| Summary: | Taking the freeze-sealing pipe roof method (FSPR) adopted in the Gongbei Tunnel project as the background, this study develops a simplified calculation model by considering different soil freezing points, tube layout, and site conditions. The analytical solution of the linear single row tubes is then used to formulate the analytical solution of the freezing temperature field of two kinds of linear single row tubes, with equal spacing in the image plane. This is achieved through conformal mapping and the variable separation method. Finally, the analytical solution to the steady-state temperature field of FSPR in the object plane is obtained. The numerical solutions of common freezing parameters in freezing engineering are analyzed to evaluate the accuracy of the analytical solution, and the influence of parameter differences on the freezing temperature field are also discussed, to provide a theoretical reference for popularization and application of similar construction methods.
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