摘要本設計包括三個部分：一般部分、專題部分和翻譯部分。一般部分為永煤集團城郊煤礦300萬t/a新井設計。全篇共分為十個部分：礦井概況及井田地質特征、井田境界及儲量、礦井工作制度、設計生產能力及服務年限、井田開拓、準備方式、采煤方法、井下運輸、礦井提升、礦井通風與安全和礦井主要經濟技術指標。城郊礦位于河南省永城市境內。井田南北長約12km，東西寬約11km，勘探面積約103km2。井田內可采煤層為二2煤層，其賦存穩定，平均厚度3.5m，煤層最小傾角4°，最大傾角15°，平均傾角為8°。井田內工業儲量為4.4855億t，可采儲量為3.3059億t。礦井平均涌水量為180～220m3/h，井田中各煤層沼氣含量一般小于0.5cm3/g，屬低沼氣礦井。各煤層均無煤塵爆炸危險。各煤層均屬不自燃發火煤層；地溫一般低于30℃。城郊煤礦年設計生產能力為300萬t/a，服務年限為78.7年。采用立井開拓，石門暗斜井延深的開拓方式。工作制度為“三八”制。第一水平標高為－500m，第二水平標高為-860m。礦井采用綜合機械化采煤法，一次采全高。礦井布置兩個綜采工作面，面長200m。煤炭通過膠帶輸送機運輸。礦井通風方式為分區域式通風。專題部分：專題題目為“深井軟巖巷道支護原理與技術”。翻譯部分：翻譯題目為“巷道錨桿支護設計視為均質結構的數值方法”。關鍵詞：立井；暗斜井；帶區；膠帶運輸；分區域式ABSTRACTThisdesigncontainsthreeparts:thegeneral，thespecialsubjectandthetranslation.ThegeneralpartisanewdesignofChengjiaoMineinYongchengcoal&electricitycombine.Thewholearticleisdividedintotenparts:theoutlineofthemine,theminefieldgeology,theboundaryandreserves,thedesignedproductivecapacity,theservicelifeandworkingarea,thecoaltransportation,theminelifting,theventilationandsafety,andthemaineconomicalandtechnologicalindexofthemine.TheChengjiaoMinefieldliesinYongchenginHenanprovince.Theboundaryoftheminefieldruns12kmfromnorthtosouthand11kmfromwesttoeast.Thetotalareaofthemineisabout103km2.Thereisonlyoneexploringlayer--numbertwo.Itsaveragethicknessoftheseamis3.5mandit’sstableandflatlyinclined.Itsdipangleis8degreeonaverage.Theindustryreservesoftheminefieldare448.55milliontonsandtheuseablereservesare330.59milliontons.TheaverageinflowrateinChengjiaomineis180~220m3/h.Itisalowergassymine.Thecoaldustdoesn’thaveexplosionhazardaswellastheself-combustiontendency.TheproductivecapacityofChengjiaoMineis3.0milliontonsperyear，andtheservicelifeis78.7years.Theworksystemis3-shiftwitha8-hourworkday.There’retwoworkinglevelsinthemine.Thefirstdevelopmentlevelislocatedatthe-500m,andthesecondisatthelevelof-860m.ThecomprehensivemechanizedcavingmethodisusedinChengjiaoMine.Therearetwoworkingfacesinthemine.Itiscomprehensivemechanizedcoalface.Thelengthofthefaceis200m,andthedesignedproductivecapacityofthefaceis3.0milliontonsperyear.Coalistransportedbybeltconveyerandthe\o"查找:regional"regionalventilationsystemisusedinChengjiao.Thetitleofspecialsubjectis“Principlesandtechniquesofdeepsoftrocksupported-roadway”.Thetitleoftranslationpartis“Anumericalapproachfordesignofbolt-supportedtunnelsregardedashomogenizedstructures”.Keywords：shaft;darkinclined;stripdistrict;belttransport;\o"查找:regional"regional

目錄TOC\h\z\t"標題,3,一級標題,1,二級標題,2,專題題目,1"一般部分1礦井概述及井田地質特征 頁英文原文Anumericalapproachfordesignofbolt-supportedtunnelsregardedashomogenizedstructuresDeniseBernauda,SamirMaghousa,*,PatrickdeBuhanb,EduardoCoutoaaDepartmentofCivilEngineering,FederalUniversityofRioGrandedoSul,Av.OsvaldoAranha,99,90540-041PortoAlegre–RS,BrazilbUnitédeRechercheNavier,EcoleNationaledesPontsetChaussées,Marne-la-Vallée,FranceAbstract:Thispaperisdevotedtothetheoreticalmodelingandnumericalsimulationbyhomogenizationapproachofthebehaviourofatunnelreinforcedbyfullygroutedbolts,regardedasperiodicallydistributedlinearinclusions.Owingtothefactthatadirectnumericalsimulationwouldrequirethegroundandthereinforcingboltsbeseparatelydiscretized,leadingthustoahighlycomplexandoversizedproblem,ahomogenizationprocedureisdeveloped,aimedatcircumventingthedifficultiesconnectedwiththeimplementationofadirectsimulation.Thesituationsofreinforcementbyradialboltsandhorizontalanchorsinstalledaheadtheexcavationfacearebothinvestigated.ConsideringaDrucker–Pragerrockmaterial,elastoplasticconstitutiveequationsareformulatedfortheboltedrockmassregardedasahomogenizedanisotropicmediumatthemacroscopicscale.Specialattentionispaidtothedescriptionofthealgorithmofplasticintegrationinvolvedinthefiniteelementimplementation.Atthisrespect,closed-formexpressionsarederivedforthestressprojectionontothemacroscopicyieldsurface.Thefiniteelementprocedureisthuscarriedoutforsimulatingtheadvancementofabolt-supportedtunnelandcomputingthedisplacementsofthetunnelwallsandthefacingastheexcavationproceeds.Aparametricstudy,varyingsomerelevantparametersdefiningtheboltreinforcementscheme,isundertakenbymeansofthefiniteelementtool.Thecombinationofrockboltingwithaclassicalliningsupportsystemsuchasashotcretelayerisalsoexamined,thusprovidingsomeguidelinesfortheoptimaldesignofthereinforcementpattern.Keywords:Tunnel,Fullygroutedbolts,Homogenization,Elastoplasticity,Finiteelementmethod1.IntroductionDesigningappropriatesupportsystemsfortunnelstogetherwiththeabilitytoreliablypredicttheircontributiontocontrollingthedeformationofthesurroundinggroundremainamajorconcerninundergroundengineering.Inthiscontext,theuseofmetallicorfiber-glassboltsisnowadaysconsideredasaneffectivereinforcementtechniquefortunnelsexcavatedinsoftrocks,specificallyintheframeworkofNATMtunnelingortheso-called‘convergence-confinement’approachfortunnelconstruction(Panet,1995).Fullygroutedradialboltingcontributestocontrollingtheradialdisplacementsofthetunnelwalls,thusmaintainingthetunnelconvergencewithinanallowablelimit,compatiblewithsubsequentoperatingconditions.Similarly,groutedhorizontalfiberglassboltsinstalledaheadtheexcavationfaceplayanimportantroleduringtheexcavationprocessbyimprovingthedegreeofstabilityofthetunnelface.Rockboltinghasbeensuccessfullyappliedinanumberoftunnelprojectsandtheincreasinguseofthisreinforcementtechniqueinthefieldofrocktunnellinghasbeenfavouredmainlybythefollowingreasons:(1)itiseasytocarryout,(2)itisveryflexiblesincetheboltdensitycanbepunctuallyadaptedtoaccountforlocalgeotechnicalproperties,and(3)itisefficientwhencomparedforexampletoaclassicalsteelframesupport,whichrequiresheavyequipmentforinstallation.2.TheboltedtunnelasahomogenizedmediumThetunnelunderconsiderationisahorizontalcylindricalundergroundopeningofradiusR,excavatedinahomogeneousmedium.Thisstructureisreinforcedbyasystemofbolts,introducedintotherockmassastheexcavationprocessproceeds.Perfectadherenceisassumedbetweentheboltsandtherock.Theboltsareregularlydisposedfollowingtheradialdirectionortheface(i.e.,boltsplacedatthetunnelface).Fromapracticalpointofview,thesetwokindsofboltingcanbeusedseparatelyorinassociation.ThegeometricalcharacteristicsoftheproblemaredefinedinFig.1:Radialboltsplacedaroundthetunnel,perpendiculartotheaxiszofthetunnel.Theyareregularlydistributedalongthetunnelaxis(horizontalspacingpr)andwithineachtransversalsection(angularspacingβr).Theradialboltlengthisdenotedbylr.Faceboltsplacedatthetunnelface,paralleltothetunnelaxisz.Thecorrespondinglengthislf.Theyareregularlydistributedatthetunnelfacefollowingarectangulargridpf×bf.Fig.1.Geometricalcharacteristicsoftheproblem.Forsakeofsimplicity,thefollowingabbreviationswillbeusedinthesequel.Thezoneoftherockmassreinforcedbyradialboltsisreferredtoby(ZR),whilethezoneaheadthetunnelfacereinforcedbyfaceboltsisdesignatedby(ZF).Providedthatthedensityofthereinforcementpatternsin(ZR)and(ZF)isdenseenough,i.e.thatthequantitiesβr/π,pr/R,pf/Randbf/Raremuchsmallwithrespecttounity,theboltedrockcanthereforeberegardedfromamacroscopicviewpoint(atthescaleofthetunnel)asahomogenizedanisotropicmedium.Atthisscale,region(ZR)isalocallyorthotropiccontinuumabouttheradialdirectioner,andtheregion(ZF)ishomogeneousorthotropicaboutdirectionez.Suchahomogenizationprocedureconsiderablysimplifiestheinitialproblem,sincethecomponentsoftheboltedrockmasshavenomoretobeconsideredseparately,thusavoidingthedifficultiesconnectedwithfinediscretizationthatadirectfiniteelementanalysiswouldrequireforcapturingthestrongheterogeneityoftheboltedzones.Fig.2.Representativeelementaryvolumesandhomogenizedstructure.TherepresentativeelementaryvolumesdisplayedinFig.2areprismaticandparallelepipedicfor(ZR)and(ZF),respectively.Theyemphasizetherelevantreinforcementparametersinvolvedinthepresentanalysis:Thevolumeproportionofreinforcementg,definedastheratiobetweenthecross-sectionareaofthebolts(SrforradialboltsandSfforfacebolts)andthecorrespondingareaoftherepresentativevolume:(1)whereSr(resp.Sf)referstothetransversalareaoftheradial(resp.face)bolts.Thisnon-dimensionalparameterisconstantin(ZF),whileitappearstobeadecreasingfunctionofthedistancertothetunnelaxisin(ZR)(r:distancefollowingtheradialdirectioner).Thisissimplyduetothefactthatinthelatterregion,theboltspacingincreasesasmovingawayfromthetunnelwall.Thedensityofreinforcementd,definedasthenumberofboltsperunitareaonthetunnelwall(r=R)for(ZR)andonthetunnelfacefor(ZF):(2)Parameterδisexpressedinbolts/m2.Theformulationoftheconstitutivelawofthehomogenizedmaterial,fromtheknowledgeofthemechanicalpropertiesofitsindividualconstituents,isachievedfollowingtheprocedureoutlinedinFig.3.Fig.3.Procedureusedfortheformulationoftheconstitutivelawforthehomogenizedmaterial.3.HomogenizedelasticmoduliDerivingthemacroscopicelasticitytensoristhefirststepfortheformulationofconstitutiverelationshipsfortheboltedrockmass.Bothconstituents(rockmaterialandbolts)areassumedtoexhibitisotropicandlinearelasticproperties.Moreprecisely,therockmaterialischaracterizedbyitsLamécoefficients(λm,μm)or,alternativelybytheYoung’smodulusEmandthePoisson’scoefficientνm.Asregardstheelasticpropertiesofthebolts,(λi,μi)or(Ei,νi)willrefertotheLamécoefficientsortheYoung’smodulusandPoisson’scoefficientoftheconstituentmaterialofthebolts.Subscriptsi=randi=f,respectively,refertotheboltsin(ZR)and(ZF).Thevolumeproportionoftheboltreinforcementisquitesmall,thatisη?1(usualvalues:η~10-4–10-3),whereastheboltmaterialismuchstifferthantherockmaterial,thatisEr?EmandEf?Em,itmaybeproved(Greuell,1993)thattheboltedrockmassbehavesmacroscopicallyasanelasticmediumtransverselyisotropicabouttheradialdirectionerandtheaxialdirectionezintheregions(ZR)and(ZF),respectively.TherelationshipbetweenthemacroscopicstresstensorΣandmacroscopicstraintensorεwrites:(3)wherethesubscriptiandthecoefficientKaredefinedas:i=randK=ηr(r)Erinregion(ZR).i=fandK=ηfEfinregion(ZF).ThecoefficientKaccountsforthecontributionoftheboltstotheoverallelasticstiffness.Similarlytothevolumefractionηofreinforcement,thisparameterremainsconstantalong(ZF)anddecreaseswithrin(ZR).Theright-handmemberinrelationship(3)isthesumoftwoterms:thefirsttermsimplycorrespondstotheelasticbehaviouroftherockmaterial,whiletheadditionaltermstandsforthereinforcementduetothebolts.DenotingbyAmthefourth-ordertensorofelasticmodulioftherockmaterial,thelinearrelationships(3)mayconvenientlybeexpressedasfollows:(4)Ahomrepresentsthefourth-ordertensorofhomogenizedelasticmoduli.OneshouldnotethatthisresultisconsistentwiththoseobtainedforinstancebyGerrard(1982a,b).TheelastictensorAhomcanbecharacterisedbythefollowingparameters:ThelongitudinalYoung’smodulus(i.e.elasticmodulusinthedirectionofreinforcementei)(5)ThetransversalYoung’smodulus(6)Theshearmoduli(7)4.Elastoplasticconstitutiveequationsforthehomogenizedmedium4.1.MacroscopicstrengthcriterionThedeterminationofthemacroscopicstrengthcriterionisbasedontheapplicationofthetoolsoftheyielddesignhomogenizationforperiodiccomposites.Atthisrespect,onemayreferforinstancetodeBuhan(1986),deBuhanandSalencon(1990)ordeBuhanandTaliercio(1991).ExtendingtheresultsobtainedbydeBuhanandTaliercio(1991),theyieldfunctionfhomfortheboltedrockmaybeexpressedas:(8)wherefmistheyieldfunctionoftherockmaterialwithoutreinforcement,i=rinregion(ZR)andi=finregion(ZF).TheintervalIisdefinedby(9)representsthestrengthunderuniaxialtensionoftheboltsandkisanon-dimensionalnumberrangingbetween0and1whichaccountsforareductioninthecompressivestrengthoftheboltsduetostructuralbuckling.Clearlyenough,thevaluesofandkmaydependonthereinforcedzoneunderconsideration:(,kr)fortheradialbolts,(,kf)forthefacebolts.Itcanbenotedthatthequantityrepresentsthestrengthoftheboltperunittransverseareaatthecurrentpoint.Across-sectionalviewofthestrengthdomainGhom,definedbytheyieldcondition,inanarbitraryplaneofmacroscopicstresses(Σii,Σhk)issketchedinFig.4.Geometrically,thestrengthdomainGhomcanbeinterpretedinthespaceR6ofmacroscopicstressastheconvexenvelopeoftwodomainsobtainedbytranslatingthestrengthdomainGmoftherockmaterialbyalgebraicdistancesandparalleltotheaxisΣii-axis(Fig.4).Thesetranslationsinthespaceofmacroscopicstressesaretheexpressionofthereinforcementduetothepresenceofbolts.Fig.4.GeometricalrepresentationofthemacroscopicstrengthdomaininastressplaneΣii,Σhk.4.2.ElasticplasticconstitutiveequationsTheconstructionoftheconstitutivebehaviorfortheboltedrockmassstemsfromtheheuristicideathatthemacroscopicstrengthdomainGhomcanberegardedastheelasticitydomainforthehomogenizedmaterialwiththeelasticpropertiesdefinedbythetensorAhomgivenby(4).Suchareasoningconsiststhereforeinmodelingtheboltedrockasahomogenizedelasticperfectlyplasticmaterial,wherethestrengthcriterionisadoptedasaplasticitycriterion.Thismeansinparticularthatthehardeningwhichwouldresultatthemacroscopicscalefromarigoroushomogenizationprocess(Suquet,1985)isneglected.Inthecontextofinfinitesimalstrains,thisconstitutivelawisexpressedby(10)whereisthetotalstrainrate,thecorrespondingelasticpartandtheplasticpart.TheelasticpartofthestrainrateisrelatedtostressrateΣbymeansofthemacroscopicelastictensor:(11)Asregardstheevolutionsoftheplasticstrain,anassociatedplasticflowruleisassumedatthemacroscopicscale.Accordingly,isgivenbythenormalityrule:(12)wheredenotestheplasticmultiplier.Iftherockmaterialexhibitsplasticdilatancyproperties,asimplifiedwaytoaccountforatthemacroscopicscalemaybeachievedasfollows.Aplasticpotentialghomcanbedefinedforthehomogenizedmaterialfromtheexpressionoffhombysubstitutinginthelatter,thefrictionangleφmoftherockmaterialbytheplasticdilatancyangleψm:.5.ThecaseofDrucker–Pragerrockmatrix5.1.ExplicitformulationoftheconstitutiverelationshipTheyieldfunctionofthehomogenizedmaterialdefinedby(8)canberewrittenas:(13)withinterval.Theconvexityoftheyieldfunctionwithrespecttoitsargumentsimpliesthat:(14)whereistheprojectionontointervalIofthesingle(convexityoffm)solutionofequation(15)withrespecttounknown.Thismeansthat(16)Tocompletethecharacterisationoftheconstitutivelaw,andmorespecificallytheformulationoftheplasticflowrule(12),itisnecessarytospecifytheexpressionof.Remindingdefinition(16)of,itisshowninBernaudetal.(1995)that:(17)ThisrelationshipwillnowbeillustratedinthecasewhentherockmaterialobeysaDrucker–Prageryieldcondition.Introducingthenormofasecond-ordertensor,theDrucker–Pragercriterionmaybeexpressedinthefollowingform:(18)wheres=dev(σ)isthedeviatoricpartofσandσmrepresentstheelasticlimitofthematerialunderuniaxialtensilestress.Thescalarαmisanon-dimensionalparameterrangingbetween0(criterionofvonMises)and1,whichaccountsforthedependenceofthecriteriononthehydrostaticstress.Observingthat(19)andsolvingEq.(15)yields(20)whereS=dev(Σ)denotesthedeviatoricpartofthemacroscopicstresstensor.Thecorrespondingvalueofσ*(Σ)canthereforebecalculatedbymeansofEqs.(16).AlternativelytoEqs.(16),aconvenientwaytocharacterizeσ*(Σ)consistsinwriting(21)with(22)Itisrecalledthatthesubscript‘i’takesvaluerinthezonereinforcedbyradialbolts(i.e.,RZ),andvaluezalongthezonereinforcedbyfacebolts(i.e.,FZ).Actually,theabovecharacterizationofσ*(Σ)provestobeusefulforthetechnicaldevelopmentsprovidedinSection5.2.Finally,expression(17)reducesinthepresentcaseofDrucker–Pragercriterion(18)to:(23)5.2.NumericalimplementationThissectiondealswiththefiniteelementimplementationoftheanisotropicelasticperfectlyplasticconstitutivelawformulatedaboveforthehomogenizedboltedrockmass.Suchconstitutivelawisdescribedbythesetofequations(10)–(12).Theiterativealgorithmusedforplasticity(returnmapping)requiresbeingabletocomputetheprojectionofanystressstateontotheconvexelasticdomainGhom.AdetaileddescriptionofsuchaniterativealgorithmmaybefoundforexampleinCrisfield(1991)orSimoandHughes(1998).LetΣbeagivenstressstatelyingoutsidedomainGhom,whichcanbeexpressedbyconditionfhom(Σ)>0.TheprojectionofΣdenotedby(Fig.5)ontotheconvexGhomisdefinedby(24)whereistheLagrangemultiplier.Fig.5.ProjectionofΣ(inthesenseoftheelasticscalarproduct)ontotheelasticdomainGhom.Atwo-stageprocedureisusedinordertomakeexplicittheaboveequationinthecaseofaDrucker–Pragerrockmatrix.Step1:Firstofall,denotingbyσ*(Σ)andσ*()thescalarsdefinedthroughEq.(19)andassociated,respectively,withΣand,itwillbeestablishedthat.Indeed,introducingexpression(4)ofthehomogenizedelasticitytensorAhominto(24)yields(25)with(26)isthedeviatoricpartof(seeEq.(22)).Takingthedeviatoricpartofbothmembersin(25),itcomesoutthat(27)The(i,i)componentintheaboveequationreads(28)Combining(27)and(28)yields(29)whichinturnimplies(30)Takingintoaccount(20),theconjunctionof(28)and(30)leadstothefundamentalidentity(31)whichisonthebasisoftheproofofidentity.Step2:WenowproceedtothedeterminationoftheprojectionofΣ.Naturally,thetwosituationsandhavetobedistinguished.,thenandbyvirtueofEq.(19).Introducingthelatterconditioninto(25)yields(32)andthus(33)Relationship(23)expressedintermsofmeanpart(i.e.,hydrostaticcomponent)reads(34)inwhichconditiondefiningthevalueofhasbeenused.ItisrecalledthatthebulkmodulusKmoftherockmaterialisgivenby.CombiningEqs.(33)and(34)withconditionleadsto(35)TheabovevalueoftheLagrangemultiplierisintroducedinto(30)and(32)andtheexpressionoftheprojectionishenceobtained(36),thenor.Itisshowninthiscasethat(37)where(38),AandBbeingcomputednumericallyasfunctionsofΣ.6.Finiteelementanalysis:geometrymodelandbasicassumptionsWeconsiderthesimplifiedconfigurationofacirculartunnelofradiusRexcavatedatgreatdepthH?Rinahomogeneousandisotropicrockmassinitiallysubmittedahydrostaticstressfieldσ0=-P01(Fig.6).Theinitial‘‘confining”stressisassumedtobeconstantP0=γH,whereγisthespecificweightoftherock.Indeed,sincethedepthismuchgreaterthanthetunnelradius,theeffectofgravityinthevicinityofthetunnelcanbeomittedalongtheanalysis(γR?P0).Thetwokindofboltreinforcementareconsideredherein:radialboltswithcharacteristics(length,transversalarea,densityofreinforcement)=(lr,Sr,δr)andfaceboltswithcharacteristics(lf,Sf,δf).Theradialboltsareplacedintotherockmassinallradialdirection(cross-sectionAA')atadistanced0bfromthetunnelfacing.Thefaceboltsareintroducedatthetunnelfacefollowingaregulardistribution,symmetricwithrespecttothecenterr=0(cross-sectionBB').AccordingtothehomogenizationproceduredescribedinSection2,andunderthengeometryassumptionsabovementioned,thereinforcedzonescanbemodeledasfollows:acylindricalring-shapedzoneparalleltothetunnelaxisdefinedbyR≤r≤R+lr,surroundingthetunnelandmadeupofalocallyorthotropicmaterialabouttheradialdirectioner;acylindricalzoneparalleltothetunnelaxis,ofradiusRandlengthlf,lyingaheadthetunnelfaceandmadeupofalocallyorthotropicmaterialabouttheaxialdirectionez.Fig.6.Bolt-supportedtunnelexcavatedatgreatdepthinanisotropicrockmass:asimplifiedconfiguration.Theoriginalproblemisathree-dimensionaloneasitcanbeobservedfromFig.6,wherethecross-sectionAA'clearlyillustratesthedependenceoftheconstitutivematerialonthecoordinateθ.Incontrast,thehomogenizedproblemturnstobeindependentonthecircumferentialcoordinateθ,andmaythusbetreatedasanaxisymmetricproblemwithinanyplane(r,z)passingthroughthetunnelaxis.Theaimofthepresentparametricstudyistoassesthedisplacementfieldinducedwithintherockmassbytheexcavationprocess,andtogiveaquantitativeinsightonthecontributionofboltstothereductionofradialandaxialconvergenceofthetunnel.7.ConclusionStartingfromtheheuristicideathattheboltedrockmassmaybemodeledatthemacroscopicscale(i.e.,thescaleofthetunnel)asahomogenizedanisotropicmedium,anumericalprocedurebaseduponahomogenizationtechniquehasbeendeveloped.Themainadvantageofsuchanapproachistoavoidtediousnumericaldifficultieswhichshallarisefromanindividualdiscretizationoftheboltedmaterialcomponentsthatadirectapproachwouldimply.Ithasresultedinelaboratingafiniteelementcomputationaltoolspecificallydevisedforsimulatingtheprocessesofexcavation/advancingface/boltplacement,andincorporatingtheconstitutiveequationsofthehomogenizedmaterial.Eventhoughthenumericalanalysiswasrestrictedtoaxisymmetricconditions,quitesignificantresultshavealreadybeenobtainedasregardstherelevantparameterscontrollingtheproblem,providingusefulindicationsfortheoptimaldesignofsuchgeotechnicalstructures.Inaddition,thestudypointedoutthestrongmechanicalcouplingbetweentherockmass,theboltsandthelininginstalledonthetunnelwall.Aproperwaytocapturetheground-reinforcementinteractionrequiresthereforethatthenumericalprocedureaccountsfortheprocessesofexcavation/advancingtunnelfaceandreinforcementplacement.Thetheoreticalmodelingaswellasandthenumericalmethoddevelopedinthispapercanreadilybeappliedtoanalyzethemechanicalbehaviorunderprescribedloadingofsoilstructuresinvolvingreinforcementbylinearinclusions:reinforcedearthwalls,soilnailedretainingstructures,foundationsoilsreinforcedbyadensenetworkofmicropiles(Sudretetal.,1998).Themainissuethatstillneedstobeaddressedconsistsinthethree-dimensionalnumericalimplementationofthemodel.Thiskeycomponentfortunnelmodelingisnecessarytodealwithmorecomplexsituationsasregardsthegeometryandloading:shallowdepthtunnelsforwhichtheinitialstateofstressisnomoreisotropic,non-circularcross-sectionofthetunnel,non-symmetricdistributionoftheboltaroundthetunneloraheadthefacing,etc.Conceptually,theconstitutivemodelinghasbeenproposedwithinathree-dimensionalframework.Thenumericalimplementationwithina3Dsettingistheobjectofacurrentresearch.Finally,itshouldberecalledthatthehomogenizedbehaviorformulatedfortheboltedrockassumesperfectbondingbetweentheboltsandthesurroundingground.Inaddition,thehardeningofthehomogenizedmaterialisnotaccountedforinthemodeling,sincethemacroscopicfailureconditionisinterpretedasplasticityconditionforthehomogenizedmaterial.Thesemodelassumptionsmayactuallyleadtooverestimatethereinforcementeffect(deBuhanetal.,2008).AfirstattempttoaccountforapossibleslippagebetweentheboltsandthesurroundinggroundhasbeenproposedbyWongetal.(2004),whointroducedalimitedstrengthfortheinterfacebolts/ground.Thismethodwasappliedtothepredictionofthebehaviorofabolt-supportedtunnelfacingbymeansofasimplifiedanalyticalmodel.ReferencesBernaud,D.,Rousset,G.,1996.Thenewimplicitmethodfortunnelanalysis.Int.J.Numer.Anal.MethodsGeomech.20(9),673–690.Bernaud,D.,deBuhan,P.,Maghous,S.,1995.Numericalsimulationoftheconvergenceofabolt-supportedtunnelthroughahomogenizationmethod.Int.J.Numer.Anal.MethodsGeomech.19,267–288.Crisfield,M.A.,1991.Non-linearFiniteElementAnalysisofSolidsandStructures.Essentials,vol.1.Wiley,NewYork.deBuhan,P.,Salenern,J.,1990.Yieldstrengthofreinforcedsoilsasanisotropicmedia.In:Boehler,J.P.(Ed.).YieldingDamageandfailureofAnisotropicMedia,pp.791–201.deBuhan,P.,Taliercio,A.,1991.Ahomogenizationapproachtotheyieldstrengthofcompositematerials.Eur.J.Mech.A/Solids10,129–154.deBuhan,P.,Mangiavacchi,R.,Nova,R.,Pelligrini,G.,Salenern,J.,1989.Yielddesignofreinforcedearthwallsbyahomogenizationmethod.Geotechnique39,189–201.deBuhan,P.,Bourgeois,E.,Hassen,G.,2008.Numericalsimulationofboltsupportedtunnelsbymeansofamultiphasemodelconceivedasanimprovedhomogenizationprocedure.Int.J.Numer.Anal.MethodsGeomech.32(13),1597–1615.Gerrard,C.M.,1982a.Equivalentelasticmoduliofrockmassconsistingoforthorhombiclayers.Int.J.RockMech.Min.Sci.Min.Sci.Geomech.Abstr.19,9–14.Gerrard,C.M.,1982b.Reinforcedsoil:anorthorhombicmaterial.IntJ.Geotech.Eng.Div.ASCE108,1460–1474.Greuell,E.,1993.Etudedusoutènementdestunnelsparboulons