## 2 FE Modeling and SSI Analysis Method
### Modeling of the Soil for SSI Analysis  
Shear wave velocity is an important input parameter for calculating soil and structures' seismic responses. The process of identifying different geotechnical material properties for each soil layer and simplifying the spatial inhomogeneity of shear wave velocity that varies with depth within each layer to a single value requires geotechnical expertise. Additionally, it is necessary to calculate quantitative values based on data that reflect the topographical and geological characteristics of the target area. Considering these complexities, numerical evaluation and prediction are more efficient when using a single stiffness value for each type of geotechnical layer rather than directly applying the shear wave velocity of the soil. [PERSON] et al. [16] analyzed field-measured seismic wave data from 183 sites in Korea, and reclassified subsurface soils and rocks into five geotechnical types: Fill (FI), Alluvial Soil (AS), Weathered Soil (WS), Weathered Rock (WR), and bedrock (BR). Also, they proposed standard values of shear wave velocity for each soil type. This study adopted four representative soil types (FI, AS, WS, and WR), excluding bedrock for SSI analyses. The target soils were simplified as a single soil layer for modeling convenience, and the material properties proposed by [PERSON] et al. [17] were applied as the input parameters of *MAT_MOHR_COULOMB (Table 7). The Mohr-Coulomb model is a constitutive model widely used in earthquake engineering to simulate dynamic soil behavior under seismic loading conditions. In this study, the selection of the Mohr-Coulomb model for soil modeling was based on its recognized application in previous seismic analyses and SSI studies [18;19]. The soil model was constructed for a finite domain, and perfectly matched layer (PML) elements were applied around the soil boundaries to reduce computational costs. PML is a boundary condition that absorbs waves of all frequencies incident at all angles and is useful for modeling infinite domains by reducing the size to a finite region [20; 21; 22]. The material constants of the PML elements were set identically to those of the boundary-adjacent soil material (*MAT_MOHR_COULOMB) to satisfy the requirements. Additionally, to ensure the proper implementation of the PML, the following conditions were applied: (1) The PML material should form a parallelepiped box around the bounded domain, and the box should be aligned with the coordinate axes; (2) the outer boundary of the PML should be fixed; (3) the PML layer may typically have 5-8 elements through its depth; and (4) the PML \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**High-Rise Structure**} & \multicolumn{2}{c}{**Low-Rise Structure**} \\ \cline{2-4}
**Mode** & **1 st** & **2 nd** & **1 st** \\ \hline x-bending & 0.23 & 0.90 & 3.70 \\ y-bending & 0.27 & 1.40 & 5.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Natural frequencies of the fixed-end models (unit: \(\mathrm{Hz}\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Soil Type** & **FI** & **AS** & **WS** & **WR** \\ \hline Density (\(\rho_{soil}\)) (t/mm\({}^{3}\)) & 1.70 \(\times\) 10\({}^{-9}\) & 1.84 \(\times\) 10\({}^{-9}\) & 1.90 \(\times\) 10\({}^{-9}\) & 1.99 \(\times\) 10\({}^{-9}\) \\ Unit weight (\(\gamma_{soil}\)) (N/m\({}^{3}\)) & 16,670 & 18,000 & 18,640 & 19,510 \\ Shear modulus (\(G\)) (MPa) & 58.813 & 136.151 & 211.835 & 720.461 \\ Young’s modulus (\(E_{soil}\)) (MPa) & 158.796 & 353.993 & 550.772 & 1801.154 \\ Bulk modulus (\(K\)) (MPa) & 176.440 & 294.994 & 458.976 & 1200.769 \\ Poisson’s ratio (\(v\)) & 0.35 & 0.30 & 0.30 & 0.25 \\ Shear wave velocity (\(V_{S}\)) (m/s) & 186 & 283 & 353 & 651 \\ Compressional wave velocity (\(V_{P}\)) (m/s) & 387 & 529 & 660 & 1128 \\ Friction angle (\(\phi\)) (\({}^{\circ}\)) & 30 & 30 & 31 & 33 \\ Cohesion value (\(\mathbb{C}\)) (MPa) & 0 & 0.01 & 0.02 & 0.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Material properties of the four soil types.