## 4 DBP-EP Pile Soil Thermomechanical Response Test
### DBP-EP Thermomechanical Response Analysis
#### 4.1.2 DBP-EP Side Friction Resistance Analysis  
Figure 7 illustrates the variations in lateral friction force for DBP-EP piles across various working conditions, where constant loads of 0 kN, 0.26 kN, and 0.78 kN are applied to the top of the pile. The calculation of the lateral friction force for the piles is derived from the observed axial strain, Young's modulus, and the cross-sectional area of the pile. Here, the axial observed strain represents the average of the strains measured across each pile cross-section. The positive lateral friction is specified to indicate the upward displacement of the pile, and negative friction is used to indicate the downward displacement of the pile. \[f=\frac{E(A_{i}\bar{\varepsilon}_{i}-A_{i+1}\bar{\varepsilon}_{i+1})}{\pi DL_ {i}} \tag{1}\]  
In this context, \(f\) represents the mean side friction of the pile (kPa), \(A_{i}\) denotes the cross-sectional area of the \(i\)-th segment of the energy pile (m\({}^{2}\)), \(\bar{\varepsilon_{i}}\) indicates the average axial observed strain at the \(i\)-th cross-section (\(\mu\epsilon\)), \(E\) signifies the modulus of elasticity of the material used for the pile, \(L_{i}\) refers to the length of the pile segment located between the \(i\)-th and the \((i+1)\)-th cross-sections (m), and \(D\) represents the diameter of the pile's cross-section (m). \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Operating Temperature (\({}^{\circ}\)C)**} & \multicolumn{2}{c}{\(t=2\) h} & \multicolumn{2}{c}{\(t=8\) h} & \multicolumn{2}{c}{\(t=24\) h} \\  & \(d=0.05\) m & \(d=0.05\) m & \(d=0.015\) m & \(d=0.05\) m & \(d=0.015\) m & \(d=0.05\) m \\ \hline \(T_{in}=30\) & \(-0.046\)\({}^{\circ}\)C & 0.154 \({}^{\circ}\)C & \(-0.099\)\({}^{\circ}\)C & 0.0188 \({}^{\circ}\)C & 0.0324 \({}^{\circ}\)C & 0.226 \({}^{\circ}\)C \\ \(T_{in}=35\) & 0.469 \({}^{\circ}\)C & 0.657 \({}^{\circ}\)C & 0.575 \({}^{\circ}\)C & 0.843 \({}^{\circ}\)C & 0.186 \({}^{\circ}\)C & 0.422 \({}^{\circ}\)C \\ \(T_{in}=40\) & 0.794 \({}^{\circ}\)C & 0.844 \({}^{\circ}\)C & 0.692 \({}^{\circ}\)C & 0.840 \({}^{\circ}\)C & 0.840 \({}^{\circ}\)C & 1.123 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table} 
Table 2: Difference between the temperature at the end of the pile and the average temperature of the pile as a whole. As illustrated in Figure 7, the resistance against friction on the side of the pile steadily rises as the duration of DBP-EP operations lengthens. Furthermore, the side friction resistance of the pile also escalates with an increase in the water temperature at the inlet. Analyzing the variations in the side friction resistance curve reveals a consistent overall trend: negative friction resistance is present in the upper section of the pile, whereas positive friction resistance can be found in the lower section. The structural configuration of DBP-EP affects these behaviors, leading to thermal expansion and upward displacement  
Figure 6: Curve of observed strain change of the pile body during heating under different working conditions. (**a**) \(F_{top}=0\) kN inside wall of pile. (**b**) \(F_{top}=0\) kN side wall of pile. (**c**) \(F_{top}=0.26\) kN inside wall of pile. (**d**) \(F_{top}=0.26\) kN side wall of pile. (**e**) \(F_{top}=0.78\) kN inside wall of pile. (**f**) \(F_{top}=0.78\) kN side wall of pile. of the surrounding soil beneath the pile. However, due to the overlying soil pressure exerted by gravity, the upward displacement of the soil is constrained, preventing this expansion and extrusion from affecting the middle and upper soil layers around the pile. Consequently, negative friction resistance is generated near the bottom of the pile. The variation in side friction resistance at the top of the pile is primarily influenced by the pile top load, which to some extent, inhibits the formation of negative friction resistance. Table 3 shows the difference in side friction resistance at the pile end for different time periods.