Analytical solution to temperature distribution of frozen soil wall by multi-row-piped freezing with the boundary separation method

The existing formulae for calculating temperature field distribution of frozen soil wall by double-row- and triple-row-piped freezing are deduced for specific arrangements of freezing pipes, where the pipe spacing and row spacing among different rows are assumed the same. And they cannot satisfy the needs of projects construction because the flexible arrangements for double-row- and multi-row-piped freezing are increasingly adopted. In this paper, analytical solutions to steady-state temperature field for double-row-piped freezing with different pipe spacing, row spacing and row staggered distances are theoretical derived based on the linear superposition of formula to temperature field for single-row-piped freezing. Then, with the superposition method mentioned above, analytical solution to temperature field distribution by multi-row-piped freezing in isotropic area is obtained. After that, the triple-row-piped freezing problem is taken as an example to show the application of the derived formula. And the formula to temperature distribution by aligned triple-row-piped freezing generated from the general solution shares the same form as the existing formula. And the calculating result of the formula for a special triple-row-piped problem shows good consistent with the numerical thermal results.