A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass

Abstract

A simple numerical procedure for calculating the distribution of stresses and radial displacements around a circular tunnel excavated in a strain-softening Mohr–Coulomb or generalized Hoek–Brown rock mass is proposed. The problem is considered as axisymmetric, i.e. the initial stress state is assumed to be hydrostatic and the rock mass is said to be isotropic. By invoking the finite difference approximation of the equilibrium and compatibility equations, the increments of stresses and strains for each ring, starting from the outmost one for which boundary conditions are known a priori, are calculated in a successive manner. In the proposed approach, the potential plastic zone is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium equation. For the strain-softening behavior, it is assumed that all the strength parameters are a linear function of deviatoric plastic strain. Several illustrative examples are given to demonstrate the performance of the proposed method. For the brittle–plastic case, the results show a very good agreement with the closed-form solution. For strain-softening cases, the predictions by the proposed method are also in good agreement with the known rigorous numerical solutions. It is shown that the approximate solution converges to the exact solution when the increment of stress for each ring becomes smaller. The influence of the strength parameter ‘a’, appearing in the generalized Hoek–Brown criterion, on the elasto-plastic solutions is examined through the establishment of ground reaction curves and the discussion for the locations of the plastic radii.