Elasto-plastic analysis of a circular opening in strain-softening rock mass

Abstract

Geo-materials generally show strain-softening behavior after peak-load. To avoid the difficulty of describing variable material properties during the post-failure process in a strain-softening rock mass, a multi-step brittle–plastic model (MBPM) was proposed on the assumption that rock mass properties were uniform in a very small region. Then the post-peak rock mass can be divided into a number of annular regions and the rock mass in each region can be considered to conform to classical plasticity theory. For the strain-softening behavior, material properties of rock mass such as strength and deformation parameters were assumed to follow a piecewise linear function of plastic shear plastic strain. Then the equations for solving the annulus' radius were given on the basis of the material properties and its corresponding plastic shear plastic strain in each annulus, and the radii were calculated in a successive manner by combining the secant and Newton–Raphson method from the outmost one whose initial radius is assumed. Several sets of examples are analyzed to validate the new approach. For elasto-brittle–plastic behavior, the results show high consistency with closed-form solutions. For the strain-softening behavior, the new approach also shows high consistency with the numerical results. Finally, the influence of shear modulus on the rock mass deformation was analyzed and the results show that it can affect the range of residual and softening radius lightly but influence the rock mass deformation heavily, which usually occurs in the geo-engineering, especially in the deep underground engineering.