Analytical solution to steady-state temperature field for straight-row-piped freezing based on superposition of thermal potential

The existing analytical solutions to steady-state temperature field for straight row-piped freezing in artificial ground freezing cover single-piped, multi-piped, single-row-piped and double-row-piped freezing, yet they are not sufficient to meet the needs of construction projects because triple-row-piped or even multi-row-piped freezing are increasingly adopted. In this paper, the original engineering problems of the temperature field of single-piped and row-piped freezing are firstly converted to the solving of a plain Laplace equation under specified boundary conditions. Based on superposition of thermal potential, the analytical solutions to steady-state temperature field for single-piped, single-row-piped, double-row-piped freezing are deduced in succession and then the solution for triple-row-piped freezing is obtained, which is then validated through comparison with the thermal numerical analysis. Furthermore, the formula for calculating the thickness of triple-row-piped frozen soil wall is proposed, which is important in construction management of artificial ground freezing.