三维岩样单轴压缩自由面剪应变率及位移分布数值模拟
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摘要
以往FLAC对岩样变形、破坏进行数值模拟主要是针对平面应变二维问题,离三维岩样单轴压缩的试验条件还有不少差距。因此,本文采用FLAC-3D研究了三维岩样在单轴压缩及强烈端面约束条件下,自由面的剪切应变率、离面位移及面内位移的分布及演变规律,研究了自由面垂直对称轴上定点位移随时步的演变规律。在应力峰值之前及之后,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。计算表明:在应力–时步曲线的应力峰值之前,自由面上的剪切应变率由均匀向不均匀分布转变;在应变软化阶段,试样的变形由对称性向非对称性转变。通过分析各个自由面的剪切带图案发现,在试样内部形成了两个空间剪切带,其中一个更占优势。在试样变形的对称性丧失之前,三维离面及面内位移曲面是光滑的、平坦的;在对称性丧失之后,三维曲面已变得凹凸不平了。在剪切带的位置,面内位移有显著的改变。自由面垂直对称轴上的离面位移在应力–时步曲线应力峰值之前发生了分离,而水平及垂直位移–时步曲线转折于应力峰值稍后或应变软化阶段。从离面位移易于识别出试样破坏的前兆。此外,在应变软化阶段,随着时步的增加,还观测到了离面位移的三种不同的变化规律:基本保持不变、增加及降低(反弹)。
Previously numerical simulations of deformation and failure of rock specimen using Fast Lagrangian Analysis of Continua(FLAC) were mainly limited to plane strain condition different from the actual test condition of three-dimensional rock specimen in uniaxial compression.In the paper,three-dimensional rock specimen with rough ends was modeled by FLAC-3D.Distribution and evolution of shear strain rate,in-and off-plane displacements in free surfaces were investigated.Evolution of in-and off-plane displacements in vertical symmetrical axis of a free surface was monitored.In elastic stage,the adopted constitutive relation was linear elastic;in strain-softening stage,a composite Mohr-Coulomb criterion with tension cut-off was used and the post-peak constitutive relation was also linear.It was shown that uniform distribution of shear strain rate in free surfaces was changed to non-uniform state prior to peak stress.Symmetrical deformation mode of the specimen was converted into asymmetrical pattern beyond peak stress.Two spatial shear planes were found to be generated within specimen through analysis of the patterns of shear band on four free surfaces.One plane was superior to the others from the viewpoint of area of shear plane.Three-dimensional curved surfaces of in-and off-plane displacements were smooth and flat before losing of symmetry of deformation.Concavo-convex three-dimensional curved surfaces wee observed once the symmetry of deformation was violated.Positions where in-plane displacement changed remarkably corresponded to shear bands.Precursor to deformation and failure of the specimen could be identified form off-plane displacement in vertical symmetrical axis of a free surface since the separation of off-plane displacement-timestep curves occurred prior to peak stress.As timestep increased,three kinds of tendencies of off-plane displacement were observed in strain-softening stage.
Previously numerical simulations of deformation and failure of rock specimen using Fast Lagrangian Analysis of Continua(FLAC) were mainly limited to plane strain condition different from the actual test condition of three-dimensional rock specimen in uniaxial compression.In the paper,three-dimensional rock specimen with rough ends was modeled by FLAC-3D.Distribution and evolution of shear strain rate,in-and off-plane displacements in free surfaces were investigated.Evolution of in-and off-plane displacements in vertical symmetrical axis of a free surface was monitored.In elastic stage,the adopted constitutive relation was linear elastic;in strain-softening stage,a composite Mohr-Coulomb criterion with tension cut-off was used and the post-peak constitutive relation was also linear.It was shown that uniform distribution of shear strain rate in free surfaces was changed to non-uniform state prior to peak stress.Symmetrical deformation mode of the specimen was converted into asymmetrical pattern beyond peak stress.Two spatial shear planes were found to be generated within specimen through analysis of the patterns of shear band on four free surfaces.One plane was superior to the others from the viewpoint of area of shear plane.Three-dimensional curved surfaces of in-and off-plane displacements were smooth and flat before losing of symmetry of deformation.Concavo-convex three-dimensional curved surfaces wee observed once the symmetry of deformation was violated.Positions where in-plane displacement changed remarkably corresponded to shear bands.Precursor to deformation and failure of the specimen could be identified form off-plane displacement in vertical symmetrical axis of a free surface since the separation of off-plane displacement-timestep curves occurred prior to peak stress.As timestep increased,three kinds of tendencies of off-plane displacement were observed in strain-softening stage.
引文
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[2]牛安福,张晶,延旭东,等.西南地区强震前后地壳变形异常强度场特征研究[J].地震,2002,22(1):61–69.(NIU An-fu,ZHANG Jing,YAN Xu-dong,et al.On the characteristics of anomaly deformation field around strong earthquakes in Southwest China area[J].Earthquake,2002,22(1):61–69.(in Chinese))
[3]王学滨.平面应变压缩岩样侧向变形特征数值模拟[J].岩土工程学报,2005,27(5):525–530.(WANG Xue-bin.Numerical simulation of lateral deformation of rock specimen in plane strain compression[J].Chinese Journal of Geotechnical Engineering,2005,27(5):525–530.(in Chinese))
[4]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.(WANG Xue-bin,PAN Yi-shan,DING Xiu-li,et al.Numerical simulation of localized deformation field for rock in plane strain state[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(4):521–524.(in Chinese))
[5]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.(WANG Xue-bin,ZHAO Yang-feng,DAI Shu-hong,et al.Numerical simulation of conjugate shear fracture bands for seismic block model[J].Disaster Prevention and Mitigation Engrg,2004,24(2):119–125.(in Chinese))
[6]王学滨.地震前兆特征与岩样剪切应变率异常数值模拟[J].大地测量与地球动力学,2005,25(1):102–107,122.(WANG Xue-bin.Numerical simulation of anomalies in shear strain rate of rock in biaxial plane strain compression[J].Journal of Geodesy and Geodynamics,2005,25(1):102–107,122.(in Chinese))
[7]FINNO R J,HARRIS W W,MOONEY M A,et al.Strain localization and undrained steady state of sand[J].Journal of Geotechnical Engineering,ASCE,1996,122(6):462–473.
[8]SHAH S P,SANKAR R.Interal cracking and strain-softening response of concrete under uniaxial compression[J].ACI Material Journal,1987,84(3):200–212.
[9]TANG Chun-an,FU Yu-fang,ZHAO Wen.A new approach to numerical simulation of source development of earthquake[J].Acta Seismologica Sinica,1997,10(4):425–434.
[10]孙吉主,唐春安.断层地震孕震的椭圆形区域及其前兆规律[J].地震,1996,16(4):355–362.(SUN Ji-zhu,TANG Chun-an.Ellipse area and precursor law of fault earthquakes[J].Earthquake,1996,16(4):355–362.(in Chinese))
[11]王学滨,潘一山,海龙.基于剪切应变梯度塑性理论的断层岩爆失稳判据[J].岩石力学与工程学报,2004,23(4):588–591.(WANG Xue-bin,PAN Yi-shan,HAI Long.Instability criterion of fault rock burst based on gradient-dependent plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(4):588–591.(in Chinese))
[12]王学滨,海龙,宋维源,等.断层岩爆是应变局部化导致的失稳回跳[J].岩石力学与工程学报,2004,23(18):3102–3105.(WANG Xue-bin,HAI Long,SONG Wei-yuan,et al.Fault rockburst is snap-back due to shear strain localization[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(18):3102–3105.(in Chinese))
[13]朱令人,周仕勇,杨马陵,等.地震复杂性前兆与强震多重分形谱异常[J].地震,1997,17(4):331–339.(ZHU Ling-ren,ZHOU Shi-yong,YANG Ma-ling,et al.Earthquake complexity precursor and anomaly of multi-fractal spectrum of strong earthquakes[J].Earthquake,1997,17(4):331–339.(in Chinese))
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