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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。
Artificial ground freezing technology is widely used in underground construction. The calculation of freezing temperature field is the basis of the theoretical study of artificial freezing method, and also an important basis for the freezing construction design. Artificial frozen ground construction often uses a circular loop of frozen tube freezing, and so far no analytical solution of its temperature field. Based on the principle of water-heat heterogeneous similarity, according to the similarity between the heat transfer process and the groundwater flow, the analytic solution of the steady-state temperature field of the unimorphic ring freezing tube was derived by using the conformal mapping, the reflection of Huiyuan and the principle of superposition of potential functions. Simulation method to be verified, at the same time proposed a simplified analytical formula. The results show that the results of analytical solution are in good agreement with the numerical simulation results. The simplified formulas are basically the same as the original analytical formulas. Based on the analytical formula, the formula of the external frozen wall thickness is obtained after simplification and backstepping. Analytical solution, simplified formula and thickness formula can provide theoretical basis and guidance for the construction and design of annular single-ring freezing.