Abstract 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 °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.

中文翻译：

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考虑限流管运行的拱北隧道冻封管顶稳态温度场解析解

摘要 为解决具有复杂边界条件的稳态温度场问题，为冻封管顶（FSPR）方法提供更完整的理论指导，该方法是一种新型的隧道施工预支护体系。本文基于拱北隧道简化考虑限制管运行提出了FSPR冻结模型，并首先利用拉普拉斯方程的叠加和边界分离方法研究了稳态温度场的解析解。然后通过将解析结果与不同特征截面的数值结果进行对比，验证解析解的准确性。最后，介绍了拱北隧道现场监测方案，并对现场实测数据进行了分析。结果表明，解析解与数值模拟和现场实测吻合良好。计算值与现场温度值的最大误差在2°C以内，证明了分析结果在实际工程中的适用性。现场试验还表明，限流管在不影响FSPR方法整体水封效果的情况下，可以有效控制冻土局部发育。