## 3 Results and Discussion
### Bending Stiffness Reduction Factor of Corroded Spun Pile
Table 5 shows the bending stiffness reduction factor (\(\eta\)) of the corroded spun pile from FB-FEA, FA-1, and FA-2. Figure 10 illustrates the comparison of the bending stiffness reduction factor of corroded spun pile from FB-FEA, FA-1, and FA-2. The bending stiffness reduction factor of corroded spun pile used in FA-1 has a much smaller value than those used in FB-FEA and FA-2 for corrosion degrees greater than 2%. This is because FA-1 refers to Equations (20)-(22), which use rust thickness as the main factor in determining the bending stiffness reduction factor [5]. Equations (20)-(22) are considered to have relatively conservative results compared to the proposed Equations (23)-(28). The decrease in the bending stiffness of the corroded spun pile led to an increase in the natural period of the PSWs. Table 6 displays the natural periods of PSW-A and PSW-B for up to 75 years. The maximum differences in the natural periods of corroded PSWs according to FA-1 and FA-2 were 15.96% and 0.35%, respectively, compared to the FB-FEA results. Figure 10: Corrosion-based bending stiffness reduction factor. (**a**) Pile A; (**b**) Piles B and C. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pile** & \begin{tabular}{c} **Corrosion** \\ **Degree** \\ \end{tabular} & \begin{tabular}{c} **Rust Thickness of** \\ **PC Bar, \(d_{1}\) (mm)** \\ \end{tabular} & \begin{tabular}{c} **FB-FEA** \\ \end{tabular} & \
\begin{tabular}{c} **FA-1** \\ \end{tabular} &
\begin{tabular}{c} **FA-2** \\ \end{tabular} \\ \hline Pile A & 0.00\% & 0.000 & 1.000 & 1.000 & 1.000 \\  & 4.68\% & 0.197 & 0.982 & 0.740 & 0.977 \\  & 9.67\% & 0.497 & 0.960 & 0.590 & 0.951 \\  & 12.20\% & 0.669 & 0.938 & 0.570 & 0.927 \\  & 14.74\% & 0.852 & 0.885 & 0.550 & 0.882 \\  & 18.56\% & 1.144 & 0.789 & 0.530 & 0.778 \\ \hline Piles B and C & 0.00\% & 0.000 & 1.000 & 1.000 & 1.000 \\  & 4.68\% & 0.197 & 0.999 & 0.740 & 0.990 \\  & 9.67\% & 0.497 & 0.974 & 0.590 & 0.964 \\  & 12.20\% & 0.669 & 0.950 & 0.570 & 0.939 \\  & 14.74\% & 0.852 & 0.902 & 0.550 & 0.897 \\  & 18.56\% & 1.144 & 0.799 & 0.530 & 0.788 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Bending stiffness reduction factor of the corroded spun pile. The conservative bending stiffness reduction factor of the corroded spun pile calculation in FA-1 results in a significant increase in the natural periods of the corroded PSW as the degree of corrosion increases, which in turn affects the inertial force (\(\bar{r}i\)) calculation. Furthermore, the inaccurate estimation of inertial forces contributed to errors in estimating the seismic response of corroded PSWs. This study considered site-specific spectral acceleration (SA) for port facilities in Indonesia [61] developed based on earthquake ground motion records in Indonesia for the site class of medium soil (SD) (Figure 11). Table 7 compares the inertial forces of the corroded PSW calculated based on the SA and the natural periods of the corroded PSW by FB-FEA, FA-1, and FA-2. As the corrosion degree increased, the inertial force of the corroded PSW decreased. The inertial force calculated by FB-FEA, FA-1, and FA-2 did not differ significantly under intact conditions. However, when the corrosion degree exceeded 4.68%, the inertial force calculated by FA-1 was substantially different from that calculated by FB-FEA, up to a maximum of 16.22% for PSW-A and 12.24% for PSW-B. In contrast, the inertial force calculated by FA-2 for PSW-A and PSW-B differed slightly from that calculated by FB-FEA by 0.23% for PSW-A and 0.42% for PSW-B. The comparison of the inertial forces for PSWs with different corrosion degrees indicates the importance of accurately estimating the bending stiffness reduction factor of corroded spun piles in the nonlinear seismic response analysis of corroded PSWs using FA.