岩样单轴压缩轴向及侧向变形耗散能量及稳定性分析

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

DISSIPATED ENERGIES AND STABILITIES OF AXIAL AND LATERAL DEFORMATIONS OF ROCK SPECIMENS IN UNIAXIAL COMPRESSION

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.