## 3 Methodology
### Finite Element Method  
The 3D modeling of the single pile and group pile used tetrahedral meshing with 15-node elements. For the single pile, the values of x-max, x-min, y-max, and y-min are obtained as 5 D from the global coordinate. The x-max and y-max are 4 m and the x-min and y-min are \(-\)4 m. For the group pile, the distance from the tip of the pile to the end of the mesh, namely x-max, x-min, y-max, and y-min, was taken by 5 B (B = pile cap width)  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Parameters** & **Methods** & **Unit** & **MH** & **MH** & **SC-SM** & **SC-SM** & **CL** \\ \hline Depth & & M & 0.00–5.50 & 5.50–8.50 & 8.50–11.50 & 11.50–14.50 & 14.50–17.50 \\ \(\overline{\text{N}}_{60}\) & & & 12 & 11 & 14 & 28 & 34 \\  & [PERSON] et al., 2019 [23] & & 176.67 & 172.18 & 194.68 & 233.75 & 243.14 \\ V\({}_{\text{s}}\) & [PERSON] and [PERSON], & m/s & & & & & \\  & 2006 in Hammam and & & 204.80 & 200.34 & 208.53 & 249.35 & 269.12 \\  & Eliwa [22] & & & & & & \\  & [PERSON] and [PERSON], & 2011 [24] & & 237.39 & 230.90 & 209.41 & 269.15 & 334.70 \\ \hline
**Parameters** & **Methods** & **Unit** & **MH** & **SM** & **SM** & **MH** & **CL-ML** \\ \hline Depth & & M & 17.50–20.00 & 20.00–23.50 & 23.50–26.50 & 26.50–29.50 & 29.50–30.00 \\ \(\overline{\text{N}}_{60}\) & & & 44 & 68 & 55 & 54 & 55 \\  & [PERSON] et al., 2010 [23] & & 263.66 & 296.06 & 279.39 & 279.36 & 241.78 \\ V\({}_{\text{s}}\) & [PERSON] and [PERSON], & m/s & & & & & \\  & 2006 in Hammam and & & 288.43 & 314.14 & 296.83 & 303.06 & 305.09 \\  & [PERSON] [22] & & & 365.18 & 372.23 & 343.76 & 388.62 & 456.36 \\  & [PERSON] and [PERSON], & & & & & & \\  & 2011 [24] & & & & & & \\ \hline \end{tabular}
\end{table}
Table 2: N\({}_{60}\) and V\({}_{\text{s}}\) value derived from SPT data.  
Figure 5: Bored pile elevation and N-SPT data.  
Figure 6: Finite element group pile modeling (**a**) group pile, (**b**) single pile.  
For software input, in the case of the single pile, the axial and lateral loads are point loads with a load value equal to the allowable axial bearing capacity and combination lateral loads. For the case of group piles, the input value is the total combination lateral loads from static equivalent earthquake loads and soil pressure on the semi-basement wall for lateral loading. One pile cap consists of five columns. Thus, there were five-point vertical loads, and each point load's coordinates were adjusted from the detailed pile cap drawing (Figure 6a). The interface in the soil-structure interaction is weaker and more flexible than the surrounding soil. Therefore, the R\({}_{\text{inter}}\) value should be less than 1 [26].  
The default standard pinch boundary conditions were used, in which the standard pinch limit means that the x-min, x-max, y-min, and y-max were normally fixed, z-min was fully fixed, and z-max was free for 3D analysis.  
Stage construction consists of four phases: the initial phase, pile construction, plate construction, and loading phase. In the initial phase, all structural geometries are inactive. In the pile construction phase, pile materials and interfaces are activated. The plate construction phase activates the plate material, while the whole pile geometry and point loads are activated in the loading phase. The axial load is activated when analyzing the lateral load.