## 4 Reliability Analysis of the PSC-I Girder  
### Performance Degradation Analysis Considering a Corrosive Environment  
The performance degradation of the PSC-I girder bridge was calculated based on the corrosion model presented in Section 2. In the analysis, the degradation due to corrosion of the slab was confirmed to be small. Therefore, the performance degradation due to slab corrosion was not considered in the analysis of the performance degradation of the composite PSC-I girder. In order to examine the difference in performance degradation for environments of varying corrosiveness, the corrosive environments were classified as mild, normal, and severe. Parameters such as the surface chloride content, chloride diffusion coefficient, and carbonation rate coefficient (\(a_{d}\)) that greatly influence the corrosion of the PSC-I girder were varied in different corrosive environments for analysis. To determine the penetration ratio (\(R\)), experiments should be performed that consider each corrosion condition. However, determining the penetration ratio by actual experiments is difficult. This study referred to [PERSON] and [PERSON]'s work [11] to determine the penetration ratio. Table 11 presents the corrosion parameters used in the analysis [8; 10; 11; 17]. To consider the effect of cracks on the resistance capacity, the existence and size of cracks in the girder were classified in the analysis. Based on the concrete component condition assessment criteria specified by the Korea Infrastructure Safety and Technology Corporation (Seoul, Korea) [18], the time until the concrete experiences performance degradation was analyzed under normal conditions (without cracks) and when cracks formed with widths ranging from 0.1 to 0.3 mm. Table 12 lists the conditions for resistance capacity degradation caused by chloride attack and carbonation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material/Fabrication** & \multicolumn{2}{c}{**Modeling**} & \multicolumn{2}{c}{**Resistance**} \\ \hline
**Bias Factor** & **COV** & **Bias Factor** & **COV** & **Bias Factor** & **COV** \\ \hline
1.043 & 0.024 & 1.01 & 0.06 & 1.053 & 0.064 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistical parameters for the resistance capacity of the example PSC-I girder. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Mild Environment** & **Normal Environment** & **Severe Environment** \\ \hline \(c_{0}\) & 2.0 kg/m\({}^{3}\) & 3.5 kg/m\({}^{3}\) & 8.5 kg/m\({}^{3}\) \\ \(a_{d}\) & \(-0.0463f^{\prime}_{c}+1.7048\) & \(-0.0265f^{\prime}_{c}+1.2538\) & \(-0.0184f^{\prime}_{c}+0.8556\) \\ \(w/c\) & 0.6 & 0.6 & 0.6 \\ \(D_{0}\) & \(3.87\times 10^{-12}\) cm\({}^{2}\)/year & \(3.87\times 10^{-12}\) cm\({}^{2}\)/year & \(3.87\times 10^{-12}\) cm\({}^{2}\)/year \\ \(R\) & 5 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Description of corrosion parameters for various corrosive environments. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Deterioration Factor** & **Variable** & **Initial Condition** \\ \hline Chloride attack & \(C(x,t)=C_{0}\left|1-erf\left(\frac{x}{2\sqrt{D\cdot f}(w_{c})\cdot t}\right)\right|\) & \(C(x,t)>1.2\) kg/m\({}^{3}\) \\ Carbonation & \(y_{p}=\left[\frac{4.6w/c-1.76}{\sqrt{7.2}}\frac{1}{a_{d}}\right]\sqrt{t}\) & \(y_{p}>y_{\text{lim}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Conditions for resistance capacity degradation caused by chloride attack and carbonation. The degradation initiation time (\(t_{i}\)) was estimated based on the corrosive environments of the bridge and the crack width of the PSC-I girder bridge. The results are presented in Table 13. The analysis results showed that the time until performance degradation of a PSC-I girder under normal conditions was 48.4 years in a mild environment, 16.2 years in a normal environment, and 6.4 years in a severe environment. This appeared to be the result of differences in the surface chloride content according to regional characteristics.