## 3 Results and Discussion
### Pushover Curves  
Figures 17 and 18 show the pushover curves of corroded PSW-A and PSW-B, respectively. The pushover curves of the corroded PSWs obtained from FB-FEA were different from those obtained from FA-1 and FA-2. The 2D PSW model with distributed plasticity (FB-FEA) generated a smoother pushover curve than FA-1 and FA-2, considering an idealized plasticity approach (concentrated hinge). In FB-FEA, the spun pile section was discretized into multiple areas (material points), each corresponding to a predetermined material stress-strain curve. The moment-curvature relationship of the spun pile was calculated based on the stress-strain curve of each material point. As a result, the material nonlinearity and bending stiffness of corroded spun piles can be properly accounted for, resulting in smoother pushover curves. On the other hand, FA-1 and FA-2 considered the bending stiffness reduction factor and hinge property settings to characterize the inelastic behavior of the corroded spun piles. The hinge property settings reflect the moment-curvature and P-M capacity definitions for corroded spun piles. The pushover curves of FA-1 and FA-2 were influenced by the combination of the hinge property settings and the bending stiffness reduction factor of the corroded spun pile. Figure 16: Distribution of plastic hinges resulting from FB-FEA, FA-1, and FA-2. (**a**) PSW-A; (**b**) PSW-B. Figure 19 shows the effects of corrosion on the load-displacement curves of PSW-A according to FB-FEA, FA-1, and FA-2 for corrosion degrees of 0, 4.68, 9.67, 12.20, 14.74, and 18.56%. In the intact state (\(\psi=0\%\)), FB-FEA estimated the load capacity of PSW-A to be 689.05 kN. FA-1 produced a smaller load capacity of 635.97 kN, and FA-2 produced a slightly lower load capacity of 687.75 kN. In addition, FB-FEA led to a 22.06% decrease in the load capacity of PSW-A under a corrosion degree of 18.58%. In contrast, FA-1 and FA-2 led to 26.24% and 22.16% decreases in the load capacity of PSW-A under a corrosion degree of 18.58%, respectively. Figure 20 shows the load-displacement curve of corroded PSW-B with different corrosion degrees ranging from 0% to 18.56%. FB-FEA determined the non-corroded PSW-B to have a load capacity of 635.20 kN, whereas FA-1 and FA-2 produced load capacities of 600.31 and 636.32 kN, respectively. Furthermore, FB-FEA resulted in a 24.25% decrease in the load capacity of PSW-B under a corrosion degree of 18.58%, while FA-1 and FA-2 resulted in 29.70% and 24.72% decreases, respectively. The different definitions of the moment-curvature relationship, defined as hinge properties of spun pile, used in FA-1 and FA-2 (i.e., ultimate capacity and ultimate curvature of the spun pile) result in the different load capacities of the non-corroded PSWs compared to the FB-FEA results. Furthermore, the bending stiffness reduction factor of the corroded spun pile used in FA-1 exacerbates the difference in load capacity reduction for the corroded PSW compared to the FB-FEA results. Figure 17: Load–displacement curves of corroded PSW-A. (**a**) FB-FEA; (**b**) FA-1; (**c**) FA-2. Figure 18: Load–displacement curves of corroded PSW-B. (**a**) FB-FEA; (**b**) FA-1; (**c**) FA-2. Figure 19: PSW-A load–displacement curve comparison for various corrosion degrees. (**a**) \(\psi=0.00\%\); (**b**) \(\psi=4.68\%\); (**c**) \(\psi=9.67\%\); (**d**) \(\psi=12.20\%\); (**e**) \(\psi=14.74\%\); (**f**) \(\psi=18.56\%\). Table 10 compares the load capacities of PSW-A and PSW-B in the range of corrosion degrees from 0 to 18.58%. The maximum differences in the load capacity results for the corroded PSWs from FA-1 and FA-2 were 12.66% and 0.44%, respectively, compared to the FB-FEA results. The load capacity and pushover curves of the corroded PSW-A and PSW-B obtained through FA-2 were more consistent with the FB-FEA results than those obtained through FA-1.