Viscoelastoplastic Displacement Solution for Deep Buried Circular Tunnel Based on a Fractional Derivative Creep Model

Abstract

Time-dependent deformation of surrounding rock is a common phenomenon for tunnels situated in soft rock stratum or hard rock stratum with high geo-stress. To describe this phenomenon, a creep model combining the Abel dashpot and a non-Newton viscous element was adopted, and the analytical solution about the viscoelastoplastic deformation for circular tunnel was obtained based on this creep model. Then, the auxiliary tunnel of Jinping II hydropower station was taken as an example to reveal the influence of creep parameters on the creep deformation. The research shows that (1) the creep model can well describe the whole creep stage of rocks, that is, the decay, constant, and accelerated creep stages, (2) the creep deformation has a positive relation with the value of fractional order of Abel dashpot and the order of the non-Newton viscous element, and (3) the creep curves between test results and analytical solutions are well consistent with each other, which demonstrate the validity of the analytical solution.