## 4 Results and Discussions
### Simulation Results
#### 4.2.5 Pile Internal Stress and Side Friction  
Table 5 and Figure 11 show the variations in the axial stress of the energy piles under continuous heating for 140 h at the flow rate of 1500 mL/min. Negative values represent compressive stress, while positive values indicate tensile stress. From Figure 11, it can be observed that there was a gradual transformation of the axial stress in the piles, shifting from compressive stress to tensile stress during the heating process. The internal stress of the FR pile gradually decreased as the depth increased. The maximum tensile stress occurred at a depth of 0.25 m for the FR pile with a value of 0.405 MPa and 750 mm for the FRPC pile with a value of 0.184 MPa. The stress difference in the two energy piles reached the maximum at the buried depth of 250 mm, with values of 0.308 MPa and 0.348 MPa when heating for 12 h and 140 h, respectively.  
Figure 9: Comparison of the simulated results of the unit heat power of different piles under different flow rates. (**a**) Heat power under 1500 mL/min flow. (**b**) Heat power under 3000 mL/min flow. (**c**) Heat power under 4500 mL/min flow. (**d**) Maximal heat power under different flow. (**e**) Minimal heat power under different flow. (**f**) Quantity of heat under different flow.  
The thermal stress difference at different buried depths was used to calculate the pile side friction. Under the continuous thermal load, the piles' and soil's thermal expansion caused relative displacement, resulting in pile-side friction. The pile-side friction resistance at different depths \(f_{\text{T,S}}\) was calculated using Equation (11):  
\[f_{\text{T,S}}=D\big{(}\sigma_{\text{JT}}-\sigma_{\text{JT-1}}\big{)}\big{/}4 \Delta L \tag{11}\]  
where \(D\) represents the pile diameter, \(\sigma_{\text{JT}}-\sigma_{\text{JT-1}}\) is the stress difference between the adjacent two measuring points, and \(\Delta L\) is the distance between the two strain measuring points. The side friction resistance was assumed to be positive upwards and negative downwards.  
Figure 12 compares the variation in side friction between the FRPC pile and the FR pile after continuous heating of 140 h at a flow rate of 1500 mL/min. It can be observed  
Figure 11: Stress changes in two energy piles along the depth at a 1500 mL/min flow rate.  
Figure 10: Displacement and temperature changes at the top of the energy piles and soil near the pile under continuous heating for 140 h at a flow rate of 1500 mL/min.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Time**} & \multirow{2}{*}{**Energy File**} & \multicolumn{3}{c}{**Stress at Different Buried Depths in the Pile (MPa)**} \\  & & **0.25 m** & **0.5 m** & **0.75 m** & **1.00 m** & **1.25 m** \\ \hline \multirow{2}{*}{12 h} & FRPC pile & \(-\)0.321 & \(-\)0.363 & \(-\)0.163 & \(-\)0.433 & \(-\)0.767 \\  & FR pile & \(-\)0.013 & \(-\)0.136 & \(-\)0.145 & \(-\)0.228 & \(-\)0.477 \\  & FRPC pile & \(-\)0.224 & \(-\)0.261 & \(-\)0.083 & \(-\)0.344 & \(-\)0.674 \\  & FR pile & 0.184 & 0.089 & 0.075 & \(-\)0.016 & \(-\)0.265 \\  & FRPC pile & 0.057 & 0.021 & 0.184 & \(-\)0.025 & \(-\)0.306 \\  & FR pile & 0.405 & 0.354 & 0.347 & 0.265 & 0.042 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Stress values at different buried depths in the piles at different times under continuous heating conditions with a flow rate of 1500 mL/min.  
that the pile-side frictional resistance of the FR pile was entirely downward, indicating that the entire pile expanded and moved upward. In contrast, the FRPC pile exhibited upward frictional resistance at a depth of 0.25-0.5 m.