Abstract: Based on Nishihara model, the first derivative of the deviatoric strain tensor of the viscoplastic element is assumed to be proportional to the difference between the transient deviatoric stress tensor and the steady-state deviatoric stress tensor. Thus, the constitutive equation of ground in viscoplastic region is obtained. The viscoelasto-viscoplastic solutions are derived by means of Laplace transform and Laplace reverse transform. While the time t is close to 0, the viscoelasto-viscoplastic solutions could be degenerated into linear elastic solutions. While the time t tends to infinity, the solutions could be simplified into perfectly elastic-plastic solutions. The time-dependent performances of ground displacement, ground stress and the plastic zone are investigated through an engineering example. When the support force remains constant, the ground displacement and the radius of plastic zone increase continuously with time and then tend to be stable. The influence of time-dependent behavior on the radial stress and tangential stress of viscoelastic region are not very obvious, while the influence on the tangential stress in viscoplastic region is much larger. For the rock mass around the wall in viscoplastic region, the tangential stress changes faster with time. In addition, the tangential stress of tunnel wall under different supporting forces is larger at the initial stage of support, so the strategy of timely support should be adopted. Considering the influence of ground time-dependent performances on the support, the ductile support is suggested to ensure the stability of the surrounding rock and lining.

Key words: circular tunnel, viscoelasto-viscoplastic, Nishihara model, Laplace transform, analytical solution