# Numerical Investigations of Pile Group Foundations under Different Pile Length Conditions
## 3 Model Building  
To investigate the stability of a group pile foundation with varying pile lengths in multiple strata, the FLAC3D simulation and calculation software is utilized to simulate the corresponding model. FLAC3D is capable of three-dimensional modeling and analysis, supports multi-physics coupling, utilizes multi-core processors and cluster computing systems for parallel computing, and has powerful post-processing capabilities. However, FLAC3D has limited modeling capabilities and requires the assistance of external tools. Rhino 7 (a 3D modeling software package known for its powerful modeling capabilities and flexibility, Rhino's NURBSD modeling technology accurately describes surfaces and curves, enabling users to create high-quality geometric models) can draw a slope model according to the actual project, Griddle (a built-in plugin in Rhino that allows more refined meshing),  
Figure 1: Pile load arrangement. and HyperMesh 2019 (professional finite element pre-processing software that provides powerful tools for the creation and preparation of finite element models; it supports various meshing techniques, including automatic and manual meshing, ensuring the accuracy and efficiency of numerical simulations) can generate a grid according to the model. The official websites of all software are displayed in Appendix A. The generation of grids using Rhino with Griddle may result in errors and mesh tearing; therefore, using Rhino with HyperMesh is a more suitable choice, ensuring a more coherent and aesthetically pleasing grid. The slope model is initially created using Rhino and exported as a STEP format file. This exported model file is then imported into HyperMesh for grid generation. The mesh type selected is Tetra (the type of grid is triangular), with a minimum size of 0.5 m and a maximum size of 3 m. After the necessary processing, the input format file can be opened within the Grid option of FLAC3D. The dimensions of the slope model are 48 m \(\times\) 239.5 m \(\times\) 400 m, with an average slope of 25.9\({}^{\circ}\). In this model, the X direction represents the 48 m length, with point O situated at the middle of this shorter side. The Y direction corresponds to the 400 m length of the model, and the Z direction represents the height of the model, measuring 239.5 m. The two side faces perpendicular to the X-axis constrain the X-direction displacement, while the two side faces perpendicular to the Y-axis constrain the Y-direction displacement. The bottom face constrains the Z-direction displacement. The model consists of three different soil layers, namely gravel soil, strongly weathered sandstone, and weakly weathered sandstone. The average slope of the gravel soil layer is 26.4\({}^{\circ}\) while the average slopes of the strongly weathered sandstone layer and the weakly weathered sandstone layer are 31.4\({}^{\circ}\) and 30.9\({}^{\circ}\), respectively. The main mechanical parameters of the rock layers in the slope are presented in Table 1.  
The slope-cap-group piles in this study are modeled using an elastic model, known for their fast computation speed. This model provides a simplified representation of stress and deformation behaviors in the grid and helps identify areas of stress concentration. It requires two parameters, bulk modulus, and shear modulus, and quickly achieves an initial stress balance in the ground. Once the initial stress balance is achieved, the gravel soil layer is excavated, and group piles are installed. Each foundation pile extends through the gravel soil layer and the highly weathered rock layer until reaching the weakly weathered rock layer, which acts as the holding layer. The group piles are arranged in a 9 \(\times\) 8 layout, with 9 rows perpendicular to the loading direction and 8 rows parallel to it.