Analytical heat transfer model of energy piles in layered and anisotropic soils considering interfacial thermal resistance

The energy pile, as an innovative renewable energy system integrating ground source heat pump technology with pile foundation structures, exhibits thermal performance that is significantly influenced by complex soil conditions. To address the complications in heat transfer mechanisms caused by the layered characteristics of natural soils and their cross-anisotropy, this study develops a heat transfer model for energy piles embedded in layered and cross-anisotropic soils while accounting for interfacial thermal resistance. A semi-analytical solution in the Laplace domain is derived using the finite Hankel transform and Laplace transform, and the temperature response in the time domain is obtained via the Crump numerical inversion method. Comparative validation against COMSOL numerical solutions, classical analytical solutions, and experimental data demonstrates that the temperature prediction error of the proposed model remains below 2.1 % relative to numerical solutions. Compared to experimental measurements, the root-mean-square error (RMSE) is reduced by more than 42 % compared to conventional isotropic models. The near-field temperature response analysis reveals that the horizontal and vertical thermal conductivities of the soil exhibit distinctly different influences on the temperature distribution, with the horizontal thermal conductivity of the pile body playing a more dominant role in soil temperature response. Using an equivalent average thermal conductivity leads to deviations in temperature predictions. Parametric study indicates that the variations in the horizontal and vertical thermal conductivity of the soil have different impacts on temperature. In addition, the thermal anisotropy ratio (TAR) and interlayer thermal conductivity ratio (ITCR) significantly influence the interfacial temperature jump. Furthermore, under different thermal conductivity conditions, the effect of changes in the thermal anisotropy ratio on the temperature jump also varies.