Stability analysis of tunnel structures based on the twin-shear unified strength theory with strain-softening effect

This paper focuses on the analysis of the stability behavior of tunnel structures with circular openings based on the twin-shear unified strength theory with strain-softening model. A simplified numerical approach is proposed for analyzing elasto-plastic behavior of surrounding rocks. Modifying the difference method, this paper proposes a constitutive equation associated with flow rule based on the generalized unified failure criterion. For the strain-softening behavior, plastic strain increment is chosen as the softening parameter, and it is assumed that all the strength parameters are linearly correlated to the softening parameter. The solution of the elastic zone is imposed by Lamé solution. The solution in plastic zone is achieved by subdividing it into infinitesimal annuli, in which the radial stresses are assumed to decrease monotonically along each annulus. Then, equilibrium, constitutive and geometrical equations are established to determine the relationship of the increment of stresses and strains between the adjacent two annuli. The numerical solution of each annulus is calculated from the outmost annulus at the elastic-plastic interface. The stress, strain, and radial displacement results are obtained by programming in MATLAB environment. In addition, the impact of intermediate principal stress factor and the critical softening parameter on the solution are investigated, and the factors influencing plastic radius are discussed.