Mathematical Solution of Temperature Field in Non-Hollow Frozen Soil Cylinder Formed by Annular Layout of Freezing Pipes

Zequn Hong (), Rongjian Shi, Fengtian Yue, Jiaguang Yang and Yuanhao Wu
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Zequn Hong: School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Rongjian Shi: School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Fengtian Yue: School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Jiaguang Yang: Natural Resources Bureau of Longsheng Multi-Ethnic Autonomous County, Guilin 541799, China
Yuanhao Wu: China Construction Eighth Engineering Division Co., Ltd., Shanghai 200112, China

Mathematics, 2023, vol. 11, issue 8, 1-15

Abstract: With the wide application of the artificial ground freezing method in municipal underground engineering, the annular layout of freezing pipes is often adopted to form a frozen soil cylinder. However, there is still no analytical solution that can calculate the temperature distribution of frozen soil formed in this case. In this paper, a mathematical model of a steady-state temperature field of single-circle freezing is established, in which the inside of the freeze ring is completely frozen; that is, the temperature of all excavation sections is below the freezing point. Then, the analytical solution of temperature distribution is deduced through the complex variable method and potential superposition method. Comparison results of the analytical solution with those of the numerical simulation show that the analytical solution is precise enough. The temperature distribution of the main section and the intersection is approximately the same on the inner side, but the freezing effect of the main section is relatively better near the freezing pipes and outside the freeze ring. Besides, according to the derived analytical solution and common freezing parameters, a simplified formula to calculate the temperature field with enough accuracy was proposed, and the error can be controlled below 1‰. Finally, based on the simplified formula, a calculation method for frozen soil thickness and the average temperature is also given in this paper.

Keywords: temperature field; analytical solution; ground freezing; frozen soil cylinder (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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