# Finite Element Analysis of Combined Energy Piles with Long and Short Heat Exchanger Tubes
## 3 Model Overview
### Model Building  
The 3D finite element model of Abaqus was established. [PERSON] et al. [25; 26] believed that the temperature influence radii of different types of foundation soils such as sand and clay were 6 m and 4 m, respectively. In addition, [PERSON] et al. [27] found that, in the numerical model, when the net distance between the lower boundary of the foundation and the bottom of the energy pile is greater than 10 m, the influence of the setting of the bottom  
Figure 3: Schematic diagram of single deep–shallow combined buried energy pile. boundary condition on the temperature change of the entire foundation is negligible, to a certain extent. The pile foundation is a precast pipe pile with a length of 40 m and 100 mm thick cement soil on the outside of the pile; therefore, the height of the soil layer model is 100 m (2.5 times the length of the precast pile). The energy pile is planted in the middle of the model, and the soil layer is 25 times the pile diameter to form a 3D model of 20 m \(\times\) 20 m \(\times\) 100 m (the boundary exceeds the radius of influence of soil temperature). The soil layer is simplified into three layers: the upper 40 m is clay, the lower 60 m is sand, and there is a flowing groundwater seepage at a depth of 65-70 m.  
The elastic constitutive model is adopted for precast piles, the heat exchange tube, and water, and the Mohr-Coulomb elastoplastic model is adopted for cement soil and pile circumferential soil, which does not consider the influence of heat transfer liquid flow in the heat exchanger tubes on the temperature distribution. Studies have shown that precast piles work together with cement during loading, so they can be considered as a whole [28]. The initial temperature of the soil, groundwater, and cement soil was set to 20 \({}^{\circ}\)C. The Mohr-Coulomb friction penalty function was used to control the contact of the cement-soil interface, the contact relationship was the master-slave contact, the side of the cement soil was the main control surface, the soil body was the subordinate surface, and the friction coefficient was 0.3. For the displacement boundary, the bottom of the model foundation was fixed while the top of the model was free, and the normal deformations surrounding the periphery of the model were constrained. For the temperature boundary, the periphery and bottom of the model were set as the thermal insulating boundary. The finite element mesh is divided based on experience, and a trial calculation is performed. Then the calculation results are compared against the results by both finer and coarser grid divisions. The grid division is depicted in Figure 4, wherein the depth dimensions of the soil, pile, and cement soil were set as 2 m, and the element size of the pile shaft and cement soil section was 0.1 m. Finally, 11,028 soil units, 960 pile units, and 2640 cement-soil units were considered for the simulation. For the heat exchange tube, the depth dimension was 0.2 m and its cross-section dimension was 0.01 m. Moreover, 6400 units were considered for the two 40 m long heat exchange tubes. For the coupled heat flow analysis, the DC3D8 and FC3D8 grid attributes were employed in the heat transfer model and the water flow, respectively. The heat exchanger tubes are simplified to the column heat source in the 3D model, heat exchanger tubes material PE100 and heat exchanger tubes model DN38. The outer diameter of the heat exchanger tubes is 38 mm, the wall thickness is 2.5 mm, the length of the heat exchanger tubes on the outside of the pile is the same as the length of the pile, and the heat exchanger tubes are located on the inner side of the pile. The precast pile is composed of C80 concrete. The specific model material parameters are shown in Table 1.