Visco-plastic deformation analysis of rock tunnels based on fractional derivatives

Abstract

The squeezing of rock tunnels in soft strata is often encountered during and after excavation, which is closely related to the viscoplasticity of rock mass. However, previous studies involved multiple creep elements in the calculation of visco-plastic deformation, which cost much time to identify creep parameters. In this paper, a novel four-element fractional visco-plastic (FVP) model, which includes two Abel dashpots, one spring and one visco-plastic body, is established using fractional derivatives. Three-dimensional creep equation of the FVP model is first derived using the von Mises equivalent plastic stress-strain relationship. Then the closed-form solution of visco-plastic deformation of the surrounding rock around circular tunnels is derived by the FVP model combining with the non-associated flow rule and the Hoek-Brown criterion. Next, taking rock tunnels that are excavated in three different quality rock salt as examples, parametric investigations of time-dependent parameters and time-independent parameters are carried out. Visco-plastic deformation curves of rock tunnels, which includes (a) the displacement of tunnel wall versus time; (b) the displacement of visco-plastic zone versus depth, are analyzed. Finally, the auxiliary tunnel of Jinping II hydropower station is taken as a typical example for studying the time-dependent deformation of rock tunnels. The analytical results are in good agreement with the experimental and monitoring data. This paper may blaze a new trail to quickly evaluate the visco-plastic deformation of rock tunnels during the early design process.