# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 3 Improved Penzien Model Validation
### Validation of the Soil-Structure Interaction Simplified Model
#### 3.2.2 Simplified Model Validation  
In the numerical simulation conducted using ANSYS software, the superstructure was represented by COMBIN40 elements, while the equivalent single pile was modeled using BEAM188 elements with a diameter of 0.636 m. The soil was represented by SOLID185 elements with a vertical thickness of 16 m. The horizontal extent, informed by the study of [PERSON] et al. [41], was selected as 100 m by 100 m. The boundary condition was set as fixed at the base and free along the perimeter. After the six-story framework structure model was simplified into a shear-cut model, the superstructure did not reach the nonlinear stage under the seismic effect of the EL-central wave with a peak acceleration of 0.4 g. The seismic responses of the third, fourth, and sixth stories, which were representative of the structure, were compared and analyzed. Table 3 presents a comparison of peak displacements, velocities, and accelerations. Table 3 indicates that the greatest difference in peak displacements occurs in the third story, at 13.97%. Similarly, the greatest difference in peak velocity occurs in the third story, at 8.74%, while the greatest difference in peak accelerations occurs in the sixth story, at 1.44%. The results from the two models were highly comparable, with the relative differences in peak responses of each story not exceeding 14%. Figure 3 illustrates that the displacement, velocity, and acceleration time-history curves of the MATLAB model and the ANSYS model were largely congruent, with only minor discrepancies in amplitude. A comparison of the response spectra in Figure 4 reveals that the overall response spectra of the two models were consistent. In the short-period range, the displacement, velocity, and acceleration response spectra values of each story in the MATLAB model were found to be largely consistent with those of the ANSYS model. In the peak regions, the response spectra values for displacement, velocity, and acceleration in the MATLAB model were slightly higher than those in the ANSYS model. In the long-period range, the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Soil Type** & \begin{tabular}{c} **Shear Wave** \\ **Velocity (m/s)** \\ \end{tabular} & \begin{tabular}{c} **Density** \\ **(kg/m3)** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio (-)** \\ \end{tabular} & \begin{tabular}{c} **Damping** \\ **Ratio (-)** \\ \end{tabular} & \begin{tabular}{c} **Shear Modulus** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Elasticity Modulus** \\ **(MPa)** \\ \end{tabular} \\ \hline \begin{tabular}{c} Dense sandy \\ Medium dense \\ sandy \\ \end{tabular} & 350 & 2100 & 0.30 & 0.01 & 257 & 669 \\ \begin{tabular}{c} Medium dense \\ sandy \\ \end{tabular} & 340 & 2010 & 0.30 & 0.01 & 232 & 604 \\ \begin{tabular}{c} Silty soil \\ Silty clay \\ \end{tabular} & 338 & 2010 & 0.30 & 0.01 & 230 & 598 \\ \
\begin{tabular}{c} Silty clay \\ \end{tabular} & 210 & 1930 & 0.32 & 0.01 & 85 & 224 \\
\begin{tabular}{c} Clay \\ \end{tabular} & 135 & 1820 & 0.35 & 0.01 & 33 & 89 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Soil material parameters (based on [40]). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Peak Displacements (m)**} & \multicolumn{3}{c}{**Peak Velocities (m/s)**} & \multicolumn{3}{c}{**Peak Accelerations (m/s2)**} \\ \cline{2-9}
**Story** & & & **Relative** & & & **Relative** & & **Relative** \\
**Number** & **ANSYS** & **MATLAB** & **Difference** & **ANSYS** & **MATLAB** & **Difference** & **ANSYS** & **MATLAB** & **Difference** \\  & & & **(\%)** & & & **(\%)** & & **(\%)** \\ \hline
3 & 0.082 & 0.070 & 13.97 & 0.806 & 0.736 & 8.74 & 12.421 & 12.287 & 1.08 \\
4 & 0.097 & 0.087 & 10.87 & 1.018 & 0.967 & 5.01 & 13.780 & 13.888 & \(-0.78\) \\
6 & 0.114 & 0.106 & 7.25 & 1.269 & 1.248 & 1.61 & 15.157 & 14.939 & 1.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Peak structure responses.