环形单圈管冻结稳态温度场解析解

人工地层冻结技术被广泛应用于地下工程施工中。冻结温度场的计算是人工冻结法理论研究的基础，也是冻结施工设计的重要依据。人工地层冻结施工常使用环形单圈冻结管冻结，而至今尚无关于其温度场的解析解。基于水-热异类相似原理，根据传热过程与地下水流动相似的特点，利用保角映射、汇源反映和势函数叠加原理，类比推导了环形单圈冻结管稳态温度场解析解，并用热学数值模拟方法加以验证，同时提出了简化的解析公式。结果表明，解析解计算结果与数值模拟结果较吻合，其简化公式得到的结果与原解析公式基本一致。在解析公式的基础上，经过简化，反推得到外部冻结壁厚度公式。解析解、简化公式以及厚度公式可为环形单圈冻结施工与设计提供理论的依据与指导。

Analytical solution to steady-state temperature field of single-circle-pipe freezing

Artificial ground freezing is widely used in the construction of underground engineering. The calculation of freezing temperature field is not only the basement of theory research on artificial ground freezing, but also an important basis of the freezing construction design. Single-circle-pipe freezing method is often applied to artificial ground freezing projects, while the analytical solution of this situation has never been published. Thus it’s necessary to get the solution to benefit our engineering practice. Based on the theory of analogy between thermal and hydraulic problems, using conformal mapping, mirror reflection of sources and sinks, and the superposition of potential function, this paper gives an analytical solution to the steady-state temperature field of single-circle-pipe freezing and demonstrates its correctness by numerical thermal analysis. Comparison of the analytical solution with the numerical thermal analysis shows that the analytical solution is precise enough and will afford reasonable guidance in single-circle-pipe freezing projects. A simplified formula is also given and is proven to be precise enough. Based on the simplified formula, the thickness formula of the outer part of frozen wall is derived. The analytical solution, simplified formula and thickness formula can provide guidance and theoretical basement for construction and design of single-circle-pipe freezing projects.