## 4 Results and Discussion
### p-Multiplier  
The p-multiplier (p\({}_{\text{m}}\)) parameter was used to consider group pile effects. The p-multiplier is calculated using the single pile p-y curve divided by the p-y curve for each pile group row. The p-y curve obtained with the help of finite difference software for the single pile and the group pile is calculated using the API [7] method approach with ultimate soil resistance, p\({}_{\text{u}}\), from the first row to the fourth row also being obtained based on numerical calculations based on the finite difference method (Figure 13a). Pile modeling with the finite difference method is the same with the 3D finite element method and the relationship between soil resistance and deflection (p-y curve) was taken at a depth of 0.00 m to match the pile group's deflection output from the 3D finite element analysis. The 3D finite element analysis found that a higher p-multiplier was followed by a larger deflection. This is in contrast to the study by [PERSON] et al. [8], where p\({}_{\text{m}}\) decreases gradually with y, revealing that the pile group effect depends on the pile deflection. As the pile deflection increases, the protective effect becomes more significant and causes a considerable decrease in p\({}_{\text{m}}\). This difference may occur due to the diversity of methodology, soil type, and geometric parameters used between studies to derive the p-multiplier. Other reasons that can cause this difference in results are the reduction of the earth pressure limit, group effect, and inconstant depth [36]. The biggest reason for this study is the irregular pile configuration and the greatest lateral resistance lies in the direction opposite to the loading direction. [PERSON] and [PERSON] [35] have shown that the p-multiplier depends on the configuration of the group piles. The constant value of the p-multiplier based on the analytical method despite the increasing deflection is because the p-multiplier is based on the distance between the piles and the pile diameter. Thus, the deflection does not affect the p-multiplier. This study shows that the analytical method from FEMA P-751 [14], Reese and Impe [15], and AASHTO [16] does not show the effect function of combination lateral loads, pile stiffness, and soil stiffness. Although the p-multiplier changes with increasing pile deflection [11]. Figure 13b shows the p-multiplier value based on the numerical method and analytical method obtained by 0.79 based on FEMA P-751 [14], 0.80 based on Reese and Impe [15], and 0.93 based on AASHTO [16] for the first-row pile. In the second row, it is 0.57 from FEMA P-751 [14], 0.40 from [PERSON] and [PERSON] [15], and 0.58 from AASHTO [16]. In the third- and fourth-row pile, it is 0.41 from FEMA P-751 [14], 0.30 from [PERSON] and [PERSON] [15], and 0.58 from AASHTO [16]. The analytical method used by AASHTO [16] yielded the highest p\({}_{\text{m}}\) values for the three variables, followed by [PERSON] and [PERSON] [15] and FEMA P-751 [14]. This may be because AASHTO [16] used data from most of the tests in the 3 \(\times\) 3 pile group, and there were no fixed-head conditions in the AASHTO [16] database. [PERSON] and [PERSON] [15] generally matches or approaches the p\({}_{\text{m}}\) value from the 3D finite element method  
obtained in this study. This is appropriate because [PERSON] and [PERSON] [15] not only considers the effects of the adjacent, parallel piles but also considers misaligned piles concerning the applied load. In addition, the first row of piles has the largest \(\mathrm{p_{m}}\) value, and its value continues to decrease as the row of piles increases. This is in accordance with the behavior of the lateral load capacity, where the farther the pile is from the lateral load, the lower the \(\mathrm{p_{m}}\) will be. [PERSON] and [PERSON] [11] also revealed that the p-multiplier decreases approximately from the leading row to the last row in the subgroup, whereas the p-multiplier of the leading row in the final subgroup is equal to or even greater than the last row in the front group.