Analytical Method for Temperature Field Distribution of Annular Double-Loop Freezing Pipes in Adjacent Urban Tunnels

The complex condition of an adjacent tunnel in urban city includes high water content, limited construction space, and the presence of an adjacent tunnel. To address these challenges, the artificial ground freezing method is employed to ensure construction safety and stability. Considering the complex problem of temperature field interaction in the freezing construction process of adjacent tunnels, for the first time, this paper proposes a generalized analytical solution for two-dimensional steady-state temperature fields suitable for the annular double-loop freezing system of adjacent tunnels. Based on the polar coordinate heat conduction control equation and the conformal transformation method, the complex geometric arrangement is mapped into a linear system that can be solved, and the analytical solution expression is constructed by combining the heat source superposition principle. In this paper, a numerical model of the adjacent tunnel annular double-loop freezing pipe is established through COMSOL Multiphysics 6.2 software. At the same time, the formula of the analytical method is programmed and solved using Python 3.12, and finally the temperature fields obtained by the two methods are compared. The results show that the analytical solution has good consistency in isotherm distribution, temperature field trend and characterization of frozen core area, which verifies the theoretical rationality and practicability of the constructed model.