The influence of out‐of‐plane stress on a plane strain problem in rock mechanics

Abstract

This paper analyses the stresses and displacements in a uniformly prestressed Mohr-Coulomb continuum, caused by the excavation of an infinitely long cylindrical cavity. It is shown that the solution to this axisymmetric problem passes through three stages as the pressure at the cavity wall is progressively reduced. In the first two stages it is possible to determine the stresses and displacements in the r θ -plane without consideration of the out-of plane stress . In the third stage it is shown that an inner plastic zone develops in which, so that the stress states lie on a singularity of the plastic yield surface. Using the correct flow rule for this situation, an analytic solution for the radial displacements is obtained. Numerical examples are given to demonstrate that a proper consideration of this third stage can have a significant effect on the cavity wall displacements.

Elasto-plastic analysis of a circular tunnel including the effect of the axial in situ stress

“…The axisymmetrical elasto-plastic analysis with arbitrary value p z as a general case (p z ¼ 2mp þ Ee 0 , E is Young's modulus of elasticity of the rock) has not been discussed in the previous studies. Only in [16] was the case with p z ¼ p discussed.…”

Numerical approach for strain-softening rock with axial stress

“…When the internal support pressure is sufficiently large after a tunnel is excavated, the surrounding rock is in the elastic state. Then, solutions of stress and displacement in the elastic region can be expressed as (Reed, 1988) 1:…”

“…According to published theories (Pan and Brown, 1996;Reed, 1988;Wang et al, 2012), the following will be the cases when the out-of-plane stress is the major, intermediate or minor principal stress.…”

“…Many researchers have contributed to knowledge on the stress and displacement of tunnels and many technical problems have been solved in practice (Lu et al, 2010;Pan and Brown, 1996;Pan and Reed, 1991;Reed, 1986Reed, , 1988Sharan, 2008;Zhang et al, 2012). However, only a few theoretical solutions that incorporate the effect of out-of-plane stress and the generalised Hoek-Brown (H-B) failure criterion, particularly those for strain-softening surrounding rock, have been reported in the technical literature.…”

Theoretical solutions for a circular opening in an elastic–brittle–plastic rock mass incorporating the out-of-plane stress and seepage force

“…For instance, Reed (1988) studied the relationship between the out-of-plane stress and major, intermediate, and minor principal stresses. Pan et al (1996) studied the effects of out-ofplane stress and dilation on the convergence of rock and stability.…”