A simple numerical procedure for the elasto-plastic coupling finite strain analysis of circular tunnels in strain-softening rock masses

Abstract

This paper presents a numerical finite strain solution for a circular tunnel in Mohr-Coulomb and generalized Hoek-Brown strain-softening rock masses. By approximating the differential equations with a difference method in the deformed coordinates, an efficient procedure is presented to calculate the displacements and stresses. The proposed solution is verified by another numerical method for both elasto-brittle-plastic and strain-softening finite strain examples. The parametric analysis indicates that (1) with the decrease in Young’s modulus of the residual region, the displacement increases, and the thickness of the softening region decreases. The displacement and the thickness of the softening and residual regions remain relatively stable when the deterioration coefficient of Young’s modulus is less than 0.01. (2) The displacement and the thickness of the softening and residual regions decrease with the increasing Poisson’s ratio, and increase with the increasing parameter α for the generalized Hoek-Brown rock mass. (3) With the increase in the in-situ stress, the dimensionless displacement of the tunnel wall increases and tends to 1.0, and the thicknesses of plastic and residual region first increase to their maximum values and then decrease. The finite strain solution is necessary for the displacement prediction and supporting design, rather than the small strain solution.