUREWHICHISKEPTMOTIONLESSISAVELOCITYJUMPLINESINCEITISANARCOFTHELOGSPIRALOFANGLEANDFOCUSTHEVELOCITYMDISCONTINUITYATANYPOINTOFTHISLINEISINCLINEDATANGLEWMWITHRESPECTTOTHETANGENTATTHESAMEPOINTTHEWORKDONEBYTHEEXTERNALFORCESANDTHEMAXIMUMRESISTINGWORKDEVELOPEDINSUCHAMECHANISMMAYBEWRITTENASSEECHENANDLIU1990MAGHOUSETAL1998WHEREANDDIMENSIONLESSFUNCTIONS,AND1AND2ANGLESEWMESPECIFYINGTHEPOSITIONOFTHECENTEROFROTATIONSINCETHEKINEMATICAPPROACHOFYIELDDESIGNSTATESTHATANECESSARYCONDITIONFORTHESTRUCTURETOBESTABLEWRITESITFOLLOWSFROMEQS5AND6THATTHEBESTUPPERBOUNDESTIMATEDERIVEDFROMTHISRSTCLASSOFMECHANISMISOBTAINEDBYMINIMIZATIONWITHRESPECTTO1AND2WHICHMAYBEDETERMINEDNUMERICALLYPIECEWISERIGIDBLOCKFAILUREMECHANISMFIG4BTHESECONDCLASSOFFAILUREMECHANISMSINVOLVESTWOTRANSLATINGBLOCKSOFHOMOGENIZEDMATERIALITISDENEDBYVEANGULARPARAMETERSINORDERTOAVOIDANYMISINTERPRETATION,ITSHOULDBESPECIEDTHATTHETERMINOLOGYOFBLOCKDOESNOTREFERHERETOTHELUMPSOFROCKMATRIXINTHEINITIALSTRUCTURE,BUTMERELYMEANSTHAT,INTHEFRAMEWORKOFTHEYIELDDESIGNKINEMATICAPPROACH,AWEDGEOFHOMOGENIZEDJOINTEDROCKMASSISGIVENAVIRTUALRIGIDBODYMOTIONTHEIMPLEMENTATIONOFTHEUPPERBOUNDKINEMATICAPPROACH,MAKINGUSEOFOFTHISSECONDCLASSOFFAILUREMECHANISM,LEADSTOTHEFOLLOWINGRESULTSWHEREUREPRESENTSTHENORMOFTHEVELOCITYOFTHELOWERBLOCKHENCE,THEFOLLOWINGUPPERBOUNDESTIMATEFORKRESULTSANDCOMPARISONWITHDIRECTCALCULATIONTHEOPTIMALBOUNDHASBEENCOMPUTEDNUMERICALLYFORTHEFOLLOWINGSETOFPARAMETERSTHERESULTOBTAINEDFROMTHEHOMOGENIZATIONAPPROACHCANTHENBECOMPAREDWITHTHATDERIVEDFROMADIRECTCALCULATION,USINGTHEUDECCOMPUTERSOFTWAREHARTETAL1988SINCETHELATTERCANHANDLESITUATIONSWHERETHEPOSITIONOFEACHINDIVIDUALJOINTISSPECIED,ASERIESOFCALCULATIONSHASBEENPERFORMEDVARYINGTHENUMBERNOFREGULARLYSPACEDJOINTS,INCLINEDATTHESAMEANGLE10WITHTHEHORIZONTAL,ANDINTERSECTINGTHEFACINGOFTHEEXCAVATION,ASSKETCHEDINFIG5THECORRESPONDINGESTIMATESOFTHESTABILITYFACTORHAVEBEENPLOTTEDAGAINSTNINTHESAMEGUREITCANBEOBSERVEDTHATTHESENUMERICALESTIMATESDECREASEWITHTHENUMBEROFINTERSECTINGJOINTSDOWNTOTHEESTIMATEPRODUCEDBYTHEHOMOGENIZATIONAPPROACHTHEOBSERVEDDISCREPANCYBETWEENHOMOGENIZATIONANDDIRECTAPPROACHES,COULDBEREGARDEDASASIZEORSCALEEFFECTWHICHISNOTINCLUDEDINTHECLASSICALHOMOGENIZATIONMODELAPOSSIBLEWAYTOOVERCOMESUCHALIMITATIONOFTHELATTER,WHILESTILLTAKINGADVANTAGEOFTHEHOMOGENIZATIONCONCEPTASACOMPUTATIONALTIMESAVINGALTERNATIVEFORDESIGNPURPOSES,COULDBETORESORTTOADESCRIPTIONOFTHEFRACTUREDROCKMEDIUMASACOSSERATORMICROPOLARCONTINUUM,ASADVOCATEDFORINSTANCEBYBIOT1967BESDO1985ADHIKARYANDDYSKIN1997ANDSULEMANDMULHAUS1997FORSTRATIEDORBLOCKSTRUCTURESTHESECONDPARTOFTHISPAPERISDEVOTEDTOAPPLYINGSUCHAMODELTODESCRIBINGTHEFAILUREPROPERTIESOFJOINTEDROCKMEDIA均质各向异性裂隙岩体的破坏特性概述由于岩体表面的裂隙或节理大小与倾向不同，人们通常把岩体看做是非连续的。尽管裂隙或节理表现出的力学性质要远远低于岩体本身，但是它们在岩体结构性质方面起着重要的作用，岩体本身的变形和破坏模式也主要是由这些节理所决定的。从地质力学工程角度而言，在涉及到节理岩体结构的设计方法中，软弱表面是一个很重要的考虑因素。解决这种问题最简单的方法就是把岩体看作是许多完整岩块的集合，这些岩块之间有很多相交的节理面。这种方法在过去的几十年中被设计者们广泛采用，其中比较著名的是“块体理论”，该理论试图从几何学和运动学的角度用来判别潜在的不稳定岩块（GOODMANMAGHOUS等1998）。现在可以精确地表示平面应变条件下，两组相互正交节理的特殊情况，建立沿节理方向的正交坐标系O21，并引入下列应力变量宏观破坏条件可简化为其中，假定宏观准则的一种简便表示方法是画出均质材料倾向面上的强度包络线，其单位法线N的倾角为节理的方向，分别用N和N表示这个面上的正应力和切应力，用,表示条件（3），推求出一组许可应力N,N,然后求解出倾角。当121M时，相应的区域表示如图2所示，并对此做出两个注解如下1从图2中可以清楚的看出，节理的存在导致了岩体强度的降低。通常当时，强度包络线和岩基破坏条件相一致，其前半部分被两个正交的半条线切MJH去。2宏观各向异性很显著。比如，图2中的强度包络线决定于方位角。应该抛弃固有曲线和各向异性粘聚力与摩擦角的概念，其中后一个概念是由JAEGER（1960）或MCLAMOREGRAY（1967）所引入的。通过莫尔库伦条件进行扩展，利用各向异性张量的方法来描述各向异性也