Analytical solution model of heat transfer for energy soldier piles during excavation to backfilling

This paper presents a two-dimensional heat transfer model for energy soldier piles during excavation and after backfilling. Based on Green's function and separation of variables method, this model considers the heat transfer process from various angles during excavation and after backfilling, deriving a series of analytical solutions for the heat transfer processes. It is more suitable for solving the heat transfer problem of energy soldier piles. The accuracy of the analytical solution was verified by numerical simulation and classical analytical solutions. Then, the effects of air convection coefficient and backfill materials' thermal diffusivity on heat transfer are analyzed. The results show that the temperature rise of both the soil and the pile in the non-excavated case (ordinary energy pile) is lower than that of the various convective coefficient cases, and the convective heat transfer contributes to the heat transfer capacity of energy soldier piles. After backfilling, materials with higher thermal diffusivity have smaller temperature rise. Conversely, materials with lower thermal diffusivity have higher temperature rise. Under the long-term operation strategy, the heat flux within the soil and backfill is higher and favorable for heat transfer by selecting the backfill with lower thermal diffusivity.