软化模量对岩样全部变形特征的影响
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摘要
采用FLAC内嵌语言编制了计算平面应变压缩岩样轴向、侧向、体积应变及泊松比的FISH函数。研究了软化模量对剪切带图案及岩样全部变形特征的影响。在峰值强度之前及之后,岩石的本构模型分别为线弹性模型及莫尔–库仑剪破坏与拉破坏复合的应变软化模型。结果表明,随着软化模量(脆性)的增加,剪切带倾角由Arthur向Coulomb倾角转变,Coulomb、Roscoe及Arthur理论对此不能解释,可能是未考虑渐进破坏;剪切带宽度降低,这可采用基于梯度塑性理论且考虑剪胀的剪切带宽度的公式予以定性的解释;岩样可以达到的最小体积增加;岩样失稳破坏的前兆越来越明显;峰后的轴向应力–轴向应变曲线、轴向应力–侧向应变曲线、侧向应变–轴向应变曲线、泊松比–轴向应变曲线及体积应变–轴向应变曲线均有稍微变陡峭的趋势,可采用基于梯度塑性理论的单轴压缩岩样受到剪切破坏时的解析解对前2种曲线的数值解的合理性进行定性的解释。
FISH functions were written to calculate axial,lateral and volumetric strains as well as Poisson’s ratio of rock specimen in plane strain compression.Influence of softening modulus on shear band(SB) patterns and entire deformational characteristics of the specimen was investigated by use of FLAC.In elastic and strain-softening stages,the linear elastic and linear strain-softening constitutive relations were adopted,respectively.Mohr-Coulomb criterion with tension cut-off was used beyond the elastic state.Numerical results showed that the increase of the softening modulus led to 1) transition of SB inclination from Arthur’s inclination to Coulomb’s inclination,which could not be explained by Coulomb,Roscoe,and Arthur’s inclinations,possibly due to neglecting the progressive failure of rock;2) decrease of SB’s thickness that could be qualitatively explained by the theoretical expression considering shear dilatancy based on gradient-dependent plasticity;3) increase of the minmum volume that the specimen in compression could obtain;4) more apparent precursor to unstable failure of the specimen;5) slightly steeper post-peak axial stress-axial strain curve,the axial stress-lateral strain curve,the lateral strain-axial strain curve,the Poisson’s ratio-axial strain curve and the volumetric strain-axial strain curve.Reasonableness of the former two numerical results was qualitatively explained by the previous analytical solutions in uniaxial compression of rock specimen subjected to shear failure.
FISH functions were written to calculate axial,lateral and volumetric strains as well as Poisson’s ratio of rock specimen in plane strain compression.Influence of softening modulus on shear band(SB) patterns and entire deformational characteristics of the specimen was investigated by use of FLAC.In elastic and strain-softening stages,the linear elastic and linear strain-softening constitutive relations were adopted,respectively.Mohr-Coulomb criterion with tension cut-off was used beyond the elastic state.Numerical results showed that the increase of the softening modulus led to 1) transition of SB inclination from Arthur’s inclination to Coulomb’s inclination,which could not be explained by Coulomb,Roscoe,and Arthur’s inclinations,possibly due to neglecting the progressive failure of rock;2) decrease of SB’s thickness that could be qualitatively explained by the theoretical expression considering shear dilatancy based on gradient-dependent plasticity;3) increase of the minmum volume that the specimen in compression could obtain;4) more apparent precursor to unstable failure of the specimen;5) slightly steeper post-peak axial stress-axial strain curve,the axial stress-lateral strain curve,the lateral strain-axial strain curve,the Poisson’s ratio-axial strain curve and the volumetric strain-axial strain curve.Reasonableness of the former two numerical results was qualitatively explained by the previous analytical solutions in uniaxial compression of rock specimen subjected to shear failure.
引文
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[10]王学滨,马剑,刘杰,等.基于梯度塑性本构理论的岩样侧向变形分析(I):基本理论及本构参数对侧向变形的影响[J].岩土力学,2004,25(6):904–908.(WANG Xue-bin,MA Jian,LIU Jie,et al.Analysis of lateral deformation of rock specimen based on gradient-dependent plasticity(I)-basic theory and effect of constitutive parameters on lateral deformation[J].Rock and Soil Mechanics,2004,25(6):904–908.)
[11]王学滨,刘杰,王雷,等.基于梯度塑性本构理论的岩样侧向变形分析(II):尺寸效应及弹性会跳[J].岩土力学,2004,25(7):1127–1130.(WANG Xue-bin,LIU Jie,WANG Lei,et al.Analysis of lateral deformation of rock specimen based on gradient-dependent plasticity(II):Size effect and snap-back[J].Rock and Soil Mechanics,2004,25(7):1127–1130.)
[12]王学滨.基于梯度塑性理论的岩样峰后变形特征研究[J].岩石力学与工程学报,2004,23(增1):4292–4295.(WANG Xue-bin.Characteristics of post-peak deformations of rock in uniaxial compression based on gradient-dependent plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(Supp.1):4292–4295.)
[13]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.)
[14]王学滨.三维岩样单轴压缩端面效应及破坏数值模拟[J].四川大学学报(工程科学版),2005,37(2):28–33.(WANG Xue-bin.Numerical simulation of end-restraint and failure process of three dimensional rock specimen in uniaxial compression[J].Journal of Sichuan University(Engineering Science Edition),2005,27(2):28–33.)
[15]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].J Disaster Prevention and Mitigation Engrg,2004,24(2):119–125.)
[16]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.)
[17]王学滨,李毅.平面应变含缺陷岩样变形破坏全过程数值模拟[J].中国矿业大学学报,2005,34(2):189–203,217.(WANG Xue-bin,LI Yi.Numerical simulation of complete failure process of rock with material imperfection in plane strain compression[J].Journal of China University of Mining&Technology,2005,34(2):189–203,217.)
[18]HOBBS B E,ORD A.Numerical simulation of shear band formation in a frictional-dilational material[J].Ingenigeur-Archiv,1989,59(3):209–220.
[19]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.)
[20]WANG Xue-bin,TANG Ju-peng,ZHANG Zhi-hui,et al.Analysis of size effect,shear deformation and dilation in direct shear test based on gradient-dependent plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(7):1095–1099.
[21]VERMEER P A.The orientation of shear bands in biaxialtests[J].Géotechnique,1990,40(2):223–236.
[22]ORD A,VARDOULAKIS I,KAJEWSKI R.Shear band formation in Gosford sandstone[J].Int J Rock Mech Min Sci&Geomech Abstr,1991,28(5):397–409.
[23]朱建明,徐秉业,岑章志.岩石类材料峰后滑移剪胀变形特征研究[J].力学与实践,2001,23(5):19–22.(ZHU Jian-ming,XU Bing-ye,CEN Zhang-zhi.Study on the deformation mechanisms of sliding dilation of post-failure rocks[J].Mechanics in Enginering,2001,23(5):19–22.)
[2]高文华,杨林德,叶为民.自立式挡墙侧向变形时效性分析与计算[J].工程力学,1997,14(增):324–328.(GAO Wen-hua,YANG Lin-de,YE Wei-min.Analysis and calculation of aging of lateral deformation for self-supporting retaining wall[J].Engineering Mechanics,1997,14(S):324–328.)
[3]刘兴旺,施祖元,益德清.软土地区基坑开挖变形性状研究[J].岩土工程学报,1999,21(4):456–460.(LIU Xing-wang,SHI Zu-yuan,YI De-qing.Deformation characteristics analysis of braced excavation on soft clay[J].Chinese Journal of Geotechnical Engineering,1999,21(4):456–460.)
[4]张农,侯朝炯,陈庆敏,等.岩石破坏后的注浆固结体的力学性能[J].岩土力学,1998,19(3):49–53.(ZHANG Nong,HOU Chao-jiong,CHEN Qing-min,et al.Mechanical properties of broken rock after grouting reinforement[J].Rock and Soil Mechanics,1998,19(3):49–53.)
[5]徐志伟,殷宗泽.粉砂侧向变形特性的真三轴试验研究[J].岩石力学与工程学报,2000,19(5):626–629.(XU Zhi-wei,YIN Zong-ze.Study on deformation characteristic of silt by true triaxial test[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(5):626–629.)
[6]王学滨,潘一山,杨小彬.准脆性材料试件应变软化尺度效应理论研究[J].岩石力学与工程学报,2003,22(3):188–191.(WANG Xue-bin,PAN Yi-shan,YANG Xiao-bin.Size effect analysis on strain softening quasi-brittle materials considering strain gradient effect[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):188–191.)
[7]WANG Xue-bin,PAN Yi-shan.Effect of relative stress on post-peak uniaxial compression fracture energy of concrete[J].Journal of Wuhan University of Technology(Materials Science Edition),2003,18(4):89–92.
[8]WANG Xue-bin,PAN Yi-shan.Size effect and snap back based on conservation of energy and gradient-dependent plasticity[C]//Lin Yunmei,et al.Second International Symposium on New Development in Rock Mechanics and Rock Engineering.New Jersey:Rinton Press,2002:89–92.
[9]王学滨,潘一山,于海军.考虑塑性应变率梯度的单轴压缩岩样轴向响应[J].岩土力学,2003,24(6):943–946.(WANG Xue-bin,PAN Yi-shan,YU Hai-jun.Axial response of rock specimen considering strain rate gradient effect in uniaxial compression[J].Rock and Soil Mechanics,2003,24(6):943–946.)
[10]王学滨,马剑,刘杰,等.基于梯度塑性本构理论的岩样侧向变形分析(I):基本理论及本构参数对侧向变形的影响[J].岩土力学,2004,25(6):904–908.(WANG Xue-bin,MA Jian,LIU Jie,et al.Analysis of lateral deformation of rock specimen based on gradient-dependent plasticity(I)-basic theory and effect of constitutive parameters on lateral deformation[J].Rock and Soil Mechanics,2004,25(6):904–908.)
[11]王学滨,刘杰,王雷,等.基于梯度塑性本构理论的岩样侧向变形分析(II):尺寸效应及弹性会跳[J].岩土力学,2004,25(7):1127–1130.(WANG Xue-bin,LIU Jie,WANG Lei,et al.Analysis of lateral deformation of rock specimen based on gradient-dependent plasticity(II):Size effect and snap-back[J].Rock and Soil Mechanics,2004,25(7):1127–1130.)
[12]王学滨.基于梯度塑性理论的岩样峰后变形特征研究[J].岩石力学与工程学报,2004,23(增1):4292–4295.(WANG Xue-bin.Characteristics of post-peak deformations of rock in uniaxial compression based on gradient-dependent plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(Supp.1):4292–4295.)
[13]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.)
[14]王学滨.三维岩样单轴压缩端面效应及破坏数值模拟[J].四川大学学报(工程科学版),2005,37(2):28–33.(WANG Xue-bin.Numerical simulation of end-restraint and failure process of three dimensional rock specimen in uniaxial compression[J].Journal of Sichuan University(Engineering Science Edition),2005,27(2):28–33.)
[15]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].J Disaster Prevention and Mitigation Engrg,2004,24(2):119–125.)
[16]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.)
[17]王学滨,李毅.平面应变含缺陷岩样变形破坏全过程数值模拟[J].中国矿业大学学报,2005,34(2):189–203,217.(WANG Xue-bin,LI Yi.Numerical simulation of complete failure process of rock with material imperfection in plane strain compression[J].Journal of China University of Mining&Technology,2005,34(2):189–203,217.)
[18]HOBBS B E,ORD A.Numerical simulation of shear band formation in a frictional-dilational material[J].Ingenigeur-Archiv,1989,59(3):209–220.
[19]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.)
[20]WANG Xue-bin,TANG Ju-peng,ZHANG Zhi-hui,et al.Analysis of size effect,shear deformation and dilation in direct shear test based on gradient-dependent plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(7):1095–1099.
[21]VERMEER P A.The orientation of shear bands in biaxialtests[J].Géotechnique,1990,40(2):223–236.
[22]ORD A,VARDOULAKIS I,KAJEWSKI R.Shear band formation in Gosford sandstone[J].Int J Rock Mech Min Sci&Geomech Abstr,1991,28(5):397–409.
[23]朱建明,徐秉业,岑章志.岩石类材料峰后滑移剪胀变形特征研究[J].力学与实践,2001,23(5):19–22.(ZHU Jian-ming,XU Bing-ye,CEN Zhang-zhi.Study on the deformation mechanisms of sliding dilation of post-failure rocks[J].Mechanics in Enginering,2001,23(5):19–22.)
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