A numerical solution of a circular tunnel in a confining pressure-dependent strain-softening rock mass

This paper presents a numerical solution for a circular tunnel excavated in a confining pressure-dependent strain-softening rock mass with linear Mohr-Coulomb (MC) and nonlinear generalized Hoek-Brown (HB) yield criteria to calculate the main geomechanical parameters, i.e., radii of plastic and residual regions, distributions of stresses and displacement. The surrounding rock is first divided into a number of thin concentric annuli with constant material parameters. The material parameters are determined by the radial stress and the plastic shear strain at the outer radius of each annulus. The equilibrium differential equation is approximated using a difference scheme to obtain the dimensionless radius of each annulus corresponding to the prior given radial stress. A simple numerical stepwise procedure is presented to recursively calculate the radius of each annulus. For elastic rock masses, a confining pressure-dependent Young's modulus leads to that the tangent stress first increases to a maximum value and then gradually decreases. The maximum concentration factor, whose position lies inside the surrounding rock, is smaller than 2.0. For the generalized confining pressure-dependent strain-softening rock mass, about 20% increase in parameter alpha induces 169.14%, 56.14% and 74.31% increase in softening radius, residual radius and displacement compared to that of alpha = 0.5.