## 3 Results and Discussion
### Application of the Proposed Method  
The SAs at the top left of the soil model for Scenario 1 for the various damping coefficients generated by the FEA are shown in Figure 15. The TE waveform has a large SA in the period shorter than 1.0 s and the ME waveform has a large SA in the period longer than 1.0 s.  
The FEA results for Scenario 1 using the TE and ME waveforms are described in Table 4. The maximum PSW acceleration was obtained directly from the FEA results. The PSW's natural period was derived from the predominant frequency of the Fourier spectra. The PSW maximum acceleration and Fourier spectra were generated for the top right (seaward side) end of the PSW deck. The PSW damping coefficients shown in Table 4 were determined so that the deck's FEA maximum accelerations matched the SAs generated by the FEA ground surface motions, as shown in Figure 15.  
Figure 14: Examples of kinematic forces using the JRA method. Figure 15: FEA: Ground surface SAs with various damping coefficients. The PSW's natural period in Scenario 1 was approximately 1.20 s. The deck's maximum acceleration from the FEA results became larger as the width of the PSW became smaller. This is because structural rigidity decreases when the PSW becomes narrower, which increases PSW deformation and acceleration. The damping coefficient becomes smaller as the PSW width decreases. The largest value of the damping coefficient was 0.07 and the smallest value was 0.04. Table 5 shows the FA results using the TE and ME waveforms. The largest deck's maximum acceleration occurred in Model 14: 5.38 and 6.53 m/s\({}^{2}\) for the TE and ME waveforms, respectively. In contrast, the smallest values occurred in Model 1: 3.61 and 5.29 m/s\({}^{2}\) for the TE and ME, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{6}{c}{**TE**} & \multicolumn{6}{c}{**ME**} \\ \cline{2-10}  & **Width** & **(m)** & **_Tn_ (s)** & _fn_ (Hz)** & \(A\)-_FEA_ & \(\xi\)** & **Width** & **_Tn_ (s)** & _fn  
The maximum acceleration for the PSW from the FA results at different damping coefficients was calculated using Equations (5) and (6):  
\[A-FA=\left(\frac{2\pi}{T_{d}}\right)^{2}Dd \tag{5}\]  
\[T_{d}=\frac{1}{fn\sqrt{1-\xi^{2}}} \tag{6}\]  
where \(Dd\) is the PSW's displacement, obtained from the FA; \(Td\) is the damped natural period; \(\xi\) is the PSW's damping coefficient; and \(fn\) is the PSW's natural frequency. The following step was taken to determine the damping coefficients that produce the best fit between the deck's maximum acceleration from the results of the FEA and FA. Table 5 describes the deck's maximum accelerations from the FA that are closest to the FEA results; the damping coefficients that produce the closest values were set as the damping coefficients of the PSW. A comparison of the FEA results (Table 4) with the FA results (Table 5) reveals good agreement between the two findings. Both analyses showed that the PSW's natural period is around 1.20 s. The damping coefficient values in models 1-4, 5-9, 10-12, and 13-14 were 0.07, 0.06, 0.05, and 0.04, respectively. This result shows that even if the waveforms used in the analysis have different characteristics, the PSW still shows consistent damping coefficients. This is because the damping coefficients were mainly affected by the structural characteristics, such as the shape, construction material, and foundation. We then conducted a parametric analysis to determine the variables influencing the PSW's damping coefficient. The width, mass, natural period, and spring constant of the PSW were set as independent variables, and we employed a statistical analysis using multiple linear regression. To prevent the occurrence of highly correlated independent variables in the regression model, we conducted a multicollinearity test using the variance inflation factor (VIF) method. The multicollinearity test demonstrated that the PSW width, mass, and spring constant have high VIF values of 1396, 6249, and 10,589, respectively.