## 4 Reliability Analysis of the PSC-I Girder
### Time-Related Reliability Analysis of the PSC-I Girder Bridge  
The reliability of sample bridges was analyzed based on the limit state equation given below. The load factor in Equation (19) represents the moment exerted by each load, and the resistance factor represents the flexural strength of the structure:  
\[g=R_{f}-D_{1}-D_{2}-LL(1+IM) \tag{19}\]  
where \(R_{f}\) is the resistance capacity (flexural strength), \(D_{1}\) is the load effect due to the girder, \(D_{2}\) is the load effect due to the barrier, sidewalk blocks, and pavement, \(LL\) is the load effect due to the live load, and \(IM\) is the impact coefficient.  
The reliability degradation during the life cycle of a sample bridge was analyzed based on the resistance capacity degradation where the flexural strength decreased because of structural deterioration during the service life, as calculated in Section 4.1, and because of the live load resulting from various traffic conditions, as determined in Section 3.1 describing the reliability analysis.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Corrosion** & \multirow{2}{*}{**No Cracked**} & \multicolumn{4}{c}{**Crack Width**} \\ \cline{3-5}
**Environment** & & **0.1 mm** & **0.2 mm** & **0.3 mm** \\ \hline Mild & 48.4 & 23.4 & 11.3 & 6.1 \\ Normal & 16.2 & 7.9 & 3.8 & 2.1 \\ Severe & 6.4 & 3.1 & 1.5 & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Degradation initiation time (year) in the PSC-I girder with and without cracks.  
Figures 4-6 present the changes in the annual reliability index depending on the service life, site environment of the sample bridge, and cracks. The reliability index varied in the range of 3.29 to 2.61 depending on the formation of cracks and traffic conditions (light, normal, heavy) in a mild corrosive environment. The reliability index varied in the range of 3.11 to 2.58 depending on the formation of cracks and traffic conditions (light, normal, heavy) in a normal corrosive environment. The reliability index varied in the range of 2.94 to 2.55 depending on the formation of cracks and traffic conditions (light, normal, heavy) in a severe corrosive environment. These results indicate that the annual reliability indices for PSC-I girder bridges with 75 years of service vary significantly depending on differences in the corrosive environment, traffic conditions, and crack formation.  
Figure 3: Resistance capacity loss ratio of the PSC-I girder bridge considering the crack width in corrosive environments: (**a**) mild; (**b**) normal; and (**c**) severe.  
Figure 4: Reliability degradation considering the crack width in a mild environment: (**a**) light traffic (AADT: 10,000, heavy vehicle proportion: 15%); (**b**) normal traffic (AADT: 20,000, heavy vehicle proportion: 25%); and (**c**) heavy traffic (AADT: 40,000, heavy vehicle proportion: 35%).  
Figure 5: Reliability degradation considering the crack width in a normal environment: (**a**) light traffic (AADT: 10,000, heavy vehicle proportion: 15%); (**b**) normal traffic (AADT: 20,000, heavy vehicle proportion: 25%); and (**c**) heavy traffic (AADT: 40,000, heavy vehicle proportion: 35%).  
Figure 6: Reliability degradation considering the crack width in a severe environment: (**a**) light traffic (AADT: 10,000, heavy vehicle proportion: 15%); (**b**) normal traffic (AADT: 20,000, heavy vehicle proportion: 25%); and (**c**) heavy traffic (AADT: 40,000, heavy vehicle proportion: 35%).