## 4 Conclusions  
Based on the heat transfer mechanism of energy piles, the differential equation governing the heat transfer of energy piles was proposed. A finite element numerical model was developed and verified, and it can be applied to analyze the unsteady-state temperature distribution and the thermomechanical behavior of the energy pile group. The temperature field evolution of the energy pile under typical intermittent working conditions and heating/cooling load imbalance conditions were analyzed using this model. Moreover, the thermal behavior of the energy pile group was investigated, and the influence of the layout mode on the thermomechanical behavior of the energy piles group was analyzed in six different scenarios. Specific conclusions are as follows:  
1. Under typical intermittent operation conditions, the temperature of the energy pile and surrounding ground near the heat exchange pipe varies periodically. The closer the distance to the heat exchange pipe, the greater the temperature gradient and the more sensitive to the change in heating load. When the distance from the center of the pile exceeds 1 m, the characteristics of intermittent operation can no longer be reflected;
2. For areas with unbalanced cold and heating load, long-term operation of energy piles leads to thermal accumulation, and the maximum temperature of energy piles occurs in the first daily cycle. The cooling and heating load should be leveled by an auxiliary cold source (cooling tower) or auxiliary heat source (solar collector), thus controlling the fluctuation of ground temperature within a reasonable temperature range;3. When the pile group is all energy piles, the DOF at the pile top is the highest, and the pile top load at different positions decreases in the order of corner pile > side pile > center pile. In summer/winter working conditions, the increase/decrease in pile temperature induces axial compression/tensile stress. The axial temperature stress induced at the top of the center pile and the bottom of the corner pile is the largest. In addition, the DOF of each pile varies in the range of 0.985-1, and the constraints between piles are very small;
4. When the pile group is partially used as the energy pile, the non-energy pile acts as the \"anchor pile\", and it generates the added tensile stress. Decreased number of energy piles generates lower DOF of center piles and induces higher temperature stress. The stress induced by the corner pile does not destroy the pile or reduce its durability. Moreover, due to the constraint of the platform, the bending moment of piles at different positions is different, and the temperature stress increases with the increase in pile spacing.  
Conceptualization, P.Z. and X.L.; methodology, L.H.; software, Y.W.; visualization, C.Z.; writing--original draft preparation P.Z. and L.H.; writing--review and editing X.L. and C.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Fundamental Research Funds for the Central Universities (grant number 2022 QN1033), QiHang project of China University of Mining and Technology (grant number 102522172), Science and Technology Project of Xuzhou, China (KC21312), and the National Key R&D Program of Jiangsu, China (grant number BE2020038).  
Not applicable.  
The relevant data are all included in the paper.  
The authors declare no conflict of interest.