## 4 Conclusions  
This study proposed using the FA method to investigate the nonlinear seismic response of PSWs with corroded spun piles. The vertical pile and batter pile configurations were considered. The nonlinear seismic response of corroded PSWs was determined by performing pushover analysis and observed for 75 years using three methods: FA using the method of the previous study (FA-1), the proposed FA method (FA-2), and FB-FEA. The following conclusions can be drawn from the results of this study:  
1. The results obtained with FA-2 are in excellent agreement with the FB-FEA results for the nonlinear seismic response of corroded PSWs in terms of the natural period, plastic hinge formation, and load capacity. The proposed method for defining the moment-curvature relationship, P-M capacity, and bending stiffness reduction factor for corroded spun piles has been introduced and applied to FA-2, resulting in differences for the natural period and load capacity of corroded PSWs that are no more than 0.35% and 0.44%, respectively, compared to the FB-FEA results. The FB-FEA itself has also been extensively validated for its ability to reproduce experimental results. 2. The FA-1 results for the P-M capacity and plastic hinge formation are the same as the FB-FEA and FA-2 results. However, FA-1 determines the bending stiffness reduction factor and moment-curvature relationship of corroded spun piles based on the results of previous studies and produces significantly different results for the natural periods and load capacities of corroded PSWs compared to the FB-FEA results. The maximum differences in the FA-1 results for the natural period and load capacity of a corroded PSW compared to the FB-FEA results were 15.96% and 12.66%, respectively. 3. The pushover curves of corroded PSWs obtained from FB-FEA differ from those obtained from the FA models. The 2D PSW model with distributed plasticity (FB-FEA) produces smoother, more precise pushover curves than the FA model with an idealized plasticity approach (concentrated hinge). However, by properly defining the bending stiffness reduction factor, moment-curvature relationship, and P-M capacity of the corroded spun piles, the FA-2 method can predict load capacities with similar accuracy as FB-FEA. 4. Corrosion has more adverse effects on the compressive axial load and bending moment capacities of spun piles than tensile axial load capacity. In this study, at a corrosion degree of 18.56%, the maximum reductions in compressive axial load capac \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**PSW-A**} & \multicolumn{3}{c}{**PSW-B**} \\ \cline{2-7}
**Corrosion** & \multicolumn{3}{c}{**Load Capacity (kN)**} & \multicolumn{3}{c}{**Load Capacity (kN)**} \\ \cline{2-7}
**Degree** & **FB-FEA** & **FA-1** & **FA-2** & **FB-FEA** & **FA-1** & **FA-2** \\ \hline
0.00\% & 689.05 & 635.97 & 687.75 & 635.20 & 600.31 & 636.32 \\
4.68\% & 666.18 & 606.85 & 664.87 & 605.74 & 568.39 & 604.63 \\
9.67\% & 632.89 & 562.82 & 630.84 & 578.03 & 527.21 & 576.32 \\
12.20\% & 611.74 & 542.64 & 609.76 & 557.93 & 495.52 & 555.87 \\
14.74\% & 579.56 & 513.07 & 577.69 & 527.06 & 462.89 & 525.13 \\
18.56\% & 537.06 & 469.08 & 535.36 & 481.14 & 422.01 & 479.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of pushover analysis results. ity and bending moment capacity were 60.84% and 48.42%, respectively. In contrast, the maximum reduction in tensile axial load capacity was only 13.26%. Conceptualization, A.N.R. and T.N. ; methodology, A.N.R. and T.N. ; software, A.N.R. ; validation, A.N.R. and T.N. ; formal analysis, A.N.R. and T.N. ; investigation, A.N.R. and T.N. ; resources, A.N.R. and T.N. ; data curation, A.N.R. ; writing--original draft preparation, A.N.R. ; writing--review and editing, T.N. ; visualization, A.N.R. ; supervision, T.N. ; project administration, A.N.R. ; funding acquisition, A.N.R. All authors have read and agreed to the published version of the manuscript. This research was funded by PT.