# A Study on the Softening Shear Model of the Energy Pile-Soil Contact Surface
## 3 Results
### Softening Shear Model of Pile-Soil Contact Surface under Large Shear Displacement Conditions
#### 3.5.3 Validation of Pile-Soil Interface Model Simulation Capability  
To verify the validity of the softening model, the indoor shear test data of Ghinonna [29] and Donna [30] were used for a comparison of the simulation. These test systems can reflect the effects of key factors, such as soil type, contact surface roughness (\(R_{n}\)), relative density (\(D_{r}\)), normal effective stress (\(\sigma_{n}\)), temperature, etc., on the softening characteristics, and the specific test conditions and parameters are shown in Table 3.  
Figures 16-18 show the test and simulation results of the shear stress-shear displacement of the contact surface of clay-concrete, sand-concrete and sand-aluminum plate, respectively. Through the data comparison, it is found that the simulated values are in good agreement with the experimental values, which indicates that the softening model proposed in this paper can simulate the relationship between the shear stress-shear displacement of the contact surface in different conditions well and calculate the softening characteristics of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & \(R_{n}\) & \(D_{r}\) (\%) & \(\sigma_{n}\) (kPa) & **Temperature (\({}^{\circ}\)C)** \\ \hline Clay-Concrete & 30 & & 50, 100, 150 & 20 \({}^{\circ}\)C, 50 \({}^{\circ}\)C \\ Sand-Concrete & 0.12 & & 50, 100, 150 & 20 \({}^{\circ}\)C, 60 \({}^{\circ}\)C \\ Sand-Aluminum Plate & 0.250 & 85 & 100, 200, 300 & Indoor temperature \\
0.125 & 35 & 50, 150, 300 & Indoor temperature \\ \hline \hline \end{tabular}
\end{table}
Table 3: Contact surface properties and test conditions.  
2. The temperature values at the pile-soil interface increase rapidly and then decrease in segments as the burial depth increases. In addition, the temperature at the junction location of different strata will cause an obvious fault to appear. The fluctuation of temperature along the burial depth at the pile-soil interface is significantly larger than the temperature change along the burial depth inside the soil body. 3. The rate of change of the axial additional temperature strain of the pile body is gradually increases with the increase in burial depth. The temperature stress induced by different strata is not the same, and the magnitude of temperature stress is not only related to the deformation modulus of the surrounding rocks, but also related to the axial constraint, which mainly comes from the constraints of the superstructure at the end of the pile and the holding layer at the bottom of the pile. 4. According to the mechanical characteristics of energy piles, this paper proposes a segmented softening function, which can consider the unloading process of energy piles in the upper part of the pile in the heat dissipation process and in the lower part of the pile in the heat extraction process; simulate the relationship between the contact surface shear stress and shear displacement in different conditions; and calculate the softening characteristics of the contact surface in a relatively accurate and quantitative manner.  
Conceptualization, H.W. and P.Z.; methodology, P.Z.; validation, X.L.; formal analysis, X.W.; writing--original draft preparation, H.W.; writing--review and editing, X.B. All authors have read and agreed to the published version of the manuscript.  
Supported by the Science and Technology Project of Xuzhou, China (KC2036); the Yunlong Lake Laboratory of Deep Underground Science and Engineering Project (104023004); the National Natural Science Foundation of China (42202299); the double innovation talent plan of Jiangsu, China (JSSCBS20221533); the Key R&D Program of Jiangsu, China (BE2022156); and the Project of Henan Provincial Bureau of Geology and Mineral Exploration and Development ([2022]1).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare no conflicts of interest.