第三章 巖石的力學性質4練習

1Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity(1)FromthedatagiveninFigure1,calculatethetangentmodulusandPoisson’sratiofortheinitialelasticbehaviourofthelimestonewithσ3=2.0MPa.Figure1.Resultsoftriaxialcompressiontestsonanooliticlimestonewithvolumetricstrainmeasurement3.6問題/Problems2Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity(2)Aporoussandstonehasauniaxialcompressivestrengthofσc=75MPa.Theresultsofaseriesoftriaxialcompressiontestsplottedonshearstress–normalstressaxesgivealinearCoulombpeakstrengthenvelopehavingaslopeof45?.Determinetheaxialstressatpeakstrengthofajacketedspecimensubjectedtoaconfiningpressureofσ3=10MPa.Ifthejackethadbeenpuncturedduringthetest,andtheporepressurehadbuiltuptoavalueequaltotheconfiningpressure,whatwouldthepeakaxialstresshavebeen?3.6問題/Problems3Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity(3)(a)Establishanapproximatepeakstrengthenvelopeforthemarbleforwhichthedatashowninfigure2wereobtained.(b)Inwhatwaysmighttheobservedstress–strainbehaviourofthespecimenshavedifferedhadthetestsbeencarriedoutinaconventionaltestingmachinehavingalongitudinalstiffnessof2.0GNm?1?Assumethatallspecimenswere50mmindiameterand100mmlong.Figure2.Completeaxialstress–axialstraincurvesobtainedintriaxialcompressiontestsonTennesseeMarbleattheconfiningpressuresindicatedbythenumbersonthecurves.3.6問題/Problems4Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity(4)Whatcausesarocktobreakwhenitiscompresseduniaxiallytofailure?Isitwhenthestressreachesacertainvalueorwhenthestrainreachesacertainvalue?Orisitwhensomeotherparameterreachesacriticalvalue,suchastheenergyinputperunitvolume,orthemicrocrackdensityperunitvolume?3.6問題/Problems(5)ThegeometryofthelinearMohr-Coulombenvelopeissuchthatanumberofusefulrelationsbetweenstrengthparameterscanbedrawnfromit.Deriveanexpressionfortheuniaxialcompressivestrengthofrockintermsofthecohesionandangleofinternalfriction5Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity(6)ThelinearMohr-Coulombenvelopewithatensilecut-offsetsadefinitelimitonthemaximaluniaxialtensilestrengthofamaterial.ByconsideringthelargestuniaxialtensileMohrcirclethatcanbedrawn,determinethistensilestrengthlimitintermsofσcand?.3.6問題/Problems(7)Afirmwhosejudgementhasbeenquestionedonapreviousoccasionhasbeenentrustedwiththestrengthtestingofrockinasiteinvestigationproject.Duringtheirfirstuniaxialcompressiontest,theequipmentfailedtomeasurethepeakaxialload,butthetechniciandidrecordthatthespecimenfailedbytheformationofasinglefractureinclinedat20°totheloadingaxis.Inasubsequenttriaxialtest,astheconfiningpressurewasbeingincreasedbeforeapplicationoftheaxialstress,thespecimenfailedprematurelywhentheconfiningpressureintheHoekcellwas85MPa.Onthebasisoftheseresults,proposeafailurecriterionoftheformσ1=aσ3+bfortherock.6Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity(8)Aservo-controlledcompressiontesthasbeenconductedonaweaksoapstonesuchthatthespecimenlengthremainedunchangedthroughout:astheaxialstress,σa,wasincreased,sotheconfiningpressure,p,wasincreasedsothatnonetaxialstrainresulted.Aplotofaxialstress(verticalaxis)againstconfiningpressure(horizontalaxis)gaveaninitialstraightlinepassingthroughtheorigin.Atacriticalconfiningpressureofp=85MPa(whenσa=39.1MPa),theslopeoftheσa-Pplotsuddenlychangedto29°andremainedconstantfortheremainderofthetest.Thischangeinslopemaybetakentorepresenttheonsetofyield.(i)Determineanelasticconstantfromtheslopeoftheinitialportionoftheσa--Pcurve.(ii)AssumingthattheMohr-Coulombcriterionisapplicable,determineσc,cand?fortherock.3.6問題/Problems7Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity(9)

王文星,巖體力學,第一章練習一之第1題.(10)

王文星,巖體力學,第一章練習一之第2題.(11)

王文星,巖體力學,第一章練習一之第4題.

3.6問題/Problems8Chapter3MechanicalPropertiesofRockTangLizhong.InstituteofRock&SoilMechanicsandEngineering,CentralSouthUniversity3.6問題/Problems(12)Theresultsinthetablebelowshowtheaxialdisplacementandradialstraininducedinacylindricalspecimenofweakchalkduringauniaxialcreeptest.Inthistest,thespecimenwasinitially250mmhighandwassubjectedtoa