# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 4 Parametric Study of the Simplified Model
### Input Seismic Waves  
When performing a free field system analysis, seismic acceleration had to be input to obtain the response of each layer of the free field system and the soil parameters. In addition, when solving the dynamic equations of the structural system, seismic acceleration was also input to solve these equations. Consequently, the input seismic waves resulted in variations in the dynamic equations. In the simplified model, seismic waves were input for both the free field system analysis and the structural system analysis under seismic effects. In this paper, four seismic waves were selected for analysis: the EL-Central wave, the Kobe \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multirow{2}{*}{**Dimensions per Story**} & \multirow{2}{*}{**Stories Number**} & \multicolumn{2}{c}{**Frequency (Hz)**} \\ \cline{3-4}  & & & **First-Order** & **Second-Order** \\ \hline Condition 1 & 2 m \(\times\) 2 m \(\times\) 2 m & 1 & 25.168 & 47.161 \\ Condition 2 & 2 m \(\times\) 2 m \(\times\) 2 m & 3 & 20.989 & 25.168 \\ Condition 3 & 2 m \(\times\) 2 m \(\times\) 2 m & 6 & 11.369 & 25.168 \\ Condition 4 & 3 m \(\times\) 3 m \(\times\) 3 m & 1 & 22.819 & 26.762 \\ Condition 5 & 3 m \(\times\) 3 m \(\times\) 3 m & 3 & 11.910 & 22.819 \\ Condition 6 & 3 m \(\times\) 3 m \(\times\) 3 m & 6 & 6.452 & 18.980 \\ \hline \hline \end{tabular}
\end{table} 
Table 24: Structural system frequencies. wave, the Taft wave, and the TS wave. The initial 10 s of each wave were utilized, with peak accelerations of 0.1 g and 0.4 g applied, resulting in a total of eight conditions for the seismic analysis of the simplified model. The peak displacements, velocities, and accelerations of the superstructure obtained from the time-history analysis under the action of different seismic waves are presented in Tables 25-30. From the data in Tables 25-30, it can be observed that there were certain differences in the peak responses of the structure when subjected to different seismic waves with the same peak acceleration. When the peak acceleration was 0.1 g, the relative differences in peak displacements for the Kobe, Taft, and TS waves were, in comparison to the EL-central wave, 23.65, 51.49, and 45.16, respectively. For velocity, the relative differences were 30.50, 45.72, and 42.83, respectively. For acceleration, the relative differences were 22.92, 56.44, and 55.88, respectively. When the peak acceleration was 0.4 g, the relative differences in peak displacements for the Kobe, Taft, and TS waves, in comparison to the EL-central wave, were 23.65, 51.92, and 45.16, respectively. For velocity, the relative differences were 30.49, 45.71, and 42.82, respectively. For acceleration, the relative differences were 22.97, 56.47, and 55.87, respectively. The comparison of the Fourier amplitude spectra of the EL wave and the TS wave, which exhibited significantly different peaks, revealed that the EL wave had a higher distribution in the high-frequency range, whereas the TS wave was mainly distributed in the low-frequency range. Given that the first-order frequency of the structural system was 11.369 Hz, the EL wave aligned more closely with the structural system frequency distribution. Similarly, a comparison of the Fourier amplitude spectra of the Taft wave and the TS wave showed that both were predominantly distributed in the low-frequency range, with fewer distributions in the high-frequency range, resulting in similar response outcomes. In conclusion, the response of the structural system to the same peak acceleration varied significantly when subjected to different seismic waves, particularly when the frequency distribution of the seismic waves was closer to that of the structural system. This could lead to larger structure responses.