Analytical Study on Heat Transfer of a Tunnel Lining-Rock-Insulation Structure in Cold Regions

In cold regions, the flow of outside air into a tunnel often causes freeze–thaw damage to the surrounding rock, and insulation methods are usually adopted to avoid this damage. In this study, the heat transfer in a multilayer tunnel structure that includes a rock layer, an initial lining, an insulation layer, and a secondary lining was investigated, and convection between the tunnel air and the inner surface of the tunnel lining was considered. A mathematical model describing the heat transfer process was established, and an analytical solution for the temperature field was developed using Duhamel’s principle and the separation-of-variables method. The model and the solution were verified by comparing the computational results of the analytical solution with the computational results and in situ measurements available in the literature. By treating the minimum temperature of the inner surface of the surrounding rock as a function of the insulation thickness, a procedure to determine the minimum insulation thickness that ensures no freeze–thaw damage to the surrounding rock was developed based on the analytical solution using the bisection method. Computational examples were presented, and the effects of different factors on the minimum temperature of the inner surface of the surrounding rock and minimum insulation thickness were investigated.