Non-linear analysis for the freezing–thawing situation of the rock surrounding the tunnel in cold regions under the conditions of different construction seasons, initial temperatures and insulations

In this paper, based on the governing differential equations of the problem of temperature field with phase change, the finite element formulae of this problem are obtained from Galerkin's method. An illustrative example of the temperature field in cold region tunnel under the conditions of the different construction seasons, different initial temperatures, different thicknesses and thermal conductivity of insulation material is provided. Then some significant results are presented, which can provide a reference for actual tunnel engineering designs in cold regions.