岩样单轴压缩轴向及侧向变形耗散能量及稳定性分析
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摘要
首先从能量的角度分析了单轴压缩岩石试件轴向及侧向塑性变形的耗散能量及其联系。根据梯度塑性理论,局部化带的尺寸由特征长度确定,得到了单轴压缩岩样由于剪切局部化而引起的轴向及侧向塑性变形所耗散能量的解析解。研究结果表明:剪切带消耗的能量等于侧向及轴向塑性变形消耗的能量的总和;轴向塑性变形消耗的能量与侧向塑性变形消耗的能量成正比,其比例系数与剪切带倾角有关;轴向塑性变形消耗的能量要大于侧向塑性变形消耗的能量;当流动应力为0时,剪切带消耗的能量达到最大值;轴向外力对试件作功等于侧向及轴向塑性变形消耗的能量的总和;增加剪切带倾角,侧向塑性变形消耗的能量占剪切带消耗的能量的比例增加。然后分析了单轴压缩岩石试件轴向及侧向变形的不稳定性。将剪切带及带外弹性岩石所受到的剪应力分解为水平及垂直剪应力,剪切带的塑性剪切变形也分解为水平及垂直变形。建立了水平剪力与侧向塑性变形及垂直剪力与轴向塑性变形的理论关系。水平剪力与侧向塑性变形曲线的斜率等于垂直剪力与轴向塑性变形曲线的斜率。由于这些关系依赖于结构尺寸,因此,不能被看作本构关系。将剪切带视为“试件”,将带外弹性体看作“试验机”。根据刚度理论,可以得到“试件”–“试验机”系统在水平及垂直两个方向上
Firstly,dissipated energies induced by axial and lateral plastic deformations due to shear strain localization initiated at peak strength in strain softening stage is analyzed. Based on gradient-dependent plasticity in which the thickness of shear band is determined by characteristic length of rock,analytical solutions of dissipated energies in axial and lateral directions of rock specimens in uniaxial compression are derived,respectively. The presented theoretical results show that dissipated energy consumed by shear band is composed of two parts,axial and lateral dissipated energies. Dissipated energy due to axial plastic deformation is proportional to that of lateral plastic deformation and the proportional coefficient is dependent on inclination angle of shear band. According to the actual measured value of shear band inclination,the dissipated energy of axial plastic deformation is greater than that of lateral plastic deformation. As flow compressive stress approaches zero,the dissipated energy by shear band,the dissipated energies of axial and lateral plastic deformations attain their maxima. Bigger inclination angle of shear band leads to bigger dissipated energy of lateral plastic deformation and smaller dissipated energy of lateral plastic deformation. Secondly,shear instabilities of axial and lateral deformations of rock specimens in uniaxial compression are investigated. Shear stress between shear band and elastic rock outside the band is decomposed to horizontal and vertical shear stresses. Similarly,plastic shear deformation of shear band is divided into axial and lateral deformations. Relation between the horizontal shear stress and lateral plastic deformation and relation between the vertical shear stress and axial plastic deformation are presented,respectively. It is shown that the slope of horizontal shear stress-lateral plastic deformation curve is equal to that of vertical shear stress-axial plastic deformation curve. The two curves are dependent on the structural size,therefore,the slope cannot be taken as a constitutive parameter of rock materials. Based on theory of stiffness,instability criterions of specimens composed of shear band and elastic rock outside the band in the axial and lateral directions are proposed analytically. The two criterions are identical,which depend on constitutive relation of rock materials and structural size of rock specimens.
Firstly,dissipated energies induced by axial and lateral plastic deformations due to shear strain localization initiated at peak strength in strain softening stage is analyzed. Based on gradient-dependent plasticity in which the thickness of shear band is determined by characteristic length of rock,analytical solutions of dissipated energies in axial and lateral directions of rock specimens in uniaxial compression are derived,respectively. The presented theoretical results show that dissipated energy consumed by shear band is composed of two parts,axial and lateral dissipated energies. Dissipated energy due to axial plastic deformation is proportional to that of lateral plastic deformation and the proportional coefficient is dependent on inclination angle of shear band. According to the actual measured value of shear band inclination,the dissipated energy of axial plastic deformation is greater than that of lateral plastic deformation. As flow compressive stress approaches zero,the dissipated energy by shear band,the dissipated energies of axial and lateral plastic deformations attain their maxima. Bigger inclination angle of shear band leads to bigger dissipated energy of lateral plastic deformation and smaller dissipated energy of lateral plastic deformation. Secondly,shear instabilities of axial and lateral deformations of rock specimens in uniaxial compression are investigated. Shear stress between shear band and elastic rock outside the band is decomposed to horizontal and vertical shear stresses. Similarly,plastic shear deformation of shear band is divided into axial and lateral deformations. Relation between the horizontal shear stress and lateral plastic deformation and relation between the vertical shear stress and axial plastic deformation are presented,respectively. It is shown that the slope of horizontal shear stress-lateral plastic deformation curve is equal to that of vertical shear stress-axial plastic deformation curve. The two curves are dependent on the structural size,therefore,the slope cannot be taken as a constitutive parameter of rock materials. Based on theory of stiffness,instability criterions of specimens composed of shear band and elastic rock outside the band in the axial and lateral directions are proposed analytically. The two criterions are identical,which depend on constitutive relation of rock materials and structural size of rock specimens.
引文
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[12]李宏,朱浮声,王泳嘉等.岩石统计细观损伤与局部弱化失稳的尺寸效应[J].岩石力学与工程学报,1999,18(1):28–32.(LiHong,ZhuFusheng,WangYongjia,et al.Size effects of statistical meso- damage and local softening instability of rock[J].ChineseJournal ofRockMechanics andEngineering,1999,18(1):28–32.(inChinese))
[13]章梦涛.冲击地压失稳理论及数值模拟[J].岩石力学与工程学报,1987,6(3):197–204.(ZhangMengtao.The instability theory and numerical simulation of rock burst[J].ChineseJournal ofRockMechanics andEngineering,1987,6(3):197–204.(inChinese))
[14]SalamonM D G.Stability instability and design of pillar working[J].Int.J.RockMech.Min.Sci.,1970,7(6):613–631.
[15]HudsonJ A,CrouchS L,FairhurstC.Soft,stiff and servo-controlled testing machines:a review with reference to rock failure[J].Engrg.Geol.,1972,6(3):155–189.
[16]尤明庆.岩样单轴压缩的失稳破坏和试验机加载性能[J].岩土力学,1998,19(3):43–49.(YouMingqing.Instability failure of rock specimen in uniaxial compression and the loading behavior of testing machine[J].Rock andSoilMechanics,1998,19(3):43–49.(inChinese))
[17]唐春安,徐小荷.岩石破裂过程失稳的尖点灾变模型[J].岩石力学与工程学报,1990,9(2):100–107.(TangChunan,XuXiaohe.A cusp catastrophic model of rock unstable failure[J].ChineseJournal ofRockMechanics andEngineering,1990,9(2):100–107.(inChinese))
[18]潘岳.伺服控制加载原理的能量分析[J].岩土工程学报,1994,16(4):75–80.(PanYue.Energy analysis of servo-control loading principle[J].ChineseJournal ofGeotechnicalEngineering,1994,16(4):75–80.(inChinese))
[19]李长洪,蔡美峰,乔兰等.岩石全应力–应变曲线与岩爆的关系[J].北京科技大学学报,1999,21(6):513–515.(LiChanghong,CaiMeifeng,QiaoLan,et al.Rock complete stress-strain and its relationship to rock burst[J].Journal ofUniversity ofScience andTechnologyBeijing,1999,21(6):513–515.(inChinese))
[2]沈珠江.应变软化材料的广义孔隙压力模型[J].岩土工程学报,1997,19(3):14–21.(ShenZhujiang.Generalized pore pressure model for strain softening materials[J].ChineseJournal ofGeotechnicalEngineering,1997,19(3):14–21.(inChinese))
[3]赵启林,牛海清,卓家寿.应变软化材料的几个基本问题研究进展[J].水利水运工程学报,2001,(3):73–77.(ZhaoQilin,NiuHaiqing,ZhuoJiashou.Basic problems of strain-softening material[J].Hydro-Science andEngineering,2001,(3):73–77.(inChinese))
[4]刘西拉,温斌.混凝土单轴拉伸的应变软化行为及描述[J].工程力学,1998,16(增):8–18.(LiuXila,WenBin.Strain-softening behavior and description of concrete in uniaxial tension[J].EngineeringMechanics,1998,16(Supp.):8–18.(inChinese))
[5]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(2):188–191.(WangXuebin,PanYishan,YangXiaobin.Size effect analysis on strain softening quasi-brittle materials considering strain gradient effect[J].ChineseJournal ofRockMechanics andEngineering,2003,22(2):188–191.(inChinese))
[6]王学滨,潘一山,刘杰.关于潘岳讨论的答复[J].岩石力学工程学报,2003,22(12):2107–2110.(WangXuebin,PanYishan,LiuJie.Answer toPanYues discussion[J].ChineseJournal ofRockMechanics andEngineering,2003,22(12):2107–2110.(inChinese))
[7]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.(WangXuebin,PanYishan,RenWeijie.Instability of shear failure and application for rock specimen based on gradient-dependent plasticity[J].ChineseJournal ofRockMechanics andEngineering,2003,22(5):747–750.(inChinese))
[8]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.(WangXuebin,PanYishan,MaJin.Analysis of strain(or the ratio of strain) in the shear band and a criterion on instability based on the energy criterion[J].EngineeringMechanics,2003,20(2):111–115.(inChinese))
[9]王学滨,潘一山,盛谦等.岩体假三轴压缩及变形局部化剪切带数值模拟[J].岩土力学,2001,22(3):323–326.(WangXuebin,PanYishan,ShengQian,et al.Simulation of triaxial compression and localization of deformation[J].Rock andSoilMechanics,2001,22(3):323–326.(inChinese))
[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.(WangXuebin,MaJian,LiuJie,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 andSoilMechanics,2004,25(6):904–908.(inChinese))
[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.(WangXuebin,LiuJie,WangLei,et al.Analysis of lateral deformation of rock specimen based on gradient-dependent plasticity(II):size effect and snap-back[J].Rock andSoilMechanics,2004,25(7):1127–1130.(inChinese))
[12]李宏,朱浮声,王泳嘉等.岩石统计细观损伤与局部弱化失稳的尺寸效应[J].岩石力学与工程学报,1999,18(1):28–32.(LiHong,ZhuFusheng,WangYongjia,et al.Size effects of statistical meso- damage and local softening instability of rock[J].ChineseJournal ofRockMechanics andEngineering,1999,18(1):28–32.(inChinese))
[13]章梦涛.冲击地压失稳理论及数值模拟[J].岩石力学与工程学报,1987,6(3):197–204.(ZhangMengtao.The instability theory and numerical simulation of rock burst[J].ChineseJournal ofRockMechanics andEngineering,1987,6(3):197–204.(inChinese))
[14]SalamonM D G.Stability instability and design of pillar working[J].Int.J.RockMech.Min.Sci.,1970,7(6):613–631.
[15]HudsonJ A,CrouchS L,FairhurstC.Soft,stiff and servo-controlled testing machines:a review with reference to rock failure[J].Engrg.Geol.,1972,6(3):155–189.
[16]尤明庆.岩样单轴压缩的失稳破坏和试验机加载性能[J].岩土力学,1998,19(3):43–49.(YouMingqing.Instability failure of rock specimen in uniaxial compression and the loading behavior of testing machine[J].Rock andSoilMechanics,1998,19(3):43–49.(inChinese))
[17]唐春安,徐小荷.岩石破裂过程失稳的尖点灾变模型[J].岩石力学与工程学报,1990,9(2):100–107.(TangChunan,XuXiaohe.A cusp catastrophic model of rock unstable failure[J].ChineseJournal ofRockMechanics andEngineering,1990,9(2):100–107.(inChinese))
[18]潘岳.伺服控制加载原理的能量分析[J].岩土工程学报,1994,16(4):75–80.(PanYue.Energy analysis of servo-control loading principle[J].ChineseJournal ofGeotechnicalEngineering,1994,16(4):75–80.(inChinese))
[19]李长洪,蔡美峰,乔兰等.岩石全应力–应变曲线与岩爆的关系[J].北京科技大学学报,1999,21(6):513–515.(LiChanghong,CaiMeifeng,QiaoLan,et al.Rock complete stress-strain and its relationship to rock burst[J].Journal ofUniversity ofScience andTechnologyBeijing,1999,21(6):513–515.(inChinese))
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