## 2 Method
### FLAC3D Modelling  
This section outlines the methodology for utilizing the reconstructed 3D surface model and FLAC3D for numerical simulation, with the objective of determining the ballast response of the rock-socketed pile. Given that the filled concrete can better accommodate the shape of the borehole, and that the shape of the pile is primarily determined by that of the borehole, it is possible to replace the geometric model of the pile with the reconstructed borehole model. In the traditional use of FLAC3D for load simulation, the lack of realistic pile geometry, and the difficulty of modeling many uneven microelements in detail, have led to the use of smooth cylinders endowed with certain shear parameters instead of real piles. However, this approach fails to account for the varying directions and magnitudes of the undulations, and the accuracy of the results is contingent upon the precise specification of the roughness and friction parameters. In this regard, this paper employs a 3D mesh model based on actual measurements for numerical simulation, which increases the model preprocessing procedure and the complexity of solving the calculation but reduces the error introduced by parameter estimation. The simulation results are more accurate, and more comprehensively reflect the bearing performance of the pile foundation. The surface model, reconstructed from the point cloud, contains a multitude of complex triangular meshes of varying dimensions. This method lacks the upper and lower surfaces of the unmeasured pile, which cannot be directly imported into FLAC3D for simulation. Accordingly, a model preprocessing stage was incorporated into the workflow to ensure the construction of a comprehensive and accurate pile-rock model. In this work, the top and bottom surfaces of the reconstructed model were complemented using Rhinoceros 8 modeling software, thereby forming a closed pile model. The pile body is subsequently positioned at the coordinate center, and several different stratigraphic models are constructed around the pile body in accordance with the actual conditions of the strata. The overall dimensions of the stratigraphic models are illustrated in Figure 5. They have a length and width of \(20D\) and a height of \(\frac{3}{2}L\), where \(D\) and \(L\) are the diameter and length of the pile, respectively. This range is sufficient to avoid the boundary effect of the geotechnical soil on the results, as previously discussed in reference [26]. The pile-rock model is imported into FLAC3D for simulation, and the load test can be divided into 3 steps. In Step 1, the initial ground stress induced by gravity in the experimental area is generated. The pile and rock are set as elastic-plastic Mohr-Coulomb materials, and the real ground material parameters are input into the FLAC3D intrinsic model. These parameters are typically derived from geotechnical tests of core materials in the field. Given that the pile body passes through different strata, care is taken to set the parameters at different depths of the pile body to the model parameters of the corresponding strata. The boundary conditions are then set according to the actual stresses, as shown in Figure 5, the normal displacements at the sides and bottom of this modeled area are fixed, and the normal displacements at the top surface of the pile and the upper surface of the strata are set to be free. In addition, the surface of the rock formation supporting the rock-socketed pile is usually covered with a soft soil layer, which contributes minimally to the side friction resistance. Modeling it as a soil layer for simulation increases the number of meshes and computation time but has a smaller effect on the simulation results. Therefore, a certain normal pressure is applied on the top of the model to simulate the pressure generated by the weight of the soft soil instead of establishing a solid model of the soil layer.