## 3 Analysis Results and Discussion  
### Effect of SSI on the Low-Frequency Structure  
First, the SSI effect on the low-frequency (high-rise) structure was analyzed. Figure 8 presents graphs of the FFT spectrum obtained using the acceleration responses at the foundation base from the free-field analysis (FF) and the top of the structure for cases considering SSI (SSI) and without considering SSI (NSSI), categorized by soil type and response direction. Figure 6: Acceleration time history of Gyeoungju earthquake recorded at DAG2 station. (**a**) peak acceleration in the east-west direction; (**b**) peak acceleration in the north–south direction. Figure 7: Acceleration response spectrum of Gyeoungju earthquake. A comparison of the responses with and without SSI shows that the maximum response generally decreases due to the SSI effect. As shown in Figure 8, the critical frequencies, the frequency of the largest amplitude decrease, were found near the natural frequencies of the structure (Table 9). Additionally, in the weakest soil type, FI, the reduction in the peak responses is more significant than in other soil types (Figure 8a,e). This phenomenon can be explained by the fact that the damping effect caused by the kinematic interaction between the structure and the ground is greater for weaker ground stiffness. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Mode** & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** & **6 th** & **7 th** \\ \hline x-bending & 0.23 & 0.90 & 1.97 & 3.32 & 5.01 & 6.86 & 9.03 \\ y-bending & 0.27 & 1.40 & 3.50 & 6.07 & 8.86 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Natural frequencies of the low-frequency structure from fixed-end model (unit: Hz). Figure 8: FFT spectrum of acceleration responses of low-frequency structure: (**a**) FI-EW; (**b**) AS-EW; (**c**) WS-EW; (**d**) WR-EW; (**e**) FI-NS; (**f**) AS-NS; (**g**) WS-NS; (**h**) WR-NS. In Figure 8a,d,e,g, the response peaks at the critical frequencies decrease significantly due to the SSI effect; consequently, the maximum response is observed at other frequencies where the decrease in response is relatively small. For example, in the EW direction of the FI soil type (Figure 8a), the maximum response occurs at 5.02 Hz when the SSI effect is not considered and at 1.94 Hz when the SSI is considered. Consequently, when SSI effects are considered, the maximum responses may occur at frequencies other than the natural frequencies obtained from the fixed-end model. Figure 9 presents graphs of the maximum relative displacement between the top of the structure and the basement floor, categorized by soil type and response direction. As shown in the figure, considering the SSI effect reduces the maximum relative displacement of the structure across all soil types and response directions. In a fixed-end model, the foundation supports the structure with infinite stiffness, but when the stiffness of the ground is included in the modeling (embedded model), a part of the inertial forces generated by the mass of the structure is transmitted to the ground, which causes the vibration energy to be absorbed or dissipated by the ground, reducing the response of the structure. The greater the difference in stiffness between the structure and the ground, the greater the effect of this phenomenon. The reduction in the maximum relative displacement with and without SSI effects was largest in the weakest soil type, FI, with a reduction of 35.6% from 114 mm to 73.4 mm in the EW direction and 16.4% from 128 mm to 107 mm in the NS direction. SSI effects similar to those obtained from this numerical analysis were also experimentally observed in previous studies. According to dynamic centrifuge model tests [25; 26], the rocking behavior of shallow foundation systems induced by SSI effects resulted in reduced seismic responses. In addition, shaking table model tests performed by [PERSON] et al. [27] confirmed that SSI significantly alters the natural frequency and dynamic responses of the structure.