基于梯度塑性理论的岩样拉压剪破坏统一失稳判据

Unified criterion for stability failure of rock specimens subject to uniaxial tension, direct shear and uniaxial compression based on gradient-dependent plasticity

提出了单轴拉伸,直剪及单轴压缩剪切破坏失稳判据的统一形式。首先对de Borst R及Muhlhaus H B关于单轴拉伸试件梯度塑性理论解析解方面的开创性工作进行了回顾、评论,并指出了他们工作的缺憾。受de Borst R等工作的启发,对直接剪切试件进行了分析,得到了快速回跳条件。并发现:岩样的快速回跳条件就是系统(由剪切带及带外弹性岩石构成)的失稳判据。又对单轴压缩岩样剪切破坏进行了分析,得到了其失稳判据。通过对单轴拉伸失稳判据、直接剪切失稳判据及单轴压缩剪切破坏失稳判据的类比,得到了失稳判据的统一形式。统一失稳判据表明:岩石材料的局部化带宽度及压缩或剪切弹性模量越小,软化模量及等效试件高度越大,试件越容易发生失稳破坏。

A unified expression for instability criterion of rock structure is proposed under uniaxial tension and compression as well as direct shear loadings in heterogeneous geo-materials considering the strain gradient effects. Firstly, the pioneer work for analytical solution of gradient-dependent plasticity due to de Borst R and Muhlhaus H B is reviewed and discussed. Several important open problems in rock mechanics (such as localized shear strain, non-uniform shear displacement, instability of direct shear and uniaxial compression etc) need further investigating are also pointed out. Then, on the basis of work by de Borst R etc, the analysis of direct shear test is carried out and the condition of snap-back is given. It is found that the criterion is in agreement with the criterion of instability for the system composed of shear band and elastic rocks outside the band. Next, analysis of uniaxial compression tests for rock specimens subject to shear failure is conducted and the criterion of instability is deduced. Finally by the way of analogy of three criteria of instability (one proposed by de Borst R etc for uniaxial tension, the other two obtained in the present paper for uniaxial compression and direct shear), a unified formula for instability of rock structure under tension, shear and compression is given, which enriches the stability theory in rock mechanics. The unified formula shows that the characteristic length (or thickness of localized band), the structural size, the softening modulus and the elastic modulus (including shear or compressive elastic moduli) have an influence on the snap-back instability. The lower ratio of the characteristic length to the softening modulus or the larger ratio of the structural size to elastic modulus can lead to instability of the rock structure.