Nonlinear analysis for the three-dimensional temperature fields in cold region tunnels

In this paper, based on the governing differential equations of the problem on temperature field with phase change, the finite element formulae of three-dimensional temperature fields are obtained from Galerkin's method. An illustrative example of the three-dimensional temperature fields in cold regions tunnel both with insulation and without insulation is presented on the basis of the air temperatures surveyed in the inside of the tunnel. The example shows that it is necessary to analyze the three-dimensional temperature fields in cold regions tunnels, and that it is effective to lessen the frozen or thawed areas of the rock surrounding the tunnels by constructing insulation, which can provide reference and numerical method for actual engineering design in cold regions.