Analytical solution to steady-state temperature field with typical freezing tube layout employed in freeze-sealing pipe roof method

Freeze-sealing pipe roof (FSPR) is an emerging auxiliary method in trenchless technology of underground engineering, which combines the advantages of Pipe-Roof Method and Artificial Ground Freezing method together. Based on practical engineering, a new typical freezing model of FSPR method with freezing tubes arranged inside jacking pipes is proposed in this paper, and then analytical solution to steady-state temperature field is obtained by transforming circular boundary condition to linear boundary condition with conformal mapping and superposition method. A comparison between the analytical results and numerical thermal results shows that the analytical solution is sufficiently precise for practical use. Temperature distribution of three characteristic sections gives an analytical validation for waterproofing performance and the results of field test bring a practical confirmation for the freezing effect of FSPR method. This paper enriches the theoretical research in steady-state temperature field of AGF and provide a reliable reference basis for FSPR design in future applications.