# Finite Element Analysis of Combined Energy Piles with Long and Short Heat Exchanger Tubes
## 4 Analysis of the Results
### Pile Axial Force  
Figure 11 shows the distribution curve of the axial force of the pile body under different combinations of heat exchanger tube lengths (\(L_{1}\) is the length of the outer heat exchanger tubes of the pile and \(L_{2}\) is the length of the inner heat exchanger tubes of the pile). The PHC600 (130) had a pile top axial force of 2493 kN only under a 50% ultimate load (shown by the black line in Figure 11), and the pile shaft force gradually decreased to 47 kN with increasing depth. When it was heated by the heat exchanger tubes on the outside of the pile and with 50% ultimate load (shown by the red line in Figure 11), the pile top axial force was 2513 kN, and the pile shaft force gradually decreased to 139 kN with increasing depth. At this time, compared with the situation where the heating load was not applied, the axial force of the pile top was increased by 0.80%, and the axial force of the pile end was increased by a factor of three. When the heat exchanger tubes on the inside of the pile were laid, the axial forces of the pile top were 2527, 2522, and 2519 kN in the three cases of \(L_{2}\) = 40, 60, and 80 m, respectively, which increased by 1.36%, 1.16%, and 1.04% compared with the situation without applying heating load. The axial forces of the pile end were 170, 169, and 160 kN, respectively, which increased by a factor of 3.6, 3.6, and 3.4 compared with the situation without applied heating load. It can be seen from the figure that, after the application of heating load, the axial force of the pile body increased significantly, especially in the lower part of the pile, and the axial force of the pile body reached the maximum increase in the middle and lower part of the pile, which was 469, 433, and 413 kN, respectively, accounting for 48.57%, 44.83%, and 42.80% of the axial force of the pile body when the temperature load was not applied. When the outer heat exchanger tubes were cooled and subjected to a 50% ultimate load (shown by the yellow line in Figure 10), the pile top axial force was 2491 kN, and the pile shaft force gradually decreased to 23 kN with increasing depth. Compared with the situation without the application of a cooling load, the axial force of the pile top was reduced by 0.08%, and the axial force of the pile end was reduced by 51.06%. When the heat exchanger tubes on the inside of the pile were laid, the axial forces of the pile top were 2486, 2487, and 2488 kN in the three cases of \(L_{2}\) = 40, 60, and 80 m, respectively, which were reduced by 0.28%, 0.24%, and 0.20% compared with the situation without applying cooling load. The axial forces of the pile end were 10, 9, and 6 kN, respectively, and the axial forces of the pile end were reduced by 78.72%, 80.85%, and 87.23% compared with the situation without cooling load. When  
Figure 10: Effect curve of groundwater seepage rate on pile top displacement. the cooling load was applied, it can be seen that the axial force of the pile body decreased, and the axial force of the pile body reached the maximum reduction in the middle and lower part of the pile, which was 115, 109, and 106 kN, respectively, accounting for 24.50%, 23.31%, and 22.59% of the axial force of the pile body without the applied temperature load. As the length of the heat exchanger tubes on the inside of the pile increased, the heat transfer between the heat exchanger tubes and the surrounding soil increased; that is, the temperature of the pile body changed less at the end of the heat exchange. Therefore, the temperature stress caused by temperature changes also decreased, and the changes in the axial force between the pile end and the pile top also decreased. Figure 12 shows the distribution curve of the axial force of the pile body under different groundwater seepage flow rates (\(v\) is the groundwater seepage flow rate).