## 2 Methodology
### Sample Preparation in PFC Modeling  
With the prepared set of particles, a soil sample was formed using specific steps to simulate the author's conducted model pile test. The sample preparation in PFC consisted of two large steps: (1) assigning a contact model with validation of the soil-soil interaction to make the particles behave like Ottawa F-55 sand; and (2) vertically confining the particles to control the lateral earth pressure coefficient (\(K_{0}\)) and the relative density within the soil sample in the DEM. First, the Rolling Resistance Linear Model (RRLM) was adopted as a contact model to achieve a realistic internal friction angle, which is herculean in the conventional Linear Model [30].  
Input parameters such as the normal and shear stiffness of the contact and the rolling friction coefficient were calibrated through a series of numerical biaxial tests in the DEM, and the following results are listed in Table 2. The soil sample was prepared at a relative density of 80%, and each was confined at a stress of 50, 100, and 200 kPa during the axial compression stage until the axial strain reached 20%. The deviatoric stress at failure was measured for each confining stress, and the subsequent results are shown in Figure 2. The peak internal friction angle was determined to be 37.8\({}^{\circ}\), which exhibits a mean absolute error of 0.5% compared with the experimental value of 38\({}^{\circ}\) obtained by [PERSON] et al. [37].  
Next, a rectangular soil container consisting of four rigid walls was prepared in a two-dimensional DEM simulation. The container has a width of 1.9 m and a depth of 1.4 m to prevent boundary effects, as demonstrated by [PERSON] et al. [39], where the boundary distance exceeds by 10-fold the outer diameter of the pile. Figure 3 presents the configuration of an overview of the PFC modeling.  
Figure 1: Particle size distribution curves of Ottawa F-55 sand and the granular assembly in the DEM model.  
Particles following the prepared PSD were then generated and suspended inside the container without any initial contact under zero gravity. The resulting porosity (\(n\)) was 0.158, corresponding to a relative density of 80%, which resulted in the generation of 68,799 particles. Note that the relative density was used as the criterion for sample preparation following the recommendation of [PERSON] et al. [40] to simulate the packing of sand, and a relative density of 80% was calculated based on the extreme porosities  
\begin{table}
\begin{tabular}{l c} \hline
**Input Parameters** & **Value** \\ \hline Soil properties & \\ Normal stiffness, \(k_{n}\) (kN/m) & \(1\times 10^{5}\) \\ Shear stiffness, \(k_{s}\) (kN/m) & \(2\times 10^{4}\) \\ Friction coefficient, \(\mu\) & 0.50 \\ Rolling friction coefficient, \(\mu_{r}\) & 0.45 \\ Specific gravity, \(G_{s}\) & 2.65 \\ \hline Wall properties & \\ Normal stiffness, \(k_{n}\) (kN/m) & \(1\times 10^{7}\) \\ Shear stiffness, \(k_{s}\) (kN/m) & \(1\times 10^{7}\) \\ Friction coefficient, \(\mu\) & 0.50 \\ \hline \end{tabular}
\end{table}
Table 2: Input parameters of the numerical model.  
Figure 3: Configuration of the overview of the PFC modeling.  
Figure 2: Peak state friction angle of the granular assembly.  
determined by the criteria suggested by [PERSON] and [PERSON] [41], which are widely used in DEM analysis [42; 43]. Figure 4 shows the concept of the evaluation of extreme porosities of granular material. The generated particles with assigned mechanical properties are finally compressed vertically by moving the upper and bottom walls toward each other to form contacts between particles.  
Figure 5 shows a lateral earth pressure (\(K_{0}\)) of 0.384 throughout the granular media after activating gravity at 9.81 m/s\({}^{2}\), along with the distribution of horizontal and vertical stress and the porosity according to depth.