基于梯度塑性理论的岩样单轴压缩扩容分析

采用梯度塑性理论，对岩样剪应变局部化引起的扩容进行了理论分析。假设岩石的剪切本构关系为弹性-应变软化双线性，局部化启动于应力峰值强度，利用局部塑性剪应变与局部塑性体积应变的线性关系，得到了局部塑性体积应变、局部塑性体积增量及剪胀引起的剪切带总塑性体积增量的解析式，这体现了该理论在研究剪胀问题时的优越性。另外，还得到了弹性阶段及应变软化阶段的轴向应力-体积应变曲线的理论关系。塑性体积应变是专指由剪切带剪胀而引起的，因而，轴向应力．体积应变不具有尺寸效应，与局部化带的尺寸无关，但扩容角、剪切降模量及泊松比却对该曲线有重要影响。在弹性阶段及应变软化阶段轴向应力-体积应变均呈线性。在相同的应力水平下，扩容角越大则剪胀程度越大；剪切降模量越大，剪胀程度越小。在应变软化阶段，泊松比不影响塑性体积应变。

DILATATION ANALYSIS OF ROCK SPECIMEN UNDER UNIAXIAL COMPRESSION BASED ON GRADIENT-DEPENDENT PLASTICITY

Non-uniform shear dilatancy of rock specimen due to plastic shear strain localization is analyzed considering strain gradient effect. The constitutive relation of rock material is linear elastic and linear strain softening. Localization is initiated in the form of a single shear band when peak strength is rearched. By resorting to the linear relation between local plastic shear strain and local plastic volumetric strain,analytical solutions for local plastic volumetric strain,increment of local plastic volume and increment of total plastic volume due to shear localization are presented,which can not be deduced from classical elasto-plastic theory. So the advantages of the gradient-dependent plasticity over the classical theory are apparent in analysis of localized shear dilatancy. In addition,a bi-linear relation between axial compressive stress and volumetric strain is proposed under uniaxial compression of rock specimen subjected to shear failure. It is noted that the exclusive reason for plastic volumetric strain is assumed to be shear dilatancy in the present paper,therefore,the relation between axial stress and volumetric strain is size-independent and is not concerned with the thinkness of shear band. However,it is influenced by dilation angle,shear softening modulus and Poisson ratio. For the same stress level,larger dilation angle leads to increment of the volumetric strain,and higher shear softening modulus results in lower volumetric strain. However,Poisson ratio does not influence the plastic volumetric strain in the stage of strain softening.