A new semi–analytical method for elastic–strain softening circular tunnel with hydraulic–mechanical coupling

Abstract

This study presents a novel coupled hydraulic–mechanical algorithm for analysing nonlinear seepage in circular tunnels with elastic strain softening characteristics. The model integrates porosity changes with permeability coefficients to formulate a set of nonlinear seepage equations. The Mohr–Coulomb criterion is used to determine the of rock stress yielding state, and the plastic strain ${\epsilon }_{\theta }^p$ is used as a softening parameter to assess the degradation of rock strength. The proposed model is validated through a comparison with established numerical and analytical solutions. The pore water pressure distribution exhibits a distinctive three-stage curve under coupling conditions, with the seepage behaviour transitioning to a classical Laplace-type equation as the coupling coefficient weights diminish. Parametric analysis reveals that the brittleness index $\beta$ is a pivotal factor governing the extent of the softening region. A decrease in residual strength ${\sigma }_c^{\ast }$ intensifies strain softening, leading to a more extensive softening zone. Conversely, a reduction in the angle of internal friction $\phi$ affects only the rock's strength without altering the softening intensity. The study also demonstrated that the pore water pressure diminishes the effective stress within the rock mass, resulting in a larger plastic zone than that under dry conditions. Finally, internal reinforcement and external support can effectively mitigate the effects of strain softening and seepage on the stability of the surrounding rock.