Analytical method for insulation layer thickness of highway tunnels with multilayer dielectric in cold regions

Yuximolegai tunnel at Tianshan Mountain of Xinjiang is built in a seasonal frozen region. The thickness of insulation layer needs to be determined against frozen damage. For the solution to this problem, a model is established. When the insulation layer has good effect and no phase change occurs, the Laplace integral transform is employed to solve the temperature field of cold-region tunnels. Compared with the stability and accuracy of the stehfest method, those of the Den Iseger method, which is based on the Gaussian quadrature rule and the fast Fourier transform, are better. Thus, this method is used to solve the inversion of Laplace transform. Based on the results of Yuximolegai tunnel, it is shown that the temperatures of the insulation layer, the linings and the surrounding rocks follow the law of simple harmonic vibration with air temperature. Since the temperature difference between the two edges of 5 cm-thick insulation layer attains 9.63℃, it can not protect the surrounding rock against frozen heave. If the tunnel needs to be protected well in design period, the thickness of insulation layer should be 27 cm at least. Based on the parameter analysis, although the influence of convective heat transfer coefficient on solid surface is large, the influence on thickness of the insulation layer is limited. The insulation layer should decrease with the increase of the annual mean temperature and increase with the safe time of tunnels. With the increase of ground temperature, the thickness of insulation layer reduces gradually. Finally, by analyzing the annual mean temperature and ground temperature, the relationship between this two factors and the thickness of insulation layer is established, which may provide the basis for the design of other tunnels in this region.