A numerical strain-softening solution of a circular opening in nonlinear yield rock masses

Abstract

Strain-softening behavior occurs when the surrounding rock reaches its peak load, complicating the prediction of stress and displacement. The linear Mohr-Coulomb yield criterion and semi-linear Hoek-Brown yield criterion are widely used in elastoplastic analysis. However, the established criteria struggle to universally describe the nonlinear behavior of various rock types. This study aims to overcome the difficulty and propose the solution of surrounding rock in a circular tunnel following any nonlinear yield criterion and plastic potential function. The derivation of the equivalent cohesive strength and frictional angle for an arbitrary nonlinear yield criterion in the form of σ1=fσ3 using the secant method, along with the determination of the equivalent dilatancy angle for any nonlinear plastic potential functions, was conducted. Concerning the elastoplastic solution of a thick-cylinder, a numerical strain-softening solution for a circular tunnel in nonlinear yield rock masses was derived. Verification of the proposed solution was performed against the established analytical and/or numerical elasto-(brittle-)plastic and strain-softening solutions in rock masses following the Mohr-Coulomb, (generalized) Hoek-Brown, and unified strength criteria. The impact of critical plastic shear strain on displacement, plastic radius, and residual radius was further analyzed. The predictions of displacement and residual region for the Jinping II project also meet the field test results.