Analytical solution to steady-state temperature field of Freeze-Sealing Pipe Roof applied to Gongbei tunnel considering operation of limiting tubes

摘要

In order to solve the problem of steady-state temperature field with complex boundary conditions and provide a more complete theoretical guidance for Freeze-Sealing Pipe Roof (FSPR) method, which is a new pre-supporting system for tunnel construction. This paper proposed a FSPR freezing model based on the simplification of Gongbei tunnel considering the operation of limiting tubes, and the analytical solution of steady-state temperature field was first investigated using the superposition and boundary separation methods of the Laplace equation. Then we verified the accuracy of the analytical solution by comparing the analytical results with the numerical results in different characteristic cross-sections. Finally, we introduced the on-site monitoring scheme of Gongbei tunnel and analyzed the field measurements. The results show that the analytical solution agrees well with the numerical simulation and field measurement. The maximum errors between calculated values and field temperature values are within 2 degrees C, which demonstrates the applicability of the analytical results in practical engineering. Field test also shows that the limiting tubes can effectively control the local development of frozen soil without affecting the overall water sealing effect of FSPR method.