# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 4 Parametric Study of the Simplified Model
### Free Field System  
Theoretically, the larger the range of the free field system selected, the more it can reflect the response under real conditions. However, once a certain range is reached, the results obtained from the seismic analysis of the free field system will not vary significantly. To investigate the impact of the free field system range on the results, four free field systems of different areas were selected as working conditions, with specific information shown in Table 4. Seismic analysis was conducted under EL-central waves with peak accelerations of 0.1 g, 0.2 g, 0.3 g, and 0.4 g, respectively. The peak velocities and displacements of each soil layer were extracted and are presented in Tables 5-12. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Condition** & **Condition 1** & **Condition 2** & **Condition 3** & **Condition 4** \\ \hline Free Field Area (m \(\times\) m) & 20 \(\times\) 20 & 50 \(\times\) 50 & 100 \(\times\) 100 & 200 \(\times\) 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Conditions of the free field area. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Peak Displacements in (m)**} & \multicolumn{4}{c}{**Relative Difference between**} \\
**Soil Layer** & \multicolumn{4}{c}{**for Condition**} & \multicolumn{4}{c}{**Adjacent Conditions (\%)**} \\ \cline{2-7}  & **1** & **2** & **3** & **4** & **1-2** & **2-3** & **3-4** \\ \hline
1 & 0.004293 & 0.002807 & 0.002389 & 0.002340 & 52.94 & 17.49 & 2.09 \\
2 & 0.003683 & 0.002473 & 0.002114 & 0.002071 & 48.95 & 16.96 & 2.07 \\
3 & 0.003017 & 0.002073 & 0.001773 & 0.001736 & 45.56 & 16.89 & 2.13 \\
4 & 0.002400 & 0.001698 & 0.001455 & 0.001424 & 41.34 & 16.71 & 2.15 \\
5 & 0.001818 & 0.001337 & 0.001154 & 0.001130 & 35.96 & 15.86 & 2.09 \\
6 & 0.001299 & 0.001016 & 0.000895 & 0.000879 & 27.86 & 13.51 & 1.84 \\
7 & 0.000763 & 0.000643 & 0.000580 & 0.000571 & 18.59 & 10.99 & 1.58 \\
8 & 0.000366 & 0.000333 & 0.000307 & 0.000303 & 9.73 & 8.52 & 1.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Peak displacements of each layer in the free field system (for input 0.1 g). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Peak Velocities in (m/s)**} & \multicolumn{4}{c}{**Relative Difference between**} \\
**Soil Layer** & \multicolumn{4}{c}{**for Condition**} & \multicolumn{4}{c}{**Adjacent Conditions (\%)**} \\ \cline{2-7}  & **1** & **2** & **3** & **4** & **1-2** & **2-3** & **3-4** \\ \hline
1 & 0.048120 & 0.039859 & 0.040681 & 0.041306 & 20.73 & \(-\)2.02 & 1.51 \\
2 & 0.041122 & 0.035265 & 0.035782 & 0.036245 & 16.61 & \(-\)1.44 & 1.28 \\
3 & 0.033539 & 0.027727 & 0.029867 & 0.030177 & 20.96 & \(-\)7.16 & 1.03 \\
4 & 0.026604 & 0.025408 & 0.024263 & 0.024452 & 4.71 & 4.72 & 0.77 \\
5 & 0.020128 & 0.019599 & 0.018996 & 0.019108 & 2.70 & 3.17 & 0.58 \\
6 & 0.015398 & 0.015442 & 0.014382 & 0.014470 & \(-\)0.28 & 7.37 & 0.61 \\
7 & 0.008485 & 0.008828 & 0.009044 & 0.009100 & \(-\)3.89 & \(-\)2.38 & 0.62 \\
8 & 0.004141 & 0.004430 & 0.004674 & 0.004702 & \(-\)6.53 & \(-\)5.23 & 0.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Peak velocities of each layer in the free field system (for input 0.1 g).