# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 5 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Story**} & \multicolumn{3}{c}{**Peak Accelerations in (m/s\({}^{2}\)) under Seismic Waves**} & \multicolumn{3}{c}{**Relative Difference with EL Wave (\%)**} \\ \cline{2-9}  & **EL Wave** & **Kobe Wave** & **Taft Wave** & **TS Wave** & **Kobe Wave** & **Taft Wave** & **TS Wave** \\ \hline
6 & 14.939 & 11.478 & 10.314 & 8.591 & 23.17 & 30.96 & 42.49 \\
5 & 14.635 & 10.418 & 9.408 & 7.934 & 16.98 & 35.72 & 45.79 \\
4 & 13.888 & 8.579 & 7.606 & 7.352 & 8.83 & 45.23 & 47.06 \\
3 & 12.278 & 6.868 & 6.281 & 6.358 & 4.15 & 48.85 & 48.22 \\
2 & 9.272 & 4.874 & 4.731 & 4.708 & 1.78 & 48.97 & 49.22 \\
1 & 5.722 & 2.550 & 2.491 & 2.525 & 0.43 & 56.47 & 55.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 27: Peak accelerations of each story of the superstructure (for input 0.1 g). (a) A comparison of the results of the seismic analysis of the 3-DOF superstructure from the literature, MATLAB software using the central difference method and Newmark method, and ANSYS layer shear model indicated that the relative differences in the peak responses of each layer among the four results were mostly within 5. This confirmed that the adoption of a bilinear restoring force model for the superstructure effectively reflected its nonlinear response and mechanical behavior. Furthermore, the utilization of two time-history dynamic integration methods in MATLAB served to demonstrate the effectiveness and accuracy of the approach, while the feasibility of simulating the superstructure using the COMBIN40 element in ANSYS was validated. (b) A simplified model of a six-story steel frame structure was established using MATLAB and ANSYS software, and a seismic analysis was carried out. The time-history curves and wave forms under the two models were essentially identical, with only a difference in amplitude. The maximum relative difference in peak displacements, velocities, and accelerations was 13.97, 8.74, and 1.44, respectively. This indicated that the nonlinear simplified calculation model of soil-structure interaction was more effective in reflecting the structure response under seismic effects. (c) When the length of the free field system was 50 times the size of the superstructure, the results obtained met the accuracy requirements of the calculation. It was observed that, within a certain range, the presence of softer soil layers in the site soil resulted in a greater structure response under seismic effects and a more significant frequency reduction. This indicated that the soil-structure interaction became more pronounced. It was of paramount importance to consider equivalent soil, with the range being selectable as 20 times the area of the equivalent single pile or the area of the superstructure's footing. The superstructure significantly impacted the simplified model, with changes in the number of superstructure layers and dimensions leading to significant variations in the structural system frequency. Therefore, when studying soil-structure interaction, it was imperative to develop and simulate the superstructure comprehensively. Moreover, the greater the degree of overlap between the high-frequency range of the input seismic waves and the structural system frequency, the more pronounced the response of the structure under seismic effects. (d) For the improved Penzien model, it is then applied to the substructure pseudo-dynamic test method, covering both theoretical research and experimental research, to further improve the effectiveness and reliability of the model in practical engineering applications. Conceptualization, Q.G. ; methodology, Q.G. ; software, P.L. ; validation, P.L. ; formal analysis, Q.G. ; investigation, P.L. ; resources, Q.G. ; data curation, P.L. ; writing--original draft preparation, P.L. ; writing--review and editing, Q.G. and P.L. ; visualization, Q.G. ; supervision, Q.G. ; project administration, Q.G. ; funding acquisition, Q.G. All authors have read and agreed to the published version of the manuscript.