三维岩样单轴压缩端面效应及破坏数值模拟
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摘要
采用三维拉格朗日元法,对三维岩样在单轴压缩及不同端面约束条件下,试样端面上压应力的分布及演化规律、试样的破坏过程及空间局部化区域的形态进行数值模拟研究。在峰值强度之前及之后,岩石的本构模型分别取为线弹性及莫尔库仑剪破坏与拉破坏复合的应变软化模型。数值结果表明,对于粗糙端面,由于强烈的端面约束,试样的弹性区是以两端面为底面的锥体;锥体一旦形成,随着时间步的增加,其体积基本保持不变;压应力集中于端面的四个边上。对于光滑端面,弹性区被塑性区所包围,随着时间步的增加,弹性区逐渐缩小,直到消失;压应力集中于端面的中心。在平面应力状态下,未观测到明显的局部化剪切带图案。无论粗糙还是光滑端面,三维岩样都发生了明显的剪切破坏。三维岩样内部的剪切应变局部化带有主有次,占主导地位的剪切带尺寸较大,应变率集中程度较大。
Compressive stress distributions and their evolutions at upper end of specimen in uniaxial compression with different end-restraints, failure process, and spatial patterns of localized shear bands are investigated numerically using FLAC-3D. In elastic stage, the adopted constitutive relation of rock is linear elastic; in strain-softening stage, a composite Mohr-Coulomb criterion with tension cut-off is used and post-peak constitutive relation is also linear strain-softening. For rough ends, two elastic cones are formed near two ends of specimen due to strong frictional forces; beyond the formation of the cones, their sizes do not decrease with timestep; compressive stress at end is concentrated at four edges of the top. However, for smooth ends, elastic core is surrounded by yielded elements and decreases in volume with increasing timestep until it vanishes.The maximum stress is reached at the center of the top. In plane stress condition, no obvious shear band is observed. However, three-dimensional specimen in uniaxial compression is subjected to evident shear failure althrough end-restraints are different. Main and secondary shear bands are generated within three-dimensional specimen. Main band has a larger volume and a higher extent of shear strain rate concentration.
Compressive stress distributions and their evolutions at upper end of specimen in uniaxial compression with different end-restraints, failure process, and spatial patterns of localized shear bands are investigated numerically using FLAC-3D. In elastic stage, the adopted constitutive relation of rock is linear elastic; in strain-softening stage, a composite Mohr-Coulomb criterion with tension cut-off is used and post-peak constitutive relation is also linear strain-softening. For rough ends, two elastic cones are formed near two ends of specimen due to strong frictional forces; beyond the formation of the cones, their sizes do not decrease with timestep; compressive stress at end is concentrated at four edges of the top. However, for smooth ends, elastic core is surrounded by yielded elements and decreases in volume with increasing timestep until it vanishes.The maximum stress is reached at the center of the top. In plane stress condition, no obvious shear band is observed. However, three-dimensional specimen in uniaxial compression is subjected to evident shear failure althrough end-restraints are different. Main and secondary shear bands are generated within three-dimensional specimen. Main band has a larger volume and a higher extent of shear strain rate concentration.
引文
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[2]WangXuebin,DaiShuhong,HaiLong.Quantitativecalculationofdissipatedenergyoffaultrockburstbasedongradient-dependentplasticity[J].JournalofUniversityofScienceandTechnologyBeijing,2004,11(3):197～201.
[3]WangXuebin,PanYishan.Effectofrelativestressonpost peakuniaxialcompressionfractureenergyofconcrete[J].JournalofWuhanUniversityofTechnology MaterialsScienceEdition,2003,18(4):89～92.
[4]WangXuebin,DaiShuhong,HaiLong,etal.Analysisoflocalizedsheardeformationofductilemetalbasedongradient dependentplasticity[J].TransNonferrousMetSocChina,2003,13(6):1348～1353.
[5]WangXuebin,YangMei,YuHaijun,etal.Localizedsheardeformationduringshearbandpropagationintitaniumconsideringinteractionsamongmicrostructures[J].TransNonferrousMetSocChina,2004,14(2):335～339.
[6]WangXuebin,YangMei,PanYishan.Analysisofplasticstrainlocalization,damagelocalizationandenergydissipatedlocalizationforstrain softeningheterogeneousmaterialbasedongradient dependentplasticity[J].KeyEngineeringMaterials,2004,274～276:99～104.
[7]WangXuebin,PanYishan.Sizeeffectandsnapbackbasedonconservationofenergyandgradient dependentplasticity[A].SecondInternationalSymposiumonNewDevelopmentinRockMechanicsandRockEngineering[C].NewJersey:RintonPress,2002.89～92.
[8]CundallPA,Numericalexperimentsonlocalizationinfrictionalmateial[J].Ingenigeur Archiv,1989,59:148～159.
[9]HobbsBE,OrdA.Numericalsimulationofshearbandformationinafrictional dilationalmaterial[J].Ingenigeur Archiv,1989,59:209～220.
[10]GutierrezM.Shearbandformationinrockswithacurvedfailuresurface[J].IntJRockMechMinSci＆GeomechAbstr,1998,35(4/5):447.
[11]EricksonSG,StrayerLM,SuppeJ.Initationandreactivationoffaultsduringmovementoverathrust faultramp:numericalmechanicalmodels[J].JournalofStructuralGeology,2001,23:11～23.
[12]StephenD,IvanG.Fractureinitation,growthandeffectonstressfield:anumericalinvestigation[J].JournalofStructuralGeology,1998,20(12):1673～1689.
[13]WangXuebin,PanYishan,DingXiuli,etal.Numericalsimulationoflocalizeddeformationfieldforrockinplanestrainstate[J].ChineseJournalofRockMechanicsandEngineering,2003,22(4):521～524.[王学滨,潘一山,丁秀丽,等.平面应变岩样局部化变形场数值模拟研究[J].岩石力学与工程学报,2003,22(4):521～524.]
[14]WangXuebin,PanYishan,ShengQian,etal.Numericalsimulationonstrainlocalizationofendconstraintofrockspecimen[J].JournalofEngineeringGeology,2002,10(3):233～236.[王学滨,潘一山,盛 谦,等.岩石试件端面效应的变形局部化数值模拟研究[J].工程地质学报,2002,10(3):233～235.]
[15]WangXuebin,PanYishan,ShengQian,etal.Numericalsimulationofdevelopmentofdynamicstrainlocalizationandsizeeffect[J].ChineseJournalofComputationalMechanics,2002,19(4):500～503.[王学滨,潘一山,盛 谦,等.动力应变局部化传播及尺寸效应数值模拟[J].计算力学学报,2002,19(4):500～503.]
[16]WangXuebin,PanYishan,YangMei.Thenumericalsimulationofshearzoneonstrainlocalizationofborehole[J].Drilling＆ProductionTechnology,2002,25(2):17～19.[王学滨,潘一山,杨 梅.井眼变形局部化剪切带数值模拟研究[J].钻采工艺,2002,25(2):17～19.]
[17]WangXuebin,ZhaoYangfeng,DaiShuhong,etal.Numericalsimulationofconjugateshearfracturebandsforseismicblockmodel[J].DisasterPreventionandMitigationEngrg,2004,24(2):119～125.[王学滨,赵扬锋,代树红,等.地震块体模型的共轭剪切破裂带数值模拟[J].防灾减灾工程学报,2004,24(2):119～125.]
[18]孙广忠.岩体结构力学[M].北京:科学出版社,1988.
[19]蔡美峰.岩石力学与工程[M].北京:科学出版社,2002.
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