# An Improvement of the Load Transfer Method for Energy Piles Under Thermo-Mechanical Loads
## 1 Introduction  
Geothermal energy, as a low-carbon and energy-saving renewable energy, can be developed and utilized in various fields all over the world. ([PERSON] et al. [1], 2015; [PERSON] et al. [2], 2010). Energy piles represent an innovative technology that integrates ground-source heat pump systems with building pile foundations. By embedding heat exchange pipes within the pile foundation and circulating a heat transfer medium, this system utilizes the stable thermal properties of subsurface soil to provide building heating and cooling. Structurally, energy piles primarily consist of load-bearing piles, embedded heat exchange pipes, and a heat pump connection system. During operation, heat transfer occurs through the pipes into the surrounding soil, leading to temperature variations in the adjacent geomaterials. Additionally, the restraint imposed by the surrounding soil on pile deformation induces thermal stresses within the energy pile. This complicates the load-transfer mechanism between the pile and soil, ultimately altering the bearing behavior of energy piles ([PERSON] et al. [3], 2006; [PERSON] et al. [4], 2019; YANGet al. [5; 6], 2023). Therefore, it is necessary to study the influence of the coupling effect of temperature and force on the working characteristics of energy piles to ensure safe and sustainable operation. At present, many researchers are devoted to the study of thermo-mechanical coupling characteristics of energy piles, and some scholars have conducted relevant field tests to investigate the effect of temperature on structural and load-bearing characteristics ([PERSON] [7], 2017. [PERSON]. [8], 2005. [PERSON] [PERSON]. [9], 2009. [PERSON] [10], 2015). The field test results show that the change of temperature will lead to the change of pile shaft force, lateral resistance, and pile top settlement. In other words, the effect of temperature on energy piles is not negligible. Although the load test in the field presents a reliable method for observing and determining the thermal-mechanical behaviors of energy piles, it is manifestly both time-consuming and costly and requires numerical modeling approaches as more efficient alternatives. Some scholars have carried out research on the operating characteristics of energy piles by means of numerical simulation and theoretical analysis. ([PERSON] et al. [11], 2024; [PERSON] et al. [12], 2020; [PERSON] et al. [13], 2021; [PERSON] et al. [14], 2019)[PERSON]  
Among the many methods, the load transfer method has received wide attention from scholars because of its simplicity and practicality of calculation and because the method requires only fundamental mechanical parameters (e.g., density and internal friction angle) that are routinely obtained through standard geotechnical investigations and geotechnical testing. [PERSON] [15] (2011) considered the effect of temperature on pile-soil action, and the first energy pile load transfer displacement coordination algorithm was established by using the [PERSON] equilibrium condition at the neutral surface. The load-bearing characteristics of energy piles under the coupling effect of temperature and force were calculated by using a segmental linear load transfer model, and the reasonableness of the method was verified by comparing it with the field-measured data. Although the method achieves good computational results, it still has the following shortcomings. (1) When the top of the pile is not restrained, that is, the top of the pile is free, the pile top axial force calculation result is not zero; thus, it is considered that this method cannot accurately reflect the constraint at the top of the pile. (2) It is necessary to assume the location of the neutral point and calculate the relatively accurate location of the neutral point by iteration, and the calculation results may not necessarily converge. (3) The segmented linear model cannot accurately reflect the progressivity of the soil deformation trend.