# Performance Analysis of Pile Group Installation in Saturated Clay
## 2 Numerical Modeling and Validation  
### Single Pile Installation Model  
In this study, the two-pile group installation and soil consolidation process are simulated using a numerical modeling technique. Firstly, the proposed method is applied to the numerical simulation of single pile installation in this section, and the reliability of the numerical model is verified by comparison with the single pile test results. The simulation process involves four stages: (1) stress equilibrium: initialization of soil stress and pore pressure; (2) pile installation: using undrained analysis, a downward velocity is applied to the pile to drive it to the specified depth; (3) consolidation analysis: performing coupled fluid-solid drainage analysis with decoupling through the master-slave process method;and (4) static load test: undrained analysis is used to obtain the pile's load-displacement curve through the displacement method. To eliminate the boundary effects, [PERSON] et al. [29] proposed that the boundary distance from the pile center should be greater than 15 times the pile diameter in the numerical model. In this study, the model dimension is set to be 30 m \(\times\) 15 m \(\times\) 2\(L\) (length \(\times\) width \(\times\) height, where \(L\) is the pile length). Considering the computational convergence and accuracy, the horizontal mesh size should not be less than 0.5 to 1 times the pile diameter, whereas the vertical mesh size can be locally refined according to the pile length. The geometry mesh is illustrated in Figure 1a. By virtue of symmetry, only half of the pile-soil system was modeled. The boundary conditions of the model are shown in Figure 1b. For the mechanical boundaries, the vertical displacement of the bottom boundary and the horizontal displacement of the right-hand boundary are restrained. For the seepage boundaries, the ground surface is permeable, the lateral boundaries are 60 times the pile diameter away from the pile center, and the pore pressure at the edges of the numerical model can be assumed to be constant; thus, the \"no permeability\" boundary conditions are applied at the lateral boundaries of the numerical model. A study by [PERSON] et al. [30] indicates that the expansion of the foundation soil from a small cavity and from zero are essentially identical in terms of computational accuracy. Therefore, an auxiliary tube penetrates the soil downwards and the pile slides after the tube with constant speed. The friction contact between the installation pile and soil can be established during pile installation. Similar approaches have been reported in studies by [PERSON], [PERSON], and [PERSON] et al. [16; 31; 32]. Thus, the equivalent pile diameter can be determined as follows:  
\[\frac{D_{\mathrm{e}}}{2}=d_{e}=\sqrt{d^{2}-d_{0}^{2}} \tag{1}\]  
where \(D_{\mathrm{e}}\) represents the equivalent diameter of the pile, \(d_{\mathrm{e}}\) denotes the equivalent radius of the pile, and \(d\) and \(d_{0}\) represent the radius of the pile and the radius of the auxiliary tube, respectively. In this section, the modeling of a single pile encompasses three stages: initial geostatic stress, installation, and consolidation. During the first stage, soil gravity is represented by a body force, and initial stress and pore pressure are established using a geostatic step. Subsequently, a vertical velocity of 5 \(\times\) 10\({}^{-5}\) m/step is applied to the pile to simulate the installation process. The pile and auxiliary tube have radii of 0.25 m and 0.04 m, respectively, with a pile tip angle of 60\({}^{\circ}\). In this study, the pile exhibits linear elastic behavior, while the  
Figure 1: (**a**) Geometry mesh and (**b**) model boundary conditions. saturated soil adheres to the Mohr-Coulomb criterion. The material parameters for the pile and soil are provided in Table 1. The soil-pile interface is modeled using frictional contact elements; when the shear stress on the contact surface exceeds the maximum allowable shear stress, separation and slippage between the pile and soil occur.