## Journal of Central South University

 第46卷    第6期    总第250期    2015年6月

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(1. 同济大学 岩土及地下工程教育部重点实验室，上海，200092；
2. 同济大学 地下建筑与工程系，上海，200092
)

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

1. Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education,
Tongji University, Shanghai 200092, China;
2. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

Abstract:Single-circle-pipe freezing method is often applied in cross passage construction and mine shaft sinking. At present, there is only one analytical solution which is aimed at the situation that the ground inside the freezing-pipe circle is frozen solid. However, a more usual situation is that the area enclosed inside the freezing-pipe circle is not frozen completely. For this situation, an analytical solution to the steady-state temperature field of single-circle-pipe freezing was proposed. The solution was derived by converting the single-circle-pipe freezing model to a special single-row-pipe freezing model using conformal mapping, and then decomposing the single-row-pipe freezing model into the single-row-pipe freezing model and a linear temperature field model according to the separability of boundary conditions for harmonic equations. Comparison of the analytical solution with the numerical thermal analysis shows that the analytical solution is precise enough. Furthermore, the solution can also be employed for the temperature field of the frozen-solid situation.

Key words: artificial ground freezing; single-circle-pipe freezing; temperature field; analytical solution; conformal mapping; harmonic equations

 中南大学学报（自然科学版） ISSN 1672-7207 CN 43-1426/NZDXZAC 中南大学学报（英文版） ISSN 2095-2899 CN 43-1516/TBJCSTFT