Analytical model for the mechanical behaviour of b

RockMech.RockEngng.(1996)29(2),73-97RockMechanicsandRockEngineering9Springer-Verlag1996PrintedinAustriaAnalyticalModelfortheMechanicalBehaviourofBoltedRockJointsSubjectedtoShearingByF.Pellet1andP.Egger2lBonnard&Gardel,ConsultingEngineers,Lausanne,Switzerland2SwissFederalInstituteofTechnology,Lausanne,SwitzerlandSummaryThisstudyproposesanewanalyticalmodelforthepredictionofthecontributionofboltstotheshearstrengthofarockjoint.Themaincharacteristicsofthismodelaretheaccountsfortheinteractionoftheaxialandtheshearforcesmobilisedinthebolt,aswellasthelargeplasticdisplacementsoftheboltoccurringduringtheloadingprocess.Thecompletecurveoftheboltcontributionasafunctionofthedisplacementalongthejointcanbecomputed,andthemaximumboltcontributionisobtainedbydissociatingtheboltcohesionandtheconfinementeffects.Thecomparisonoftheperformancesofthisanalyticalmodelwithtestresultsshowsitscapacitytodescribetheobservedphenomena.Theeffectsofthemostimportantparameterssuchasboltinclination,mechanicalpropertiesofboltmaterial,rockstrengthandjointfrictionangleareclearlyestablishedanddiscussed.1.IntroductionThereinforcementofrockmassesbyuntensionedrockboltsiswidelyusedtoensurestabilityandtorestraindeformationofrockengineeringstructures,suchasrockslopesorundergroundcavities(Fig.1).Themechanicalactionoftheboltis,however,stilldifficulttoassess,especiallyforboltsinstalledinfracturedrockmasses.Asamatteroffact,thereisnounanimouslyapprovedmethodforthedimensioningofthereinforcementsystem.Theeffectivenessofrockboltsdependsonnumerousparameterswhichmustbeconsideredforthestabilityanalysisofreinforcedrockstructures.Themostimportantarethenatureandtheconditionsoftherockmass,aswellasthebondingconditionsandthetypeofthereinforcementelement.Thepresentstudyproposesanewanalyticalmodelforthemechanicalbehaviourofboltedrockjointssubjectedtoshearing.Itallowsthecomputationofboththestrengthandthedeformabilitypropertiesofaboltedrockjoint,whenthefailuremechanisminvolvesslidingdisplacementsalongtherockjoints.Onlyuntensionedfullygroutedrockboltsareinvestigated.74F.PelletandP.EggerFig.1.Stabilityprobleminastratifiedrockmassreinforcedbyuntensionedbolts2.OutlineofpreviousstudiesConceptualModelforBoltedRockJointsWhenaboltedrockjointissubjectedtoshearing,theboltisdeformedasthejointdisplacementincreases(Fig.2).Attheintersectionbetweentheboltandthejoint,aforceRo,ismobilisedinthebolt.ThisforceresultsfromtheaxialforceNo,andtheshearforceQo,actinginthebolt.Fig.2.AboltedrockjointsubjectedtoshearingThestrengtheningeffectoftheboltcanbedividedintwoterms(EggerandPellet,1991).Thefirstone,whichisrelatedtotheparallelcomponentoftheforcetothejoint,canbetreatedasanadditionalcohesion.Thesecondone,whichisconnectedwiththenormalcomponentoftheforceinthebolt,canbeconsideredasanincreaseoftheconfiningstress.Thus,usingtheMohr-Coulombcriterion,thestrengthoftheboltedjointcanbeexpressedbyaddingthereinforcingeffectofthebolttotheintrinsicstrengthofthejoint.Itleadsto:~-=(cj+Acb)+(a~o+A~r,b)tan4~jAnalyticalModelfortheMechanicalBehaviourofBoltedRockJoints75wherecj:jointcohesionq~j:jointfrictionangleO-~o:initialconfiningstressAanb:increaseofconfiningstressprovidedbytheboltAcb:additionalcohesionprovidedbythebolt.Thedifficultyliesinthedeterminationoftheintensitiesandthedirectionsoftheforcesmobilisedintheboltduringtheshearingprocess.ExperimentalStudiesAlotofexperimentalprogramswereperformedinordertodescribeinaqualitativemannerthebehaviourofboltedrockjoint.OneofthefirstwasreportedbyBjurstr6m(1974).Hecarriedoutdirectsheartestsonblocksofgranitereinforcedbyfullygroutedbolts.Then,Azuar(1977),Haas(1981),Dight(1983),Schubert(t984),Spang(1988),EggerandZabuski(1991)andFerrero(1993)continuedexperimentalstudiesondifferenttypesofrockmaterialreinforcedbyvariouselements.Allthesestudiesenableonetodrawthefollowingconclusions:-Whentheanglebetweenthejointplaneandtheboltaxisissmall(i.e.,steeplyinclinedbolt),thedisplacementonthejointattheboltfailureisinsignificant.Ontheotherhand,foraboltplacedperpendiculartothejoint,thefailureoftheboltoccursatalargejointdisplacement.-Whenthestrengthofthehostrockishigh,thejointdisplacementatfailurebecomessmallerandthemaximumboltcontributiondecreasesslightly.-Whenthejointfrictionangleincreases,themaximumboltcontributionisimproved,dependingontheboltorientationwithrespecttothejoint.Thetensioningofthebolthasafavourableeffectbothonthestiffnessandonthestrengthoftheboltedrockjoint.AnalyticalApproachesSeveralequationshavebeendevelopedtopredictthebehaviourofaboltedrockjoint.Thesimplestofthemconsidersonlytheaxialforceactinginthebolt(Bjurstr6m,1974).Bytakingthecomponentsofthisforceonthejointplane,itisthenpossibletocomputethereinforcementeffectofthebolt.Thisapproachdoesnottakeintoaccounttheshearforcemobilisedintheboltnorthedeformationofthebolt(i.e.,boltrotation)acrossthejoint.Asaresult,thedirectionoftheforceactingintheboltisnotaccuratelydescribed.Moreelaboratedexpressionsweredevelopedtotakeintoaccountthedeforma-tionoftheboltduringtheloadingprocess.Mostofthemwerebasedonthefirstordertheoryofthebeamsonelasticsupport