Elastoplastic solution of a circular tunnel in surrounding rock with any nonlinear yield criteria and plastic flow envelopes

Besides the (semi-)linear Mohr-Coulomb and Hoek-Brown criteria, other nonlinear functions are also used to describe the plastic response of rock mass. For a nonlinear yield and plastic flow function in the form of tau = f (sigma n) and/or sigma 1 = f(sigma 3), the equivalent cohesive strength and frictional angle corresponding to the Mohr-Coulomb yield criterion were derived. The normal stress was further related to the minimum principal stress using the geometrical relationship of a Mohr circle. The equivalent dilatancy angle was also derived using the same method. According to the solution of a circular tunnel in Mohr-Coulomb rock mass, this paper derived a semianalytical solution of a circular tunnel in any nonlinear yield and plastic flow rock masses with a form of tau = f(sigma n) and/or sigma 1 = f(sigma 3). A numerical procedure was developed for the stresses and displacement using a reserve method. The proposed solution was verified by the results of a circular tunnel in elasto-perfectly(brittle-)-plastic and/or strain-softening rock mass. The strain-softening analysis of a circular tunnel in the assumed two nonlinear yield criteria and/or plastic flow rock masses was studied. For a linear deteriorated material parameters leads to a nonlinear evolution of equivalent cohesive strength, frictional angle and dilatancy angle in the plastic region.

Automated summary

In addition to the Mohr-Coulomb and Hoek-Brown criteria, other nonlinear functions are used to describe the plastic response of rock mass. This paper derived the equivalent cohesive strength, frictional angle, and dilatancy angle for nonlinear yield and plastic flow rock masses. The solution for a circular tunnel in any nonlinear yield and plastic flow rock masses was derived and verified using a numerical procedure. The analysis of strain-softening rock masses under two assumed nonlinear yield criteria was also studied.