# Numerical Investigations of Pile Group Foundations under Different Pile Length Conditions
## 3 Model Building
The spacing between piles is 3 m, and the diameter of the foundation piles is set at 3 m. The length of each row of foundation piles varies from 54 m to 70 m, as follows: 54 m, 58 m, 60 m, 62 m, 64 m, 66 m, 68 m, 70 m. The resulting model is shown in Figure 2. Different colors represent different groups. For this study, the middle row of foundation piles is chosen, and they are numbered 1 to 9 based on their order from shortest to longest. The foundation piles used in the model are C30 concrete piles. After setting up the group piles, a cap is placed on top of them, subjecting it to a uniform load of 100 kN. To improve the accuracy of the results, a control model is also created. In this control model, all foundation piles are set to a length of 70 m while maintaining other parameters consistent with the previous model. For convenience and adherence to international convention, the row of piles closest to the slope is referred to as the front pile row, the row away from the slope is called the rear pile row, and the row located in the middle of the front and rear pile rows is called the middle pile row. This naming convention is used for the sake of convenience and adherence to international standards. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Soil Layer** & **Bulk/(MPa)** & **Shear/(MPa)** & **Cohesion/(KPa)** & **Friction/(\({}^{\circ}\))** & **Poisson’s Ratio** \\ \hline gravel soil & 59.03 & 12.4 & 14.5 & 22 & 0.40 \\ strongly weathered sandstone & 335.04 & 109.64 & 180 & 45 & 0.36 \\ weakly weathered sandstone & 169.6 & 320 & 32 & 53 & 0.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of different soil layers. After setting up the slope-cap-group pile system, it is important to define the contact surfaces. Contact surfaces play a crucial role in the simulation process, especially between different materials. As the pile group undergoes stress loading, shear forces and relative displacement occur between the soil body and the cap. The contact surfaces enable the analysis of sliding, separation, and closure on these interfaces under specific loading conditions. The entire calculation process proceeds as follows: Firstly, the initial stress field generated by the self-weight of the soil body is computed as a priority. This initial stress field is then saved after achieving stress balance. Next, the gravel soil layer is excavated, and appropriate values are assigned to the cap and foundation of the group piles. Contact surfaces between the group piles and each soil layer are established. Finally, a static vertically distributed load is applied to the cap until the entire model reaches equilibrium. The resultant stress field is saved, and finite element post-processing is conducted for further analysis. To sum up, the steps of using FLAC3D for finite element simulation of the pile group foundation are as follows: Based on the actual geometry and size of the slope and pile group, create the corresponding three-dimensional finite element mesh, and import the model into FLAC3D. Define the material properties of the soil layers and assign properties to the mesh elements Bulk, Shear, Cohesion, and Friction. Apply boundary conditions by constraining the displacements at the bottom and surrounding areas of the model, while allowing displacements at the top. Perform calculations to achieve initial stress equilibrium in this scenario. Excavate the first layer, generating the initial stress field before excavation. Generate models of the cap and pile group within the slope and assign them to convenient groups. Create contact surface elements between the pile group and soil and assign properties to the contact surfaces. Assign properties to the pile group and cap, defining them as the Mohr-Coulomb constitutive model. Apply a vertical static uniformly distributed load on the cap. Run the FLAC3D simulation program, obtaining results under the effect of the strength reduction method. Finally, analyze the results of the FLAC3D simulation and perform visualization processing.