## 3 Results and Discussion  
### Bending Stiffness Reduction Factor of Corroded Spun Pile  
The bending stiffness of the spun pile decreased from its initial value over time as the corrosion degree increased. This decrease is a function of the bending stiffness reduction factor (\(\eta\)). In FB-FEA, the bending stiffness of the corroded spun pile was computed in the sectional analysis by considering the material properties of corroded spun pile and the reduction in the PC bar cross-sectional area. In the 2D FA-1 models, the bending stiffness reduction factor of corroded pile [3] was employed, and it is:  
\[EI_{corr}=\eta\ E_{p}I_{p} \tag{20}\]  
where \(EI_{corr}\) is the bending stiffness of the corroded pile, \(I_{p}\) is the moment of inertia of the spun pile (mm\({}^{4}\)), \(E_{p}\) is the modulus of elasticity of the spun pile (MPa), and \(\eta\) is the bending stiffness reduction factor of corroded pile that can be calculated as [5]:  
\[\eta=\frac{1}{A}\sum A_{i}\eta_{i} \tag{21}\]  
where \(A\) is the total cross-sectional area of the PC bar, \(A_{i}\) is the cross-sectional area of the \(i\)th PC bar after corrosion, and \(\eta_{i}\) is the stiffness reduction factor of the \(i\)th PC bar caused by corrosion, calculated as follows [5]:  
\[\eta_{i}=\left\{ \begin{array}{cc}1.0&0\leq d_{i}<0.1\\ (3.7-7d_{i})/3&0.1\leq d_{i}<0.25\\ 0.65&d_{i}\geq 0.25\end{array} \right. \tag{22}\]  
where \(d_{i}\) is the rust thickness of the \(i\)th PC bar, calculated using Equation (3). The bending stiffness reduction factor of corroded spun pile considered in FA-2 was developed by modifying the bending stiffness reduction factor of the corroded pile formulation [3] as well as the moment of inertia [60] and the modulus of elasticity [55] of the spun pile formulation. This was achieved by considering the reduction in diameter of the PC bar caused by corrosion and the material properties degradation of the corroded spun pile. Equations (23)-(28) present the bending stiffness reduction factor of the corroded spun pile as follows:  
\[\eta_{sp}=\frac{EI_{sp-corr}}{E_{p}I_{p}} \tag{23}\]  
\[EI_{sp-corr}=E_{c,corr}\left(\frac{\pi\left({d_{o}}^{4}-{d_{i}}^{4}\right)}{6 4}+\left(\frac{E_{s}}{E_{c,corr}}-1\right)\sum A_{pc,corr-i}{d_{pc-i}}^{2}\right) \tag{24}\]  
\[E_{c,corr}\ =\left(\frac{A_{co}}{A_{g}}\right)E_{co,corr}\ +n\left(\frac{A_{co}}{A_{g}} \right)E_{cc,corr} \tag{25}\]  
\[E_{co,corr}\ =4700\sqrt{f_{c,corr}} \tag{26}\]  
\[E_{cc,corr}\ =4700\sqrt{f_{cc,corr}} \tag{27}\]  
\[n=E_{co,corr}\ f_{E_{c,corr}} \tag{28}\]  
where \(\eta_{sp}\) is the bending stiffness reduction factor for the corroded spun pile, \(EI_{sp-corr}\) is the bending stiffness of the corroded spun pile, \(I_{p}\) is the moment of inertia of the spun pile (mm\({}^{4}\)), \(E_{p}\) is the modulus of elasticity of the spun pile (MPa), \(E_{c,corr}\) is the elastic modulus of corroded concrete of the spun pile (MPa), \(d_{o}\) is the outside diameter of the spun pile (mm), \(d_{i}\) is the inside diameter of the spun pile (mm), \(E_{s}\) is the PC bar elastic modulus (MPa), \(A_{pc,corr-i}\) is the \(i\)th cross-sectional area of the corroded PC bar (mm\({}^{2}\)),is the distance from the \(i\)th corroded PC bar's neutral axis to the spun pile neutral axis (mm), \(A_{co}\) is the cross-sectional area of the cover concrete of the spun pile (mm\({}^{2}\)), \(A_{sc}\) is the cross-sectional area of the core concrete of the spun pile (mm\({}^{2}\)), \(A_{g}\) is the cross-sectional area of the spun pile (mm\({}^{2}\)), \(E_{co,corr}\) is the modulus of elasticity of the corroded cover concrete (MPa), \(E_{cr,corr}\) is the modulus of elasticity of the corroded core concrete (MPa), \(n\) is the modular ratio, \(f_{c,corr}\) is the corroded cover concrete compressive strength (MPa), and \(f_{cc,corr}\) is the corroded core concrete compressive strength (MPa). In this study, the same corrosion degree was assumed to occur throughout the PC bar of the spun pile.