## 3 Experiments and Analysis
### Load Simulation Results and Analysis  
The pile-rock model is first subjected to preprocessing. The reconstructed surface model is imported into Rhinoceros 8 software for model processing, and rock models are established according to the actual situation. The subsurface 0\(\sim\)3.5 m is mudstone, 3.5\(\sim\)4.5 m is sandstone, and 3.5\(\sim\)8.5 m is granite. The pile-rock model is subsequently merged into a nonmanifold mesh, which is then divided into volume entities to construct a 3D model comprising a volume mesh. The volume mesh is subsequently imported into FLAC3D for simulation purposes, as shown in Figure 8.  
As detailed in Section 2.4, load simulations were conducted in FLAC3D. Table 2 presents the model parameters for the concrete pile body and each rock layer used for the simulation. The material properties of the concrete were determined from the markers, and the rock material data were obtained from tests on field samples. The interface parameters were calculated using the recommended values in FLAC3D. The normal and shear stiffness of the interface was determined to be \(2\times 10^{12}\) Pa, while the friction angle and cohesion were established at 80 kPa and 25.6\({}^{\circ}\), respectively. The density of the overlying Ioess layer was found to range from 1140 kg/m\({}^{3}\) to 1890 kg/m\({}^{3}\), with an intermediate value of 1500 kg/m\({}^{3}\) taken for calculation purposes. Consequently, the surface applied ground stress was determined to be 150 kPa. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline Azimuth & 0\({}^{\circ}\) & 45\({}^{\circ}\) & 90\({}^{\circ}\) & 135\({}^{\circ}\) & 180\({}^{\circ}\) & 225\({}^{\circ}\) & 270\({}^{\circ}\) & 315\({}^{\circ}\) \\ \hline RF & 0.0231 & 0.0348 & 0.0612 & 0.0411 & 0.0432 & 0.0452 & 0.0213 & 0.0184 \\ \hline \end{tabular}
\end{table} 
Table 1: \(RF\) of contour lines in different directions. Figure 8: Slicing of the mesh model in FLAC3D. Figure 9 shows the load-displacement (Q-S) curve of the pile. The Q-S curve of this pile is generally slow-varying and relatively smooth without obvious inflection points, and the cutline stiffness \(k_{s}\) (\(k_{s}=Q/S\)) decreases gradually with increasing displacement. The ultimate damage point of this rock-socket pile is not obvious, the rate of change of settlement with an increasing loading in the experimental range still tends to be stable, and the surrounding rock offers greater side resistance. Therefore, when the pile parameters are designed, the ultimate bearing capacity is limited by an allowable settlement threshold. Figure 10 shows the unit side resistance of the pile for different loads. The distribution of the pile side resistance does not exhibit a monotonic variation with depth but tends to increase and then decrease, reaching a peak at a depth of 4.5 m. This phenomenon is associated with both the displacement of strain and the type of rock mass. The displacement of the upper section is greater than that of the lower end, the shear expansion is relatively more pronounced, and the resulting stress is also greater. Moreover, the overall side resistance increases with an increasing load because as the pile moves downward due to the applied load, the sliding of the concave and convex surfaces along the interface induces radial expansion, which results in normal and shear stresses [26]. However, when the load exceeds a certain critical value (8 MPa), the side resistance in the middle and upper sections gradually stabilizes, whereas the side resistance in the lower section continues to increase. This indicates that at this point, the upper section has been destroyed by excessive displacement, and slip has occurred, whereas the lower section has not yet reached its ultimate side resistance and can continue to increase with increasing load.