Solution for a circular tunnel in strain-softening rock with seepage forces

In this study, a simple numerical approach for a circular tunnel opening in strain-softening surrounding rock is proposed considering out-of-plane stress and seepage force based on Biot\'s effective stress principle. The plastic region of strain-softening surrounding rock was divided into a finite number of concentric rings, of which the thickness was determined by the internal equilibrium equation. The increments of stress and strain for each ring, starting from the elastic-plastic interface, were obtained by successively incorporating the effect of out-of-plane stress and Biot\'s effective stress principle. The initial value of the outmost ring was determined using equilibrium and compatibility equations. Based on the Mohr–Coulomb (M–C) and generalized Hoek–Brown (H–B) failure criteria, the stress-increment approach for solving stress, displacement, and plastic radius was improved by considering the effects of Biot\'s effective stress principle and the nonlinear degradation of strength and deformation parameters in plastic zone incorporating out-of-plane stress. The correctness of the proposed approach is validated by numerical simulation.