基于梯度塑性理论的岩样在压剪条件下变形及稳定性分析

Analysis of deformation and stability of rock specimen under uniaxial compressive and shear stresses based on gradient-dependent plasticity

考虑了正应力及剪应力联合作用在岩样的端部,而且,在正应力被视为变量,剪应力被视为常量这一特殊条件下,对剪切带的变形特征及剪切带-带外弹性体系统的失稳判据进行了分析。根据剪切虎克定律及梯度塑性理论,提出了剪切带内部弹性应变、塑性应变及总应变的解析式,对上述三种应变进行积分,提出了剪切带错动弹性位移、塑性位移及总位移的解析式。利用压缩虎克定律及几何关系建立了剪切带外弹性体的刚度的表达式。根据刚度理论,建立了剪切带-带外弹性体系统的失稳判据。考虑岩样端面的剪切应力后,在流动剪切应力相同时,剪切带内部的弹性剪切应变(均匀分布)将增加;剪切带内部的塑性剪切应变(不均匀分布)将减小;剪切带的弹性剪切位移(线性分布)将增加;剪切带的塑性剪切位移(非线性分布)将减小;剪切带错动位移要小一些。另外,剪切应力对剪切带-带外弹性体系统的失稳判据没有影响。失稳判据仅和岩石的本构参数、剪切带倾角及结构尺寸有关。

Characteristics of deformations of shear band and instability criterion of system or specimen composed of shear band and elastic rock outside the band, which is subject to normal and tangential stresses at ends of system are analyzed. Normal stress is considered to be a variable; while tangential stress is regarded as a constant. According to shear Hooke’s law and gradient-dependent plasticity, elastic, plastic and total strains in shear band are derived analytically. Integrating the three strains leads to elastic, plastic and total shear displacement of shear band, respectively. Then, compressive Hooke’s law and related geometrical relation between shear displacement of elastic rock outside shear band and compressive displacement at end of system are adopted to propose expression for stiffness of the system. Instability criterion of the system is presented according to the well-known stiffness theory. If shear stress at ends of specimen is considered and the same flow shear stress level in shear band is reached, then uniform elastic strain and linear elastic shear displacement are increased; however, nonuniform plastic strain, nonlinear plastic shear displacement and total shear displacement of shear band are decreased; in addition, instability criterion of the system is not influenced by shear stress at ends of specimen. The instability criterion is only concerned with constitutive relation of rock materials, inclination angle of shear band and geometrical size of specimen or system.