Analytical solution for three-dimensional radial heat transfer in a cold-region tunnel

The study of the temperature field of cold-region tunnels is fundamental for preventing frost heave. At present, considerable knowledge has been obtained by numerical simulation and physical experimentation. In this paper a computational model for three-dimensional radial heat transfer was established according to some reasonable assumptions, and the complex boundary conditions inside the tunnel surface including axial coordinate z and time t were obtained based on the analysis of the field temperature monitoring data. The z and t terms in the boundary were split to simplify the problem. Laplace and Fourier integral transformation methods were combined to solve this problem, and the Den Iseger method was adopted to solve the Laplace inverse transformation. Yuximolegai tunnel was introduced to study its temperature distribution. The freezing length in z direction is reduced from 143 m to 70 m and the maximum radial freezing depth at the entrance is also shortened from 4.7 m to 2.4 m due to 5 cm insulation layer, which reveals that the effect of 5 cm insulation layer was remarkable. Considering the efficiency of insulation layer, it needs to be combined with other measures to prevent frost damage of surrounding rock. The analysis of convective heat transfer coefficient, formation temperature, and thickness of the insulation layer was performed to obtain their influence on the lining temperature. The results show that the influence of the convection heat transfer coefficient is small. The effect of the insulation layer improves with increasing formation temperature and worsens as the thickness of the insulation layer increases. These achievements can enrich the research of temperature fields of tunnels in cold regions and are significant for guiding tunnel design in cold regions.