Exact analytical solution for deep tunnels in viscoelastic–plastic rock considering the actual loading path

Abstract

The rock rheology and time process of tunnel construction make the mechanical responses of rock a function of time and are closely related to the loading path, however, these factors are not properly or correctly considered in analytical studies. The analytical study for deep tunnels in rheological rock is performed in this study, strictly taking into account the viscoelastic‒plastic characteristic of surrounding rocks and the actual loading path during excavation and supporting stages.The plane-strain problem of a circular tunnel in infinite plane under hydraulic far-field stress is simplified, with the time-dependent supporting pressure exerted at a specific time to consider the effect of delay installation of yielding support. The solving procedure as well as the time-dependent analytical solution of displacement, stress, and plastic radius in the excavation and supporting stages are presented in detail when the rocks satisfy the Unified strength theory and perfect plasticity. The analytical solutions agree very well with the numerical results, where the time procedure of tunnel excavation and support is simulated in the numerical model. Furthermore, the proposed solution can predict well the long-term deformation of the Shangxinzhai tunnel, which validates its applicability in real engineering. It is found that the tunnel deformation is underestimated if the unloading stage is not correctly considered. Based on the analytical solution, the influence of the supporting time, start time of the yielding stage and viscosity coefficient on the time dependence of tunnel convergence and stresses is investigated.