基于能量原理的岩样单轴压缩剪切破坏失稳判据
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摘要
利用能量原理对倾斜的剪切带-带外弹性岩石构成的系统的稳定性进行了研究。单轴压缩岩样沿轴向的变形被分解为两部分,带外弹性岩石压缩引起的变形和剪切带错动引起的变形。后者与剪切带的相对剪切变形具有简单的几何关系。系统的总势能由剪切带的弹性及耗散势能和带外弹性岩石对剪切带所作的外力功构成。剪切带的弹性及耗散势能与剪切带的体积有关系。剪切带的尺寸由梯度塑性理论确定。将系统的总势能对相对剪切变形求一阶导数(等于零),得到了弹性岩石的平衡条件。将总势能对相对剪切变形求二阶导数(小于零),得到了系统的失稳判据。它综合反映了岩石材料弹性及应变软化阶段本构参数(弹性模量及软化模量)、剪切带之外弹性岩石的尺寸、剪切带的尺寸及系统的结构形式(剪切带倾角)对系统稳定性的影响。失稳判据比以往所得到的失稳判据更严格,更精确,更具有广泛意义。
Stability of the system(rock specimen in uniaxial compression)composed of inclined shear band and elastic rock outside the band was analyzed in terms of energy principle.Axial deformation of the specimen is decomposed into two parts.One is due to the compression of elastic rock;the other is induced by the shear slip along shear band.The latter is related to the relative shear deformation between the top and base of shear band through a simple geometrical relation.Total potential energy is composed of elastic and dissipated potential energies in shear band as well as work done by external force.Potential energies in the band depend on the volume of shear band.The thickness of the band is determined by gradient-dependent plasticity.The first-order derivative equal to zero of total potential energy with respect to the relative shear deformation of shear band leads to the equilibrium condition of elastic rock.The second-order derivative less than zero of total potential energy with respect to the relative shear deformation of shear band results in the unstable criterion of the system.The present unstable criterion can reflect the influences of the constitutive parameters of rock in elastic and strain-softening stages,the volumes of elastic rock and shear band as well as the structural form on the stability of the system.The present analytical unstable criterion is strict and accurate,which is a generalization from existing analytical unstable criterion by Wang et al.
Stability of the system(rock specimen in uniaxial compression)composed of inclined shear band and elastic rock outside the band was analyzed in terms of energy principle.Axial deformation of the specimen is decomposed into two parts.One is due to the compression of elastic rock;the other is induced by the shear slip along shear band.The latter is related to the relative shear deformation between the top and base of shear band through a simple geometrical relation.Total potential energy is composed of elastic and dissipated potential energies in shear band as well as work done by external force.Potential energies in the band depend on the volume of shear band.The thickness of the band is determined by gradient-dependent plasticity.The first-order derivative equal to zero of total potential energy with respect to the relative shear deformation of shear band leads to the equilibrium condition of elastic rock.The second-order derivative less than zero of total potential energy with respect to the relative shear deformation of shear band results in the unstable criterion of the system.The present unstable criterion can reflect the influences of the constitutive parameters of rock in elastic and strain-softening stages,the volumes of elastic rock and shear band as well as the structural form on the stability of the system.The present analytical unstable criterion is strict and accurate,which is a generalization from existing analytical unstable criterion by Wang et al.
引文
[1]殷有泉,张宏.断裂带内介质的软化特性和地震的非稳定模型[J].地震学报,1984,6(2):135～145.Yin Youquan,Zhang Hong.The softening behaviour of fault zone medium and an instability model of earthquakes[J].Acta Seismological Sinica,1984,6(2):135～145.(in Chinese)
[2]章梦涛.冲击地压失稳理论与数值模拟计算[J].岩石力学与工程学报,1987,6(3):197～204.Zhang Mengtao.The instability theory and numerical simulation of rock burst[J],Chin.J.Rock Mech.Engrg,1987,6(3):197～204.(in Chinese)
[3]陈颙.地壳岩石的力学性能[M].北京:地震出版社,1988.Chen Yong.Mechanical properties of crust rocks[M].Beijing:Earthquake Press,1988.(in Chinese)
[4]卓家寿,邵国建,陈振雷.工程稳定问题中确定滑塌面、滑向与安全度的干扰能量法[J].水利学报,1997,(8):80～84,79.Zhou Jiashou,Shao Guojian,Chen Zhenlei.Disturbting energy method for determining the slipping face and direction and the safety coefficient of engineering stability[J].Journal of Hydraulic Engineering,1997,(8):80～84,79.(in Chinese)
[5]潘岳,王志强.岩体动力失稳的功、能增量——突变理论研究方法[J].岩石力学与工程学报,2004,23(9):1433～1438.Pan Yue,Wang Zhiqiang.Research approach on increment of work and energy catastrophe theory of rock dynamic destabilization[J].Chin.J.Rock Mech.Engrg,2004,23(9):1433～1438.(in Chinese)
[6]蔡美峰,孔广亚,贾立宏.岩体工程系统失稳的能量突变判断准则及其应用[J].北京科技大学学报,1997,19(4):325～328.Cai Meifeng,Kong Guangya,Jia Lihong.Criterion of energy catastrophe for rock project system failure in underground engineering[J].J.Univ.Sci.Tech.Beijing,1997,19(4):325～328.
[7]王学滨,潘一山,马瑾.剪切带内部应变(率)分析及基于能量准则的失稳判据[J].工程力学,2003,20(2):111～115.Wang Xuebin,Pan Yishan,Ma Jin.Analysis of strain(or strain rate)in the shear band and a criterion on instability based on the energy criterion[J].Engineering Mechanics,2003,20(2):111～115.(in Chinese)
[8]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 Xuebin,Pan Yishan,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)
[9]Wang Xuebin,Yang Xiaobin,Zhang Zhihui.Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion[J].J.Univ.Sci.Tech.Beijing,2004,11(1):5～9.
[10]Wang Xuebin,Dai Shuhong,Hai Long.Quantitative calculation of dissipated energy of fault rock burst based on gradient-dependent plasticity[J].J.Univ.Sci.Tech.Beijing,2004,11(3):197～201.
[11]Wang Xuebin,Dai Shuhong,Hai Long.Analysis of localized shear deformation of ductile metal based on gradient-dependent plasticity[J].Trans.Nonferrous Met.Soc.China,2003,13(6):1348～1353.
[12]Wang Xuebin,Yang Mei,Yu Haijun.Localized shear deformation during shear band propagation in Titanium considering interactions among microstructures[J].Trans.Nonferrous Met.Soc.China,2004,14(2):335～339.
[13]Wang X B,Yang M,Pan Y S.Analysis of plastic strain localization,damage localization and energy dissipated localization for strain-softening heterogeneous material based on gradient-dependent plasticity[J].Key Engineering Materials,2004,274-276:99～104.
[14]王学滨,潘一山,任伟杰.基于应变梯度理论的岩石试件剪切破坏失稳判据及应用[J].岩石力学与工程学报,2003,22(5):747～750.Wang Xuebin,Pan Yishan,Ren Weijie.Instability of shear failure and application for rock specimen based on gradient-oriented plasticity[J].Chin.J.Rock Mech.Engrg,2003,22(5):747～750.(in Chinese)
[15]王学滨,张智慧,潘一山.基于梯度塑性理论的岩样拉压剪破坏统一失稳判据[J].岩土力学,2003,24(增):138～142.Wang Xuebin,Zhang Zhihui,Pan Yishan.Unified formula for instability criterion under uniaxial tension,direct shear and uniaxial compression subjected to shear failure based on gradient-dependent plasticity[J].Rock and Soil Mechanics,2003,24(Supp.):138～142(in Chinese)
[16]Wang Xuebin,Pan Yishan.Size effect and snap back based on conservation of energy and gradient-dependent plasticity[A].Second International Symposium on New Development in Rock Mechanics and Rock Engineering[C].New Jersey:Rinton Press,2002,89～92.
[17]Wang Xuebin,Pan Yishan.Effect of relative stress on post-peak uniaxial compression fracture energy of concrete[J].J.Wuhan Univ.Technol.-Mat.Sci.Ed.,2003,18(4):89～92.
[18]Wang Xuebin.Analysis of progressive failure of pillar and instability criterion based on gradient-dependent plasticity[J].J.Cent.South Univ.Technol.,2004,11(4):445～450.
[19]Wang Xuebin.Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity[J].J.Univ.Sci.Tech.Beijing,2005,12(1):1～5.
[2]章梦涛.冲击地压失稳理论与数值模拟计算[J].岩石力学与工程学报,1987,6(3):197～204.Zhang Mengtao.The instability theory and numerical simulation of rock burst[J],Chin.J.Rock Mech.Engrg,1987,6(3):197～204.(in Chinese)
[3]陈颙.地壳岩石的力学性能[M].北京:地震出版社,1988.Chen Yong.Mechanical properties of crust rocks[M].Beijing:Earthquake Press,1988.(in Chinese)
[4]卓家寿,邵国建,陈振雷.工程稳定问题中确定滑塌面、滑向与安全度的干扰能量法[J].水利学报,1997,(8):80～84,79.Zhou Jiashou,Shao Guojian,Chen Zhenlei.Disturbting energy method for determining the slipping face and direction and the safety coefficient of engineering stability[J].Journal of Hydraulic Engineering,1997,(8):80～84,79.(in Chinese)
[5]潘岳,王志强.岩体动力失稳的功、能增量——突变理论研究方法[J].岩石力学与工程学报,2004,23(9):1433～1438.Pan Yue,Wang Zhiqiang.Research approach on increment of work and energy catastrophe theory of rock dynamic destabilization[J].Chin.J.Rock Mech.Engrg,2004,23(9):1433～1438.(in Chinese)
[6]蔡美峰,孔广亚,贾立宏.岩体工程系统失稳的能量突变判断准则及其应用[J].北京科技大学学报,1997,19(4):325～328.Cai Meifeng,Kong Guangya,Jia Lihong.Criterion of energy catastrophe for rock project system failure in underground engineering[J].J.Univ.Sci.Tech.Beijing,1997,19(4):325～328.
[7]王学滨,潘一山,马瑾.剪切带内部应变(率)分析及基于能量准则的失稳判据[J].工程力学,2003,20(2):111～115.Wang Xuebin,Pan Yishan,Ma Jin.Analysis of strain(or strain rate)in the shear band and a criterion on instability based on the energy criterion[J].Engineering Mechanics,2003,20(2):111～115.(in Chinese)
[8]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 Xuebin,Pan Yishan,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)
[9]Wang Xuebin,Yang Xiaobin,Zhang Zhihui.Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion[J].J.Univ.Sci.Tech.Beijing,2004,11(1):5～9.
[10]Wang Xuebin,Dai Shuhong,Hai Long.Quantitative calculation of dissipated energy of fault rock burst based on gradient-dependent plasticity[J].J.Univ.Sci.Tech.Beijing,2004,11(3):197～201.
[11]Wang Xuebin,Dai Shuhong,Hai Long.Analysis of localized shear deformation of ductile metal based on gradient-dependent plasticity[J].Trans.Nonferrous Met.Soc.China,2003,13(6):1348～1353.
[12]Wang Xuebin,Yang Mei,Yu Haijun.Localized shear deformation during shear band propagation in Titanium considering interactions among microstructures[J].Trans.Nonferrous Met.Soc.China,2004,14(2):335～339.
[13]Wang X B,Yang M,Pan Y S.Analysis of plastic strain localization,damage localization and energy dissipated localization for strain-softening heterogeneous material based on gradient-dependent plasticity[J].Key Engineering Materials,2004,274-276:99～104.
[14]王学滨,潘一山,任伟杰.基于应变梯度理论的岩石试件剪切破坏失稳判据及应用[J].岩石力学与工程学报,2003,22(5):747～750.Wang Xuebin,Pan Yishan,Ren Weijie.Instability of shear failure and application for rock specimen based on gradient-oriented plasticity[J].Chin.J.Rock Mech.Engrg,2003,22(5):747～750.(in Chinese)
[15]王学滨,张智慧,潘一山.基于梯度塑性理论的岩样拉压剪破坏统一失稳判据[J].岩土力学,2003,24(增):138～142.Wang Xuebin,Zhang Zhihui,Pan Yishan.Unified formula for instability criterion under uniaxial tension,direct shear and uniaxial compression subjected to shear failure based on gradient-dependent plasticity[J].Rock and Soil Mechanics,2003,24(Supp.):138～142(in Chinese)
[16]Wang Xuebin,Pan Yishan.Size effect and snap back based on conservation of energy and gradient-dependent plasticity[A].Second International Symposium on New Development in Rock Mechanics and Rock Engineering[C].New Jersey:Rinton Press,2002,89～92.
[17]Wang Xuebin,Pan Yishan.Effect of relative stress on post-peak uniaxial compression fracture energy of concrete[J].J.Wuhan Univ.Technol.-Mat.Sci.Ed.,2003,18(4):89～92.
[18]Wang Xuebin.Analysis of progressive failure of pillar and instability criterion based on gradient-dependent plasticity[J].J.Cent.South Univ.Technol.,2004,11(4):445～450.
[19]Wang Xuebin.Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity[J].J.Univ.Sci.Tech.Beijing,2005,12(1):1～5.
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