## 2 Methods
### Corrosion Effect on the Spun Pile Materials  
The corrosion mechanisms affecting the material properties of spun piles commence with the formation of rust on the PC bar due to chloride ingress from sea salt spray and repeated wetting and drying cycles. The rust expands over time, decreasing the area of the PC bar, which puts pressure on the concrete and initiates cracks. The formation of rust and cracks reduces the compressive strength of the concrete [35], the yield strength of the PC bar [39; 40], and the bond strength between the PC bar and the concrete [41; 42]. Therefore, the corrosion effect in a marine environment was simplified in this study by altering the PC bar geometry and decreasing the material properties of the spun pile (i.e., the compressive strength of the cover concrete, core concrete, and yield strength of the PC bar reduction). Furthermore, to consider the confinement effects on corroded concrete, this study employed the reduced compressive strength of confined concrete (core concrete) as well as the reduced compressive strength of unconfined concrete (cover concrete) [33]. Figure 3 illustrates the non-uniform decrease in the cross-sectional area of the PC bar considered in this study to represent the changes in the PC bar geometry. Equations (1)-(6) were utilized to determine the PC bar's corroded area and the corrosion degree [43]. \[A_{sl,corr}=2r^{2}(\theta-\sin\theta\text{cos}\,\theta) \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Layer** \\ **Code** \\ \end{tabular} } & \multirow{2}{*}{**N-SPT**} & \multirow{2}{*}{\begin{tabular}{c} **Layer** \\ **Thickness** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{**Soil Type**} & \multirow{2}{*}{\begin{tabular}{c} **Specific** \\ **Gravity** \\ **(G5)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Water** \\ **Content** \\ **W\({}_{\text{\tiny\bf m}}\) **(\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Unit** \\ **Weight** \\ **T\({}_{\text{\tiny\bf m}}\) **(\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Liquid** \\ **Limit** \\ **L1 (\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Plastic** \\ **Limit** \\ **PL (\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Friction** \\ **Angle \(\phi\)** \\ **(c)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Caseion** \\ **Case (k/N/m\({}^{2}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Shear** \\ **Wave** \\ **Velocity** \\ **Vs (m/s)** \\ \end{tabular} } \\ \hline CL01 & 2–4 & 3 & \
\begin{tabular}{c} Very Soft \\ Clay \\ \end{tabular} & 2.614 & 61.24 & 10.07 & 78.75 & 35.28 & 6 & 41.19 & 125.99 \\ CL02 & 5–6 & 9 & Soft Clay & 2.623 & 57.68 & 10.33 & 76.24 & 34.14 & 7 & 42.22 & 170.48 \\ S803 & 11–19 & 4 & Slity Sand & 2.656 & 46.2 & 10.75 & - & - & 22 & - & 217.94 \\ S804 & 28–33 & 4 &
\begin{tabular}{c} Medium \\ Sand \\ \end{tabular} & 2.663 & 15.72 & 11.09 & - & - & 30 & - & 249.76 \\ S805 & 35–60 & 20 & Dense Sand & 2.661 & 14.36 & 11.89 & - & - & 34 & - & 285.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Soil properties. Figure 2: Spun pile cross-sections. (**a**) Pile A with infilled concrete; (**b**) Pile A; (**c**) Piles B and C with infilled concrete; (**d**) Piles B and C.  
\[\theta=arccos\bigg{(}1-\frac{d_{i}}{2r}\bigg{)};\ 2/3\pi\leq d_{i}\leq 4/3\pi \tag{2}\]  
\[d_{i}=0.0116\ i_{corr}(t)\ Rt \tag{3}\]  
where \(A_{sl,corr}\) is the cross-sectional area loss of the corroded PC bar (mm\({}^{2}\)), \(r\) is the PC bar radius (mm), \(\theta\) is the angle of the rust distribution (degrees), \(d_{i}\) is the maximum rust thickness in the radial direction (mm) [44], \(R\) is a pitting factor variable ranging from 4 to 8 (=5.65 in this study based on [44]), and \(t\) is the corresponding year.