Elasto-plastic analysis of a circular opening in rock mass with confining stress-dependent strain-softening behaviour

Abstract In strain-softening rock mass, it is widely accepted that the confining stress in the plastic zone around a circular opening varies with the radial distance. The variable confining stress gives rise to a variable critical plastic softening parameter (η∗). This paper aims to take the variable η∗ into account in the development of elasto-plastic solutions for stress and strain states around a circular opening. First, a variable confining stress model (VCSM) is recommended to account for the effect of the variable η∗; a criterion is presented for judging whether or not the rock mass transfers from the plastic softening state to the residual state. Then, a new numerical procedure for the implementation of VCSM is proposed on the basis of Hoek–Brown failure criterion and the non-associated flow rule. In the proposed procedure, the plastic softening and residual zones are divided into a set of concentric rings by an assigned radial stress increment. The increments of stress and strain for each ring can be calculated in a successive manner by the finite difference method. Finally, by using the proposed procedure, a series of parametric studies is conducted to compare VCSM and existing constant confining stress models (CCSM), and also to investigate the variation of the stress components, strain-softening parameter, and strength parameters in the plastic softening zone. The results indicate that CCSM tends to underestimate the deformation of surrounding rock mass with poor quality. The effect of the critical plastic softening parameter on the stability of a circular opening in strain-softening rock mass includes two different aspects: one is to govern the strength parameters of the plastic zone, the other is to control the radii of the plastic softening and residual zones.