# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 4 Parametric Study of the Simplified Model
### Site Soil Parameters  
The properties of the site soil had a significant impact on the soil-structure interaction simplified model, with the mass of the site soil being factored into the calculation of the equivalent soil mass. Following the completion of a seismic analysis in a free field system, the obtained shear modulus and damping ratio were used to determine the stiffness and damping of the equivalent soil, as well as the stiffness and damping of the soil-pile interaction. The free field system consists of various types of soil layers. Following the seismic action analysis, the shear modulus, damping ratio, velocity, and displacement results for each layer of soil were used in the structural system calculations, thereby influencing the response of the structural system within the simplified model. For different combinations of soil types, a total of eight different types of site soils were selected as eight different conditions, with the properties of the site soil gradually becoming softer from Condition 1 to Condition 8. The types of site soil compositions for these eight conditions are shown in Table 13, and the parameters for the various soils are depicted in Table 2. Seismic action analyses were conducted under EL-central waves with peak accelerations of 0.1 g, 0.2 g, 0.3 g, and 0.4 g. Due to the limited space of the article, only the peak responses of each soil layer for peak seismic accelerations of 0.1 g and 0.4 g are shown in Figure 5.  
Figure 5 shows that under the influence of seismic waves with different peak accelerations, the peak displacements for Conditions 1 to 4 were relatively close to each other, while the curves for Conditions 5 to 8 were significantly higher than those for the first four Conditions. For peak velocities and accelerations, the peaks for each layer in Conditions 2 to 4 were quite similar, with the curve for Condition 1 being slightly higher than those for Conditions 2 to 4. The curves for Conditions 5 to 8 were significantly higher than those for Conditions 2 to 4, and there was a clear distinction between adjacent curves in Conditions 5 to 8. The maximum peak responses under the different conditions all occurred in the first layer of the free field system; therefore, only the relative differences in the first layer conditions were analyzed, and the results are presented in Tables 14-19. A final calculation of the first two orders of frequency of the structural system was conducted based on the parameters of soil density, shear modulus, and other parameters to form the mass and stiffness of the equivalent soil. The first-order frequency was 11.369 Hz, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Thickness (m)** & **4** & **4** & **8** \\ \hline Condition 1 & Dense sandy & Dense sandy & Dense sandy \\ Condition 2 & Medium dense sandy & Medium dense sandy & Dense sandy \\ Condition 3 & Silty soil & Medium dense sandy & Dense sandy \\ Condition 4 & Silty soil & Silty soil & Dense sandy \\ Condition 5 & Clay & Silty soil & Dense sandy \\ Condition 6 & Clay & Silty clay & Medium dense sandy \\ Condition 7 & Clay & Clay & Silty soil \\ Condition 8 & Clay & Clay & Silty clay \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Types of site soil composition. the second-order frequency of the structure is shown in Table 20. A comparison of the second-order frequency of adjacent conditions is shown in Table 21.  
Figure 5: Peak responses of each layer in free field systems for earthquake input 0.1 g and 0.4 g: (**a**) and (**d**) peak displacement, (**b**) and (**e**) peak velocities, (**c**) and (**f**) peak accelerations, respectively.