外文翻译锚杆的力学分析及工程应用.docx
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外文翻译锚杆的力学分析及工程应用.docx
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外文翻译锚杆的力学分析及工程应用
英文原文
Rockboltmechanicalanalysisandits
applicationtoengineering
AbstractCombinedwiththe3DFEM,end-anchoredanchorageboltsweresimulatedbyimplicitanchorageboltelement.Implicitanchorageboltelementshideintheelementsofrockmassandextremelysimplifytheelementsubdivision.Thecalculatedvalueofanchorageboltstressislargerthanthemeasuredoneforthemosttime.wefurtheranalyzedthereciprocityofanchorageboltandrockmass,andthendeducedtheanalyticalequationsofanchorageboltstressandrockmassdeformationunderelasto-plasticstate.Theresultsindicatethatitisessentialtorevisetheanchorageboltsstressbyusingtheformulasdeducedwhenrockmassissoftenedorsignificantlydeformed.Finally,acasestudyindicatesthatthecalculatedresultsagreewiththosemeasured.Somehelpfulmethodsareofferdformoreaccuratesimulationofthesupporteffectandanchorageboltsrealstressstate.
Keywordsimplicitelementofbolt,mechanicalanalysisonbolt,elasto-plasticanalysis
Introduction
Loadtransfermechanismandstrengtheningeffectofanchorboltsarethetwomajorareasofanchortheoryathomeandabroad[1].Geotechnicalinvestigatorshaveachievedagreatdealofhelpfuldatumthroughnumericalanalysis,analogtestandin-situsurveymethod[2,3].Reference[4]putforwardimplicitboltelementmethod,appliedittonumericalcalculationoflargeundergroundengineeringandhasgainedgoodeffect.References[5,6]usedsimilarmethodtosolveidiographicproblemsanddevelopedit.Byusing
Mindlin’sdisplacementsolution,Reference[7]deducedtheshearingforcedistributionalonganchoragelengthofanchorageboltwhichwaspulled.
Theresearchesabovejustpartiallyemphasizeoneitherloadtransfermechanismorstrengtheningeffect.Fewbandthetwotogethertostudyeffectively.Usingthecaseoflargeundergroundpowerstation,weanalyzethereciprocityofend-anchoredboltandsurroundingrockdeformationunderelastoplasticstate,andgetsomehelpfulconclusions.
1Basicanalysisandsimplifiedhypotheses
ThemethodofimplicitboltelementextremelysimplifiestheelementsubdivisionofFEM,further-moresimulatesthesupporteffectofrockboltspreferably.TheentireprocessofcalculabilityisprovidedinReference[4].Themethodofimplicitboltelementdistributessupporteffectaveragelyintosurroundingrockelements.Manyliteraturestakeanchorageboltandsurroundingrockascompletecom-
patibledeformation.However,thelocalinfluenceofrockboltoughttobetakenintoconsiderationinfact.Inordertohelpdeduce,thesimplifiedhypothesesaresettledasfollows.
(1)Theanchoredrockmassiselasto-plasticmaterialwhichisdoublepolygonallinearhardened.ShownintheFig.1,E1
istheelasticmodulusofrockmass;E2isthedeformationmodulusofrockmassunderplasticstate.
(2)Therockboltislongenoughtothreadtheplasticzoneofsurroundingrock,andtheanchoragesegmentisalsolongenough.
Fig.1Bilinearconstitutivemodelofanchoredrockmass
(3)Theboltisrelativelylong,andtheinteractionoftwoend-pointsofarockboltisweak.
Thedeformationofrockboltandsurroundingrockunderelasto-plasticstageareshowninFig.2.S1isthecriticalelasticdisplacementofexternalrockmasswhichisfarfromthebolt.Withthestressreleasing,whenthedisplacementvalueofexternalrocknearbytheboltbodyreachesS1,thedisplacementvalueofexternalrockfarfromtheboltbodyshouldreach.
Fig.2Deformationofrockboltandhalf-infinite
bodyofsurroundingrock
2Surroundingrockisunderelasticstage
Theforceofanchoragepalletisannularuniformedloadontheexternalrockmassofhalf-infinitebody.SupposingFistheaxisforceofanchorbolt,accordingtoelasticitymechanicsanalysis,thecentersettlementofrockboltis:
(1)
whereuisthePoisson’sradioofsurroundingrock;qistheconverteduniformedload;a1istheradiusofdrillinghole;a2istheradiusofanchoragepallet;E1istheelasticmodulusofsurroundingrock.
YouChun’a[8]simplifieditasinfinitebody,utilizedKelvin’ssolution,thendeducedtheshearingforcesdistributionofinternalanchoragesegment:
(2)
where,aistheradiusofanchoragebolt;
hereEsisthemoduluselasticityofanchoragebolt.
Accordingtotheload-displacementreciprocaltheorem,thedisplacementofouteranchorageendpointbroughtbythearbitrarypointforcePalonganchoragesegmentis:
(3)
IntegratingEqs.
(2),(3),thedisplacementofouteranchorageend-pointis
(4)
SupposingtherelativedisplacementofexternalanchoragepointandouteranchoragepointisubyFEMcalculation,sotherealrelativedisplacementconsideredanchoragebolteffectis(u-wf-wi).Constitutethebalanceequationofaxialforceofrockboltasfollows:
(5)
DisplacethecounterpointofEq.(5)byEq.
(1)andEq.(4),canattaintherealaxialforceofanchoragebolt:
(6)
3Surroundingrockisunderelasto-plasticstage
Itisacomplicatedprocessthatthesurroundingrockchangesfromcriticalelasticstagetocriticalplasticstage.Wetrytoworkoutthetwovaluesofcriticalstate,andgetothermiddlevaluesbylinearinterpolation.Undersatisfyingtheconditionofengineeringprecision,itcanreflectthattheaxialforceofanchorageboltchangesandanchoragerockmassde-formsunderelasto-plasticstage.
Whensurroundingrockisundercriticalelasticstage,thedisplacementvalueofexternalrockmasswhichisfarfromtheboltbodyisS1;therelativedisplacementofexternalanchoragepointandouteranchoragepointisu1.ThevalueofS1andu1canbeobtainedbyFEMcalculation.Consideringthelocaleffectofrockbolt,therealrelativedisplacementofexternalanchoragepointandouteranchoragepointis:
(7)
where,wf1andwi1arethedisplacementofexternalandouteranchoragepointrespectively,whichareallarousedbytheanchorageforceofrockbolt.Thevalueofwf1andwi1canbederivedfromEqs.
(1),(4),(6).
Withtheloadreleasing,whensurroundingrockdeformfurthertocriticalplasticstage,therealrelativedisplacementoftwopointsofboltis:
(8)
where,wi2isthedisplacementofouteranchoragepoint,whichisbroughtbytheforceofanchorageboltFs2whensurroundingrockisundercriticalplasticstage.
SimplifyingEq.(8)andbuildthebalanceequationoftheaxisforceandstrainofanchoragebolt:
(9)
AccordingtoEq.
(2),wi2ofEq.(9)canbegivenbyEq.(4).Whensurroundingrockisundercriticalplasticstage,theaxisforceofanchorageboltcanbederivedfromEqs.(4),(9):
(10)
Infact,itisimpossiblethatthewholerockmassisunderplasticstage.However,accordingtotheanalysisofelasto-plasticmechanism,whenthethicknessofexternalrockmassisoveronemeter(thisiseasytosatisfyinactualengineering),theerrorofsimplifyingitasplasticstageisverysmall.So,displacingE1byE2inEq.
(1),S2isgivenby:
(11)
Whensurroundingrockisunderelasto-plasticstage,supposingtheFEMcalculatingdisplacementofexternalrockmassisS,correspondingtherelativedisplacementoftwopointsofanchorageboltisup,thesettlementdisplacementofexternalanchoragepointcanbegivenbyinterpolationusingEq.(12):
(12)
Resemblingwiththesecondsection,whensurroundingrockisunderelasto-plasticstage,theaxisforceofanchorageboltcanbegivenby:
(13)
4Engineeringcasestudy
SituatedintheWutaiCountryofShanxiProvince,Xilongchipumped-storagehydropowerstationisalargeproject,itscapacityis
1200MW,thecavesofundergroundpowerstationaremadeupofmainandauxiliarypowerhouse,maintransformerhall,diversiontunnel,tailracetunnel.Mainpowerhousedimensionis150m×23m×50m(lengthwidthheight).Maintransformerhalldimensionis130.4m×16.4m×17.5m(lengthwidthheight).ThesurroundingrockgradeisⅢ,deformationmodulusE1=9GPa,E2=0.9GPa,Poisson’sratiou=0.26,cohesionC=0.95,frictionangleΨ=46.7°.The3DFEMmodelisshowninFig.3.End-anchorageboltsarepartiallyusedonthetoparchofmainpowerhouseandtrans-former,theelasticmoduleofrockboltsE1=210GPa,thediameterψ=32mm,long-shortalternatewith5mand7m,itsarrangementisshowninFig.4.
Fig.3Openingelementsof3DFEMmodel
Fig.4Rockboltsarrangementofaroundcaves
Afterexcavation,theaxisforcesofanchorageboltsareshowninTable1,thecrackstatesofrockmassaroundcaveswithoutandwithrockboltsareshowninFig.5.
Table1Comparisonofcalculationandmeasuring
fortheforceofrockbolts
Serial
numberof
rockbolts
Calculationvalue
ofcomplete
compatibledeformation
Calculationvalue
ofimproved
method
Realvalue
bymeasure
①
125
89
96
②
98
81
75
③
97
78
72
④
83
58
62
⑤
79
62
54
⑥
76
43
49
Fig.5Crackstateofsurroundingrock
FromTable1,weknowthattheaxisforcesofrockboltsbyoldcalculationmethodarelargerthanrealmeasuredvalue,andthecalculationvaluesbythismethodfitbetterwiththerealones.Thisdis-playsthemethodiscorrect.
FromFig.5,weknowthatdamagerangeisconfinedinsmallscopewithanchoragebolts,itagreeswiththosemeasured,implicitanchorageboltselementsimulatesthesupporteffectofrockboltspreferably.
5Conclusions
(1)ImplicitanchorageboltsmethodcanextremelysimplifythemodelsubdivisionofFEMmodel,effectivelysimulatethesupporteffectofrockbolts.
(2)Bythemechanicsanalysisofanchorageboltwithsurroundingrockunderelasticandplasticstage,fromEqs.(6),(13),weknowthatthelocalinfluenceeffectisgreatwhensurroundingrockissoftrock
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