岩石试件尺寸对裂纹应力场影响的数值分析
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摘要
用数值方法和岩石力学实验模拟地震断层的破裂过程时,模型或试件的尺寸选取不合适将影响断层附近的应力场.本文利用二维弹性有限元方法,计算了一个含椭圆孔的岩石试件在不同尺寸下的应力场,并与相应的无限域椭圆孔问题的解析解进行了比较.数值分析结果表明,含椭圆孔的岩石试件在单轴压缩情况下,其边界效应对内部应力场的影响不容忽视;试件的临界尺寸长宽比约为3:2,孔的尖端到边界的距离与孔的长轴的比值约为7.3.这种数值分析试件尺寸的方法,不仅可以为岩石力学实验提供理论依据,同时也为确定数值模拟断层错动等问题中几何模型的大小提供了参考价值.
In the simulation of rupture processes of seismic sources by using either numerical method or rock mechanics experiments, improper setting of the specimen size will influence the stress field near the faults. In this study, 2D finite element method (FEM) was used to calculate the stress field of rock specimens in different sizes with fixed-size elliptic holes. The calculated stress field was compared with analytic solution for elliptichole problem in an infinite medium. Numerical results showed that boundary effect of a rock specimen with an elliptic hole on stress field under uniaxial compression cannot be neglected. Critical aspect ratio of the specimen is about 3:2, and critical ratio of distance between the tip of the hole and the border of specimen to the major axis of the elliptic hole is about 7.3. Numerical analysis on rock specimen size can provide theoretical reference for rock specimen experiments, and it is also helpful for setting of model sizes in numerical simulations of fault movement.
In the simulation of rupture processes of seismic sources by using either numerical method or rock mechanics experiments, improper setting of the specimen size will influence the stress field near the faults. In this study, 2D finite element method (FEM) was used to calculate the stress field of rock specimens in different sizes with fixed-size elliptic holes. The calculated stress field was compared with analytic solution for elliptichole problem in an infinite medium. Numerical results showed that boundary effect of a rock specimen with an elliptic hole on stress field under uniaxial compression cannot be neglected. Critical aspect ratio of the specimen is about 3:2, and critical ratio of distance between the tip of the hole and the border of specimen to the major axis of the elliptic hole is about 7.3. Numerical analysis on rock specimen size can provide theoretical reference for rock specimen experiments, and it is also helpful for setting of model sizes in numerical simulations of fault movement.
引文
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JohnsonJW.1943.Effectofheightoftestingspecimenoncompressivestrengthofconcrete[J].AmerSocTestingMater Bull,120:19～21
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MogiK.1966.Someprecisemeasurementsoffracturestrengthofrocksunderuniformcompressivestress[J].RockMech EngGeol,4(1):41～55
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PengCB,Toks¨ozMN.1995.Anoptimalabsorbingboundary conditionforelastic wavemodeling[J].Geophysics,60(1):296～301
RandallCJ.1989.Absorbingboundaryconditionfortheelasticwaveequation:velocity stressformulation[J].Geophys ics,54(3):1141～1152
RobertA,EinsteinHH.1998.Fracturecoalescenceinrock typematerialsunderuniaxialandbiaxialcompression[J].IntJRockMechMinSci,35(7):863～888
RobinaHC,WongK,ChauT.1998.Crackcoalescenceinarock likematerialcontainingtwocracks[J].IntJRock MechMinSci,35(2):147～164
SpicakA,LokajicekT.1986.Faultinteractionandseismicity:laboratoryinvestigationanditsseismotectonicinterpreta tion[J].PureApplGeophys,124:857～874
ThaulowS.1962.Apparentcompressivestrengthofconcreteasaffectedbyheightoftestspecimenandfrictionbetween theloadingsurfaces[J].BullReunionInternLabEssiasRechMaterConstr,17:31～33
徐芝纶.1982.弹性力学[M].第二版.北京:人民教育出版社,130～146
赵永红,黄杰藩,侯建军,等.1995.岩石细观破裂的实验观测研究及其对认识地震活动性的启示[J].地球物理学报,38(5):627～635
ArchuletaR,FrazierG.1978.Three dimensionalnumericalsimulationsofdynamicfaultinginahalf space[J].Bull SeismSocAmer,68:541～572
BallaA.1960.Stressconditionsintriaxialcompression[J].JSoilMechFoundDiv,AmerSocCivEngrs,86(SM86):57～84
CaiYE,HeT,WangR.2000.NumericalsimulationofdynamicprocessoftheTangshanearthquakebyanewmethod LDDA[J].PureApplGeophys,157(11/12):2083～2104
DasS,AkiK.1977.Anumericalstudyoftwo dimensionalspontaneousrupturepropagation[J].GeophyJRastrSoc,50:643～668
FukuyamaE,MadariagaR.1995.Integralequationmethodforplanecrackwitharbitraryshapein3Delasticmedium[J].BullSeismSocAmer,85:614～628
FukuyamaE,MadariagaR.1998.Rupturedynamicsofaplannarfaultina3Delasticmedium:rate andslip weakening friction[J].BullSeismSocAmer,88:1～17
GonnermanHF.1925.Effectofendconditionofcylinderincompressiontestsofconcrete[J].ProcAmerSocTesting Mater,24(2):1036～1065
GrosvenorNE.1963.Specimenproportionkeytobettercompressivestrengthtests[J].MiningEng,15:31～33
HansenH,KiellandA,NielsenKEC,etal.1962.Compressivestrengthofconcrete cubeorcylinder[J].BullReunion InternLabEssaisRechMaterConstr,17:22～30
HawkesI,MellorM.1970.Uniaxialtestinginrockmechanicslaboratories[J].EngGeol,4(3):177～285
HobbsDW.1964.Rockcompressivestrength[J].CollieryEng,41:287～292
InternationalSocietyforRockMechanics.1978.Suggestedmethodsfordeterminingthestrengthofrocksmaterialsintri axialcompression[J].IntJRockMechMinSci,15(1):49～51
InternationalSocietyforRockMechanics.1979.Suggestedmethodsfordeterminingcompressionstrengthanddeform ability[J].IntJRockMechMinSci,16(2):137～140
JohnsonJW.1943.Effectofheightoftestingspecimenoncompressivestrengthofconcrete[J].AmerSocTestingMater Bull,120:19～21
MadariagaR.1976.Dynamicofanexpandingcircularfault[J].BullSeismSocAmer,66:639～667
MogiK.1966.Someprecisemeasurementsoffracturestrengthofrocksunderuniformcompressivestress[J].RockMech EngGeol,4(1):41～55
OlsenKB,MadariagaR,ArchuletaR.1997.Threedimensionaldynamicsimulationsofthe1992Landersearthquake[J].Science,278:834～838
PengCB,Toks¨ozMN.1995.Anoptimalabsorbingboundary conditionforelastic wavemodeling[J].Geophysics,60(1):296～301
RandallCJ.1989.Absorbingboundaryconditionfortheelasticwaveequation:velocity stressformulation[J].Geophys ics,54(3):1141～1152
RobertA,EinsteinHH.1998.Fracturecoalescenceinrock typematerialsunderuniaxialandbiaxialcompression[J].IntJRockMechMinSci,35(7):863～888
RobinaHC,WongK,ChauT.1998.Crackcoalescenceinarock likematerialcontainingtwocracks[J].IntJRock MechMinSci,35(2):147～164
SpicakA,LokajicekT.1986.Faultinteractionandseismicity:laboratoryinvestigationanditsseismotectonicinterpreta tion[J].PureApplGeophys,124:857～874
ThaulowS.1962.Apparentcompressivestrengthofconcreteasaffectedbyheightoftestspecimenandfrictionbetween theloadingsurfaces[J].BullReunionInternLabEssiasRechMaterConstr,17:31～33
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