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Abstract: The multi-piped freezing method is usually applied in artificial ground freezing (AGF) projects to fulfill special construction requirements, such as two-, three-, or four-piped freezing. Based on potential superposition theory, this paper gives analytical solutions to steady-state frozen temperature for two, three, and four freezing pipes with different temperatures and arranged at random. Specific solutions are derived for some particular arrangements, such as three freezing pipes in a linear arrangement with equal or unequal spacing, right and isosceles triangle arrangements, four freezing pipes in a linear arrangement with equal spacing, and rhombus and rectangle arrangements. A comparison between the analytical solutions and numerical thermal analysis shows that the analytical solutions are sufficiently precise. As a part of the theory of AGF, the analytical solutions of temperature fields for multi-piped freezing with arbitrary layouts and different temperatures of freezing pipes are approached for the first time.

This paper presents very intresting analytical solution for the mutiple tube freezing in artificial ground freezing practice, it can be used for design as a tool to estimate the freezing effect, will be very intresting for researchers in this area.

少量管冻结稳态温度场数学模型

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