## 4 DBP-EP Pile Soil Thermomechanical Response Test
### DBP-EP Pile Toe Earth Pressure Analysis  
Figure 8 demonstrates the changes in earth pressure at the base of the pile, along with the proportion of the end bearing capacity under varying working conditions, with fixed loads of 0.26 kN and 0.78 kN applied at the top of the pile. For this experiment, it is presumed that the earth pressure distribution at the pile's underside is uniform. The vertical load is calculated based on the earth pressure readings obtained from the pressure gauge, utilizing the specific equations outlined in Ref. [16], as follows:  
\[F_{toe}=\sigma_{toe}A_{toe} \tag{2}\]  
In this context, \(F_{toe}\) represents the vertical load at the base of the pile (kN), \(\sigma_{toe}\) denotes the earth pressure occurring at the pile's toe (kPa) and \(A_{toe}\) refers to the effective bearing area of the pile toe (m\({}^{2}\)). This approach serves merely as an estimated approximation of the DBP-EP vertical load; therefore, additional analysis utilizing more sophisticated sensors and techniques is necessary. The bar graphs presented in Figure 8 illustrate the real vertical loads at the toe of the pile within the DBP-EP system across various operational conditions after 24 h. As the temperature of the water intake escalates, the vertical load at the pile toe progressively  
Figure 8: Percentage of earth pressure and end bearing capacity at pile toe for different working conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operating Condition** & \multicolumn{1}{c}{**t = 0 h-t = 2 h**} & \multicolumn{1}{c}{**t = 2 h-t = 8 h**} & \multicolumn{1}{c}{**t = 8 h-t = 24 h**} \\ \hline
1-1 & \(-\)9.555 kPa & \(-\)10.314 kPa & \(-\)25.62 kPa \\
1-2 & 2.94 kPa & \(-\)7.284 kPa & 2.181 kPa \\
1-3 & 8.085 kPa & \(-\)6.125 kPa & \(-\)1.501 kPa \\
2-1 & \(-\)19.643 kPa & \(-\)15.674 kPa & \(-\)71.425 kPa \\
2-2 & \(-\)53.637 kPa & 2.701 kPa & \(-\)74.002 kPa \\
2-3 & \(-\)28.555 kPa & 3.235 kPa & \(-\)49.465 kPa \\
3-1 & \(-\)29.418 kPa & \(-\)77.396 kPa & \(-\)35.064 kPa \\
3-2 & \(-\)52.571 kPa & \(-\)70.78 kPa & \(-\)0.274 kPa \\
3-3 & \(-\)93.731 kPa & \(-\)29.988 kPa & 0.797 kPa \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Difference in side friction resistance at the pile end for different time periods. rises. Nonetheless, if the constant load applied at the top of the pile is increased, the increase in the vertical load at the toe of the pile becomes less significant for the same water intake temperature. Specifically, when the pile top load is raised from 0.26 kN to 0.78 kN, the vertical load variations at the pile toe are recorded as \(-\)0.004 kN, 0.009 kN, and 0.004 kN, respectively. This indicates that with an increase in the constant load applied at the top of the pile, the influence of the water intake temperature on the vertical load at the toe decreases. The end bearing capacity [16] can be calculated from the pile toe and pile top vertical loads, as follows:  
\[\gamma=\frac{F_{toe}}{F_{top}} \tag{3}\]  
In this context, \(\gamma\) is the percentage of end bearing capacity (%), and \(F_{top}\) is the constant load applied at the pile top (kN). The line graph in Figure 8 shows the DBP-EP end-loading percentage under different operating conditions after 24 h. The end-bearing percentage gradually increases with the rise in inlet temperature. The primary reason for this phenomenon is the downdrag effect exerted by the surrounding soil during the energy pile's operation [50]. This downward pull results in the displacement of sandy soil near the pile toe, which subsequently causes a reallocation of a portion of the vertical load that was originally carried by the adjacent sandy soil to the pile toe. As a result, the heightened vertical load at the pile toe signifies a fraction of the load that ought to have been sustained by the neighboring sandy soil. With the increase in load on the pile top, there is a gradual reduction in the proportion of end-bearing capacity.