## 3 Results and Discussion
### P-M Capacity Curves  
The capacity of a spun pile is expressed as a curve describing the combination of its axial load (P) capacity and bending moment (M) capacity, commonly known as the axial load-bending moment (P-M) capacity curve [7]. Since the pile has a biaxially symmetric cross-section, the P-M capacity curve of spun pile is described in terms of axial load capacity (P) and principal moment (Mx). Positive values of axial load capacity indicate compressive axial load capacity and negative values indicate tensile axial load capacity. In the FA method, the P-M capacity curve of the corroded spun pile must be determined to set the hinge properties. The P-M capacity applied in FA-1 was computed using SAP2000 software based on ACI 318-02 [55], while in FA-2 the P-M capacity was calculated with the help of XTRACT software [62]. Figures 12-15 show the P-M capacity curves of piles A, B, and C, respectively. Figures 12-15 also show that the P-M capacities of piles A, B, and C decreased significantly after the corrosion degree exceeded 12%. Figure 12: P-M capacity curves of corroded Pile A with infilled concrete. (**a**) FB-FEA; (**b**) FA-1; (**c**) FA-2. Figure 13: P-M capacity curves of corroded Pile A. (**a**) FB-FEA; (**b**) FA-1; (**c**) FA-2. Table 8 provides the parameters of the P-M capacity curves for non-corroded spun pile sections. Key point parameters of the P-M capacity curves of FA-1 and FA-2 are generally consistent with those obtained from the FB-FEA. The maximum deviation between FA-1, FA-2, and FB-FEA is within 3.7%. Furthermore, corrosion has more negative impact on the spun pile's compressive axial load and bending moment capacities than on its tensile axial load capacity. For an 18.56% corrosion degree, the decrease in the axial compression capacity reached 56.95% for Pile A with infilled concrete, 59.75% for Pile A, 56.46% for Piles B and C with infilled concrete, and 60.84% for Piles B and C. For the same corrosion degree (18.56%), the decrease in bending moment capacity was 46.86% for Pile A with infilled concrete, 48.42% for Pile A, 43.80% for Piles B and C with infilled concrete, and 46.25% for Piles B and C. In contrast, the axial tension capacity of the spun pile at an 18.56% corrosion degree decreased by only 13.26% for Piles A, B, and C with infilled concrete and by only 8.32% for Piles A, B, and C. Table 9 compares the compressive and tensile axial load capacities as well as the bending moment capacities for various corrosion degrees according to the FB-FEA results. Figure 14: P-M capacity curves of corroded Piles B and C with infilled concrete. (**a**) FB-FEA; (**b**) FA-1; (**c**) FA-2. Figure 15: P-M capacity curves of corroded Piles B and C. (**a**) FB-FEA; (**b**) FA-1; (**c**) FA-2. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \begin{tabular}{c} **Maximum** \\ **Compression Force** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **Maximum Tension** \\ **Force (kN)** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum** \\ **Bending Moment** \\ **(kN-m)** \\ \end{tabular} \\ \hline
\begin{tabular}{c} Pile A with infilled \\ concrete \\ FB-FEA \\ FA-1 \\ FA-2 \\ \end{tabular} & 14,303.91 & 3560.68 & 1250.46 \\
2.5 & 14,378.36 & 3663.61 & 1252.96 \\
2.5 & 14,321.07 & 3649.01 & 1251.96 \\ \hline
\begin{tabular}{c} Pile A \\ FB-FEA \\ FA-1 \\ FA-2 \\ \end{tabular} & 8699.67 & 2595.58 & 961.01 \\
2.5 & 8755.84 & 2587.32 & 962.84 \\
2.5 & 8712.28 & 2578.05 & 962.07 \\ \hline
\begin{tabular}{c} Piles B and C with \\ infilled concrete \\ FB-FEA \\ FA-1 \\ FA-2 \\ \end{tabular} & 10,820.78 & 3560.68 & 826.93 \\
2.5 & 10,878.31 & 3580.29 & 828.67 \\
2.5 & 10,834.97 & 3564.92 & 828.00 \\ \hline
\begin{tabular}{c} Piles B and C \\ FB-FEA \\ FA-1 \\ FA-2 \\ \end{tabular} & 6713.32 & 2595.58 & 654.86 \\
2.5 & 6754.47 & 2691.66 & 655.46 \\
2.5 & 6720.86 & 2678.26 & 654.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters for the P–M curves of the non-corroded spun piles. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pile** &