## 3 Results and Discussion
### Corrosion Effect on Concrete Compressive Strength  
Figure 10 depicts the stress-strain relationships of the concrete. The cover concrete compressive strength decreased slightly from 10 to 40 years but significantly from 50 to 75 years. Compared to the cover concrete, the compressive strength of the core concrete decreased less. After 75 years, the compressive strength of the cover concrete decreased to 40.21% of the initial condition, whereas the core concrete's strength dropped to just 82.87%. The nonuniform rust distribution was more detrimental to the cover concrete than the core concrete. As the corrosion degree rose, the nonuniform distribution of rust exerted internal pressure on the spun pile's outer side, causing extensive cracking of the cover concrete and a significant decrease in the cover concrete's comprehensive strength. Figure 11 shows the confining pressure for ages 0 and 75. The confining pressure of the spun pile reached a maximum value of 1.68 MPa, which was relatively low. It caused the stress-strain relationship of the core concrete to exhibit a brittle failure pattern, as shown in Figure 10b. Figure 10: _Cont._  
Figure 9: Concrete strain distributions of the corroded spun pile. (**a**) 4.68% corrosion degree. (**b**) 9.67% corrosion degree. (**c**) 14.74% corrosion degree. (**d**) 18.56% corrosion degree. Figure 12 illustrates the relationship between the corrosion degree and the concrete compressive strength. The compressive strengths of the core and cover concrete were obtained by taking the ultimate axial stress values referred to in Figure 10. When the corrosion degree reached 18.56% (75 years), the compressive strength of core concrete decreased to 82.87% of its initial value, continuously dropping with the corrosion degree. The compressive strength of the cover concrete also gradually decreased with the increase in the corrosion degree in the range of the corrosion degree 11.50% or less. In contrast to the core concrete, after the corrosion degree reached 11.50%, the compressive strength of the cover concrete significantly dropped. When the corrosion degree reached 18.56%, the compressive strength of the cover concrete was 40.21% of its initial value. Evaluation equations for the cover and core concrete compressive strengths following the corrosion degree were proposed as follows:  
\[f_{c,corr}=\bigg{(}0.25\tan^{-1}\bigg{(}\frac{0.149-\psi}{0.025}\bigg{)}+0.65 \bigg{)}f_{c,0} \tag{10}\]  
Figure 11: Confining pressure of the spun pile. (**a**) 0 years. (**b**) 75 years. Figure 10: Concrete stress–strain relationships. (**a**) Cover concrete. (**b**) Core concrete. \[f_{cc,corr}=\left(0.14\tan^{-1}\left(\frac{0.17-\psi}{0.1}\right)+0.848\right)f_{cc,0} \tag{11}\]  
where \(f_{cc,corr}\) is the corroded cover concrete compressive strength; \(f_{cc,corr}\) is the corroded core concrete compressive strength; \(f_{cc,0}\) is the initial cover concrete compressive strength; \(f_{cc,0}\) is the initial core concrete compressive strength; and \(\psi\) is the corrosion degree. Figure 12 also shows the concrete compressive strength predicted by [PERSON] et al. [14], which is expressed as follows:  
\[f_{c,corr}=(1-\lambda)f_{c,0} \tag{12}\]  
\[\lambda=2.288\psi-1.733 \tag{13}\]  
where \(f_{c,corr}\) is the corroded concrete compressive strength; \(f_{c,0}\) is the initial concrete compressive strength; \(\lambda\) is the percentage of compressive strength reduction; and \(\psi\) is the corrosion degree. As regards the core concrete, the equation by [PERSON] et al. slightly underestimated the compressive strength. The explanation is that [PERSON] et al. considered normal concrete without considering the confinement effect. As for the cover concrete, the equation by [PERSON] et al. significantly overestimated the compressive strength in the range of the corrosion degree 11.50% or larger. [PERSON] et al.