# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 5 Conclusions  
This paper presented an improved Penzien model for calculating soil-structure interaction. The effectiveness and accuracy of the computational model were validated through the establishment of simplified models of a 6-story single-span steel frame in MATLAB and ANSYS software. The models were subjected to dynamic nonlinear analysis. In the improved Penzien model, the superstructure was represented by a bilinear restoring force model, while the soil was represented by the Davidenkov equivalent linear model that accounted for its dynamic nonlinearity. The soil-structure interaction was represented by springs and damping. Based on model verification, the parameters of the model components were studied, leading to the following 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 30: Peak accelerations of each story of the superstructure (for input 0.4 g). \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 & 10.595 & 7.982 & 5.804 & 5.605 & 24.67 & 45.22 & 47.09 \\
5 & 9.451 & 7.481 & 5.404 & 5.246 & 23.65 & 42.82 & 44.49 \\
4 & 8.665 & 6.526 & 4.653 & 4.587 & 22.37 & 46.31 & 47.06 \\
3 & 7.015 & 5.200 & 3.633 & 3.740 & 20.81 & 48.21 & 46.68 \\
2 & 4.838 & 3.603 & 2.450 & 2.700 & 18.67 & 49.35 & 44.18 \\
1 & 2.521 & 1.838 & 1.212 & 1.440 & 15.80 & 51.92 & 42.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 29: Peak velocities of each story of the superstructure (for input 0.4 g). \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 31: Peak accelerations of each story of the superstructure (for input 0.4 g).