# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 4 Parametric Study of the Simplified Model
### Site Soil Parameters
As shown in Tables 20 and 21, changes in the ground conditions influenced the second natural frequency of the structural system. The second natural frequencies for Conditions 1 to 5 were found to be quite similar under the influence of the same peak seismic wave, with the relative differences all within 0.1. However, the frequencies for Conditions 5 to 8 gradually decreased and differed significantly, with the greatest difference occurring between Conditions 5 and 8, with a relative difference of approximately 60. The relative differences between Conditions 5 and 8 all exceeded 10, with the maximum being 17.453. This indicated that as the site soil properties changed from Condition 5 onwards, the softening of the soil had an increasing effect on the frequency reduction in the structural system. Under the influence of seismic waves with different peak accelerations, the peak response in Condition 1 mainly fell between those of Conditions 4 and 5. This indicated that the response of soils with a certain stiffness to seismic action can still be significant. The results for Conditions 2 to 4 showed minimal differences, indicating that the response of these three soil types to seismic action was similar. Conversely, the results for Conditions 5 to 8 differed significantly from those for Conditions 2 to 4, and there were also significant differences between adjacent conditions within Conditions 5 to 8. This indicated that once the soil properties reached those characterized in Condition 5, the softer the soil, the greater the response under seismic effects. In addition, the influence of the soil on the frequency of the structural system increased. Therefore, when the soil softness reaches the level of Condition 5, it was essential to consider the soil-structure interaction. In Condition 5, the soil composition from top to bottom was 4 m of clay, 4 m of silt and 8 m of dense sand. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**The Second-Order**} & \multicolumn{1}{c}{**0.1 g**} & \multicolumn{1}{c}{**0.2 g**} & \multicolumn{1}{c}{**0.3 g**} & \multicolumn{1}{c}{**0.4 g**} \\ \multicolumn{1}{c}{**Frequencies in (Hz) for Input**} & \multicolumn{1}{c}{} & & & & \\ \hline
1 & 31.520 & 31.255 & 30.900 & 30.511 \\
2 & 31.514 & 31.255 & 30.903 & 30.515 \\
3 & 31.513 & 31.254 & 30.901 & 30.514 \\
4 & 31.502 & 31.240 & 30.884 & 30.491 \\
5 & 31.686 & 31.448 & 31.119 & 30.755 \\
6 & 26.590 & 26.300 & 25.883 & 25.387 \\
7 & 23.701 & 23.419 & 23.035 & 22.607 \\
8 & 19.874 & 19.717 & 19.505 & 19.270 \\ \hline \hline \end{tabular}
\end{table} 
Table 20: The second-order frequencies of structural systems under different peak seismic accelerations. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Seismic** & **1–2** & **2–3** & **3–4** & **4–5** & **5–6** & **6–7** & **7–8** \\
**Acceleration** & & & & & & & \\ \hline
0.1 g & 0.018 & 0.004 & 0.035 & \(-\)0.584 & 16.082 & 10.865 & 16.147 \\
0.2 g & 0.001 & 0.004 & 0.044 & \(-\)0.666 & 16.368 & 10.954 & 15.809 \\
0.3 g & \(-\)0.009 & 0.003 & 0.058 & \(-\)0.761 & 16.824 & 11.003 & 15.325 \\
0.4 g & \(-\)0.013 & 0.003 & 0.077 & \(-\)0.866 & 17.453 & 10.949 & 14.764 \\ \hline \hline \end{tabular}
\end{table} 
Table 21: Relative difference between adjacent conditions (%) of the second-order frequencies. In summary, within a certain range, the softer the soil layers, the greater the response of the free field system under seismic effects. This led to a greater reduction in the frequency of the structural system and increased the effect of soil-structure interaction. Therefore, it was important to consider the soil-structure interaction on soft foundations where the soil softness was lower than in Condition 5.