# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 4 Parametric Study of the Simplified Model
### Site Soil Parameters
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Seismic Acceleration**} & \multicolumn{1}{c}{**1**} & \multicolumn{1}{c}{**2**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} & \multicolumn{1}{c}{**7**} & \multicolumn{1}{c}{**8**} \\ \hline
0.1 g & 2.94696 & 2.34589 & 2.36825 & 2.50786 & 3.13581 & 3.59393 & 4.69157 & 5.32391 \\
0.2 g & 5.79372 & 4.61552 & 4.66073 & 4.94772 & 6.14699 & 7.04792 & 9.19737 & 10.41477 \\
0.3 g & 8.49859 & 6.77604 & 6.84652 & 7.29171 & 8.97619 & 10.30576 & 13.44678 & 15.26319 \\
0.4 g & 11.07289 & 8.83540 & 8.93559 & 9.54552 & 11.65110 & 13.39956 & 17.47332 & 19.84260 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: The free field 1 st layer peak velocities in (cm/s) for condition. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Seismic Acceleration**} & \multicolumn{1}{c}{**1**} & \multicolumn{1}{c}{**2**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} & \multicolumn{1}{c}{**7**} & \multicolumn{1}{c}{**8**} \\ \hline
0.1 g & 1.16347 & 1.04627 & 1.04937 & 1.06718 & 1.12363 & 1.20535 & 1.34852 & 1.52690 \\
0.2 g & 2.32815 & 2.13087 & 2.13319 & 2.15903 & 2.28586 & 2.41394 & 2.66726 & 3.02455 \\
0.3 g & 3.49249 & 3.18218 & 3.20088 & 3.23067 & 3.40469 & 3.58465 & 3.95295 & 4.48361 \\
0.4 g & 4.65324 & 4.24889 & 4.25415 & 4.26863 & 4.55841 & 4.85031 & 5.21881 & 5.90990 \\ \hline \hline \end{tabular}
\end{table} 
Table 19: Relative difference between adjacent conditions (%) of the free field 1 st layer peak accelerations. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Seismic Acceleration**} & \multicolumn{1}{c}{**1**} & \multicolumn{1}{c}{**2**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} & \multicolumn{1}{c}{**7**} & \multicolumn{1}{c}{**8**} \\ \hline
0.1 g & 0.13199 & 0.12471 & 0.12491 & 0.12704 & 0.15983 & 0.22143 & 0.33524 & 0.46969 \\
0.2 g & 0.26562 & 0.25044 & 0.25088 & 0.25551 & 0.32101 & 0.44454 & 0.67540 & 0.93991 \\
0.3 g & 0.40189 & 0.37788 & 0.37862 & 0.38640 & 0.48447 & 0.67065 & 1.02352 & 1.41073 \\
0.4 g & 0.54116 & 0.50733 & 0.50846 & 0.52014 & 0.65048 & 0.90076 & 1.38067 & 1.881878 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: The free field 1 st layer peak displacements in (cm) for condition. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Seismic Acceleration**} & \multicolumn{1}{c}{**1**} & \multicolumn{1}{c}{**2**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} & \multicolumn{1}{c}{**7**} & \multicolumn{1}{c}{**8**} \\ \hline
0.1 g & 11.20 & \(-\)0.30 & \(-\)1.67 & \(-\)5.02 & \(-\)6.78 & \(-\)10.62 & \(-\)11.68 \\
0.2 g & 9.26 & \(-\)0.11 & \(-\)1.20 & \(-\)5.55 & \(-\)5.31 & \(-\)9.50 & \(-\)11.81 \\
0.3 g & 9.75 & \(-\)0.58 & \(-\)0.92 & \(-\)5.11 & \(-\)5.02 & \(-\)9.32 & \(-\)11.84 \\
0.4 g & 9.52 & \(-\)0.12 & \(-\)0 Tables 14 and 15 demonstrate that, in the free field, the peak displacements of the first layer in Condition 1 were between those of Conditions 4 and 5. Apart from Condition 1, the peak displacements in Conditions 2 to 8 increased continuously, with the relative differences between adjacent conditions in Conditions 4 to 8 all exceeding 20, with a maximum of 34.76. Tables 16 and 17 demonstrate that, for the peak velocities of the first layer in the free field, the peak velocities in Condition 1 were between those of Conditions 4 and 5. The relative differences between adjacent conditions in Conditions 4 to 8 all exceeded 10, with a maximum of 23.40. According to Tables 18 and 19, the peak accelerations of the first layer in the free field in Condition 1 were between those of Conditions 5 and 6. The relative differences between adjacent conditions from Conditions 4 to 8 all exceeded 5, with a maximum of 11.84.