Elastic visco-plastic analysis for earthquake response of tunnels in cold regions

In this paper, in order to determine the initial stresses of tunnels in cold regions before earthquake occurs, a mathematical mechanical model and the governing differential equations of the coupled problem of temperature, seepage and stress fields, with phase change, are first derived from the theory of heat transfer, the theory of seepage and frozen soil mechanics. Then, the finite element formulae of this problem are obtained from Galerkin's method. Secondly, the visco-plastic constitutive equations of frozen soil for dynamic computation are given. Finally, an illustrative example is provided. The example shows that the effect of seepage field and stress field on the frozen depth of cold region tunnels is large and the influence of frost-heaving force on the stresses of the tunnel lining is very large. This example also indicates that the influence of initial stresses of tunnels in cold regions on the time stress response of tunnels to earthquake is large. So the effects of these factors on the tunnel lining should be taken into account in cold regions engineering design.