毕业论文之英译汉范本模板.docx
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毕业论文之英译汉范本模板.docx
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毕业论文之英译汉范本模板
InternationalJournalofRockMechanicsandMiningSciences
Analysisofgeo-structuraldefectsinflexuraltopplingfailure
AbbasMajdiandMehdiAmini
Abstract
Thein-siturockstructuralweaknesses,referredtohereinasgeo—structuraldefects,suchasnaturallyinducedmicro—cracks,areextremelyresponsivetotensilestresses。
Flexuraltopplingfailureoccursbytensilestresscausedbythemomentduetotheweightoftheinclinedsuperimposedcantilever-likerockcolumns.Hence,geo—structuraldefectsthatmaynaturallyexistinrockcolumnsaremodeledbyaseriesofcracksinmaximumtensilestressplane。
Themagnitudeandlocationofthemaximumtensilestressinrockcolumnswithpotentialflexuraltopplingfailurearedetermined。
Then,theminimumfactorofsafetyforrockcolumnsarecomputedbymeansofprinciplesofsolidandfracturemechanics,independently。
Next,anewequationisproposedtodeterminethelengthofcriticalcrackinsuchrockcolumns。
Ithasbeenshownthatifthelengthofnaturalcrackissmallerthanthelengthofcriticalcrack,thentheresultbasedonsolidmechanicsapproachismoreappropriate;otherwise,theresultobtainedbasedontheprinciplesoffracturemechanicsismoreacceptable.Subsequently,forstabilizationoftheprescribedrockslopes,somenewanalyticalrelationshipsaresuggestedfordeterminationthelengthanddiameteroftherequiredfullygroutedrockbolts.Finally,forquickdesignofrockslopesagainstflexuraltopplingfailure,agraphicalapproachalongwithsomedesigncurvesarepresentedbywhichanadmissibleinclinationofsuchrockslopesandorlengthofallrequiredfullygroutedrockboltsaredetermined。
Inaddition,acasestudyhasbeenusedforpracticalverificationoftheproposedapproaches.
KeywordsGeo-structuraldefects,In—siturockstructuralweaknesses,Criticalcracklength
1.Introduction
Rockmassesarenaturalmaterialsformedinthecourseofmillionsofyears。
Sinceduringtheirformationandafterwards,theyhavebeensubjectedtohighvariablepressuresbothverticallyandhorizontally,usually,theyarenotcontinuous,andcontainnumerouscracksandfractures。
Theexertedpressures,sometimes,producejointsets。
Sincethesepressuressometimesmaynotbesufficientlyhightocreateseparatejointsetsinrockmasses,theycanproducemicrojointsandmicro—cracks。
However,theresultscannotbeconsideredasindependentjointsets。
Althoughtheeffectsofthesemicro—cracksarenotthatpronouncedcomparedwithlargesizejointsets,yettheymaycauseadrasticchangeofin—situgeomechanicalpropertiesofrockmasses.Also,inmanyinstances,duetodissolutionofin-siturockmasses,minutebubble—likecavities,etc。
,areproduced,whichcauseaseverereductionofin-situtensilestrength.Therefore,oneshouldnotreplacethisin—situstrengthbythatobtainedinthelaboratory.Ontheotherhand,measuringthein-siturocktensilestrengthduetotheinteractionofcomplexparametersisimpractical。
Hence,anappropriateapproachforestimationofthetensilestrengthshouldbesought。
Inthispaper,bymeansofprinciplesofsolidandfracturemechanics,anewapproachfordeterminationoftheeffectofgeo-structuraldefectsonflexuraltopplingfailureisproposed。
2.Abriefreviewofpreviouswork
Considerableresearchhasbeenperformedinthefieldofflexuraltopplingfailure[1],[2],[3],[4],[5],[6],[7],[8],[9]and[10].ThefirstappliedresearchwasduetoGoodmanandBray[2].Theseresearchersproposedtheindispensableconditionforflexuraltopplingfailure。
In1987,AydanandKawamoto,byemployingtheequationsoflimitequilibriumandtheboundaryconditions,proposedanequationfordeterminationofinter-columnforcesofrockmassesinopenexcavationsandundergroundopeningsenvironment[5]。
Theyverifiedthemethodbycarryingoutlaboratorybasefrictionmodeling.Onthebasisoftheseexperiments,thetotalfailureplaneofflexuraltopplingisnormaltothediscontinuities.Hence,theanglebetweenthetotalfailureplaneandthenormaltothediscontinuitiesiszero。
Itisalsoseenthattheyassumedthatiftherocklayersarestableunderagivenloadconditionintheupperpart,theinter-columnforceswillbezero。
Basedontheaforementionedassumptionsthefactorofsafetyofallrockcolumnsshouldbecomputedandconsequentlytheextensionoftotalfailureplanecanbedetermined.Adhikaryetal。
,bycarryingcentrifugemodeling,madesomechangestoAydanandKawamoto’sequationforflexuraltopplingfailureinopenexcavations[7],[8]and[9]。
Onthebasisoftheseexperiments,thetotalfailureplaneofflexuraltopplingfailureisaround10°abovenormaltothediscontinuities.In2008,MajdiandAmini[10]andAminietal。
[11],usingtheprinciplesofcompatibilityandtheequationsofequilibriumalongwiththegoverningequationstoelasticdeformationforthebeams,derivedequationsfordeterminationinter-columnforcesinrockmasseswithpotentialofflexuraltopplingfailure。
Theaforementionedresearchersprovedthattheminimumfactorofsafetyagainsttopplingfailureisequaltothefactorofsafetyofacantile:
=
(1)
(2)
whereΨisthecalculatedlengthsofrockcolumnsusedforcomputationofintercolumnsresultantforce,Cisadimensionlessgeometricalparameter,Histheheightoftheslope,δisthedipangleoftherockmassgoverningdiscontinuities,φistheanglebetweentotalfailureplaneandthelinenormaltogoverningdiscontinuities,θistheslopeanglefromslopefaceclockwisetohorizontal,γistheunitweightofintactrock,andΓistheslopeanglefromslopefacecounterclockwisetohorizonandequalto180−θ。
Hence,thefactorofsafetyofrockcolumnsagainstflexuraltopplingfailureiscomputedbymeansofthefollowingequation[10]and[11]:
(3)
wheretisthethicknessofrockcolumns,σtistheuniaxialtensilestrengthofrockcolumns,andFSisthefactorofsafety.Toverifythemethod,theyusedtheexistingmodelingresults(basefrictionexperimentsof[6]andcentrifugemodelingof[7]).
Itisimportanttobearinmindthatinalltheabovementionedequationsitwaspresumedthattherockcolumnsarehomogenous,isotropic,andcontinuous;hencetheeffectofin—siturockstructuralweaknessesonthecomputedfactorofsafetywasignored.Therefore,thecalculatedfactorofsafetybasedontheaforementionedmethodisoverestimated。
Jennings[12]definedaparameteras“jointpersistence"forinvestigationoftheinfluenceofgeo-structuralweaknessesinplanefailureofrockslopeswhichisdefinedasfollows:
(4)
wherekisthejointpersistence,anisthehalf-lengthofthenthjoint,bnisthehalf—lengthofthenthrockbridge,Nisthenumberofcracks,aishalfoftheaveragelengthofapresumedcrack,andbishalfoftheaveragelengthofapresumedrockbridge。
Determinationoftheexactvalueofthejointpersistence(or“a”and“b”parameters),likemanyotherin-situgeologicalfactorssuchasdipanddipdirectionofdiscontinuities,spacing,etc。
,maynotbepossible.Therefore,theseparametersmustbedeterminedwithstatisticalapproach。
Therefore,theparametersaandbcanbemeasuredonthesitebyjointmappingoftherockmasses(Fig.1).Themeanvaluesofthestatisticalresultscanbeusedtocomputethejointpersistence.
Fig。
1。
Crackandrockbridgeinarockcolumnwithpotentialofflexuraltopplingfailure。
ViewWithinArticle
Inthispaper,theparametersa,b,andkareusedforfurtheranalysesofgeo—structuraldefectsinflexuraltopplingfailure。
3.Effectofgeo-structuraldefectsonflexuraltopplingfailure
3.1.Criticalsectionoftheflexuraltopplingfailure
Asmentionedearlier,MajdiandAmini[10]andAminietal.[11]haveprovedthattheaccuratefactorofsafetyisequaltothatcalculatedforaseriesofinclinedrockcolumns,which,byanalogy,isequivalenttothesuperimposedinclinedcantileverbeamsasshowninFig.3。
Accordingtotheequationsoflimitequilibrium,themomentMandtheshearingforceVexistinginvariouscross—sectionalareasinthebeamscanbecalculatedasfollows:
(5)
(6)
Sincethesuperimposedinclinedrockcolumnsaresubjectedtouniformlydistributedloadscausedbytheirownweight,hence,themaximumshearingforceandmomentexistattheveryfixedend,thatis,atx=Ψ:
(7)
(8)
IfthemagnitudeofΨfromEq.
(1)issubstitutedintoEqs.
(7)and(8),thenthemagnitudesofshearingforceandthemaximummomentofequivalentbeamforrockslopesarecomputedasfollows:
(9)
(10)
whereCisadimensionlessgeometricalparameterthatisrelatedtotheinclinationsoftherockslope,thetotalfailureplaneandthedipoftherockdiscontinuitiesthatexistinrockmasses,andcanbedeterminedbymeansofcurvesshowninFig.
MmaxandVmaxwillproducethenormal(tensileandcompressive)andtheshearstressesincriticalcross—sectionalarea,respectively.However,thecombinedeffectofthemwillcauserockcolumnstofail.Itiswellunderstoodthattherocksareverysusceptibletotensilestresses,andtheeffectofmaximumshearingforceisalsonegligiblecomparedwiththeeffectoftensilestress.Thus,forthepurposeoftheultimatestability,structuraldefectsreducethecross—sectionalareaofloadbearingcapacityoftherockcolumnsand,consequently,increasethestressconcentrationinneighboringsolidareas.Thus,thein—situtensilestrengthoftherockcolumns,theshearingeffectmightbeneglectedandonlythetensilestresscausedduetomaximumbendingstresscouldbeused。
3.2。
Analysisofgeo-structuraldefects
Determinationofthequantitativeeffectofgeo-structuraldefectsinro
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