# Performance-Based Reliability Estimates for Highway Bridges Considering Previous Inspection Data
## 4 Performance-Based Reliability Analysis Considering Site Environments
### Effect of Crack on Concrete Members  
To estimate the influence of cracks in concrete members on the reliability of bridges, a reliability analysis is carried out with the calibrated model (1-W) proposed in Section 4.1. Figures 14-16 show the reliability analysis results of the calibrated model (1-W) according to the traffic characteristics, corrosive environment, and crack width. It is assumed that the cracks of the calibrated model (1-W) appeared 16 years after the completion of its construction. In the case of light traffic characteristics with a crack width of 0.1-0.3 mm and service lifespan of 75 years, the reliability was analyzed to be 2.90 (\(P_{f}=1.9\times 10^{-3}\)) to 2.56 (\(P_{f}=5.3\times 10^{-3}\)) in a mild corrosion environment, 2.59 (\(P_{f}=4.9\times 10^{-3}\)) to 2.34 (\(P_{f}=9.8\times 10^{-3}\)) in a normal corrosion environment, and 2.18 (\(P_{f}=1.5\times 10^{-2}\)) to 2.06 (\(P_{f}=2.0\times 10^{-2}\)) in a severe corrosion environment  
Based on Figures 14-16, given the same traffic characteristics; if the corrosive environment becomes severe, and the width of the cracks in the concrete members increases, the reliability decreases. These results suggest that the traffic characteristics, corrosive environment, and crack width in concrete members influence the reliability analysis results of the bridge.  
Figures 17-19 show the reliability analysis results of the calibrated model (2-W) according to the traffic characteristics, corrosive environment and crack width. It is assumed that the cracks of the calibrated model (2-W) appeared 26 years after the completion of its construction. In the case of light  
Figure 16: Reliability degradation considering crack width under heavy traffic characteristics (calibrated model (1-W)).  
Figure 15: Reliability degradation considering crack width under normal traffic characteristics (calibrated model (1-W)).  
traffic characteristics with a crack width of 0.1-0.3 mm and service lifespan of 75 years, the reliability was analyzed to be 3.05 (\(P_{f}=1.1\times 10^{-3}\)) to 2.83 (\(P_{f}=2.3\times 10^{-3}\)) in a mild corrosion environment, 2.80 (\(P_{f}=2.5\times 10^{-3}\)) to 2.65 (\(P_{f}=4.0\times 10^{-3}\)) in a normal corrosion environment, and 2.46 (\(P_{f}=6.9\times 10^{-3}\)) to 2.39 (\(P_{f}=8.3\times 10^{-3}\)) in a severe corrosion environment.  
Figure 17: Reliability degradation considering crack width under light traffic characteristics (calibrated model (2-W)).  
Figure 18: Reliability degradation considering crack width under normal traffic characteristics (calibrated model (2-W)).  
In the case of normal traffic characteristics with a crack width of 0.1-0.3 mm and service lifespan of 75 years, the reliability was analyzed to be 2.94 (\(P_{f}=1.6\times 10^{-3}\)) to 2.72 (\(P_{f}=3.2\times 10^{-3}\)) in a mild corrosion environment, 2.69 (\(P_{f}=3.5\times 10^{-3}\)) to 2.54 (\(P_{f}=5.5\times 10^{-3}\)) in a normal corrosion environment, and 2.35 (\(P_{f}=9.3\times 10^{-3}\)) to 2.29 (\(P_{f}=1.1\times 10^{-2}\)) in a severe corrosion environment.  
In the case of heavy traffic characteristics with a crack width of 0.1-0.3 mm and service lifespan of 75 years, the reliability was analyzed to be 2.86 (\(P_{f}=2.1\times 10^{-3}\)) to 2.64 (\(P_{f}=4.1\times 10^{-3}\)) in a mild corrosion environment, 2.61 (\(P_{f}=4.5\times 10^{-3}\)) to 2.46 (\(P_{f}=6.9\times 10^{-3}\)) in a normal corrosion environment, and 2.27 (\(P_{f}=1.2\times 10^{-2}\)) to 2.21 (\(P_{f}=1.4\times 10^{-2}\)) in a severe corrosion environment.