# Finite Element Analysis of Combined Energy Piles with Long and Short Heat Exchanger Tubes
## 4 Analysis of the Results
### Pile Top Displacement  
Figure 9 shows the change curve of pile top displacement under different heat exchanger tube length combinations (\(L_{1}\) is the length of the outer heat exchanger tubes of the pile and \(L_{2}\) is the length of the heat exchanger tubes inside the pile). It can be seen from the figure that the top displacement of the pile is greatly affected by the temperature in the first four days, showing a rapid increase trend, and flattens after four days. After adding the heat exchanger tubes on the inside of the pile, the heat exchanger tubes and the pile body exchange more heat than the traditional energy pile, which only arranges  
Figure 8: Cloud diagram of pile top temperature change.  
the heat exchanger tubes on the outside of the pile. With the increase of the length of the heat exchanger tubes on the inside of the pile, more heat exchange between the heat exchanger tubes and the deep soil is carried out, and the heat exchange with the pile body gradually decreases. Under a load of 2500 kN and a temperature load of 50 \({}^{\circ}\)C, the maximum displacements caused by \(L_{2}\) = 40, 60, 80, and 0 m were 4.73 mm, 4.46 mm, 4.31 mm, and 4.07 mm, respectively. Compared with the settlement generated by the piles with only the pile top load, the settlement decreased by 27.63%, 26.05%, 25.18%, and 23.77%, respectively. This is due to the continuous reduction of heat exchange between the pile body and the heat exchanger tubes so that the expansion of the pile also constantly decreases. Under the load of 2500 kN and the temperature load of 5 \({}^{\circ}\)C, the maximum displacement caused by \(L_{2}\) = 40, 60, 80, and 0 m was \(-\)2.82 mm, \(-\)2.73 mm, \(-\)2.68 mm, and \(-\)2.41 mm, respectively. Compared with the settlement generated by the piles with only the pile top load, the settlement decreased by 16.47%, 15.95%, 15.65%, and 14.08%, respectively. This is due to the continuous decrease in heat exchange between the heat exchanger tubes and the surrounding soil, which leads to a constant reduction in the settlement of the pile.  
Figure 10 shows the influence curve of groundwater seepage rate on pile top displacement (\(\upsilon\) is groundwater seepage flow rate), and it can be clearly seen that when the flow rate increased from 0 m/s to 2 \(\times\) 10\({}^{-5}\) m/s, the pile top displacement change in the temperature lifting condition was very small. The maximum displacement under the heating condition was 4.68 mm, 4.65 mm, and 4.64 mm, respectively, which decreased by 27.33%, 27.16%, and 27.10% compared with the settlement generated only under load. However, when the groundwater seepage rate reached 2 \(\times\) 10\({}^{-4}\) m/s, the pile top displacement changed greatly, and the maximum displacement was reduced to 4.31 mm, which is 25.18% less than the settlement generated only under load. It can be clearly seen that, when the flow rate increased from 0 m/s to 2 \(\times\) 10\({}^{-5}\) m/s, the maximum displacement under the cooling condition was \(-\)2.94 mm, \(-\)2.92 mm, and \(-\)2.91 mm, respectively, which increased by 17.17%, 17.06%, and 17.00% compared with the settlement generated only under load. However, when the groundwater seepage velocity reached 2 \(\times\) 10\({}^{-4}\) m/s, the top displacement of the pile had a clear change, and the maximum displacement was reduced to \(-\)2.68 mm, which is reduced by 15.65% compared with the settlement generated only under loading. This is due to the fact that, in the case of a low flow rate, the heat taken away by the heat exchange liquid in the heat exchanger tubes does not increase significantly, but when the flow rate reaches 2 \(\times\) 10\({}^{-4}\) m/s, the heat taken away by groundwater seepage exceeds a critical point,  
Figure 9: Effect curve of heat exchanger tube length on the displacement of pile top under 2 \(\times\) 10\({}^{-4}\) m/s flow rate.  
which has a greater impact on the temperature of the pile body and significantly reduces the expansion of the pile.