# Performance-Based Reliability Estimates for Highway Bridges Considering Previous Inspection Data
## 4 Performance-Based Reliability Analysis Considering Site Environments  
### Effect of Previous Inspection Data  
The performance-based resistance deterioration model proposed in Section 3 is used to analyze the reliability by considering various site environments of the bridge. To estimate the effects of previous inspection results on the reliability of the bridge, the reliability is analyzed using the standard performance degradation model proposed in Section 3 and inspection data in Tables 5 and 6. The corrosive environment and traffic characteristics presented in Section 2 are also used. The corrosive environments considered are mild, normal, and severe, and the traffic characteristics considered are light, normal, and heavy. Figures 8-10 show the calculated reliabilities of PSC-I girder bridges comprising all the previous inspection results based on a service lifespan of 75 years. The basic model presented in Section 2 represents the model that does not account for the inspection data. The standard model is a performance-based resistance deterioration model that applies the standard degradation model. The calibrated model 1-W represents the results of a previous inspection (1-W) in Table 6. The calibrated model 2-W represents the results of a previous inspection (2-W) in Table 7.  
The initial reliability of the bridge was 3.65 (\(P_{f}=1.3\times 10^{-4}\)) with light traffic characteristics, 3.54 (\(P_{f}=2.0\times 10^{-4}\)) with normal traffic characteristics, and 3.45 (\(P_{f}=2.8\times 10^{-4}\)) with heavy traffic characteristics. These results show that traffic characteristics affect the reliability of the bridge. In the case of normal corrosive environment with normal traffic characteristics and service lifespan of 75 years, the reliability is 3.02 (\(P_{f}=1.3\times 10^{-3}\)) for the basic model, 2.74 (\(P_{f}=3.1\times 10^{-3}\)) for the standard model, 2.63 (\(P_{f}=4.2\times 10^{-3}\)) for the calibrated model (1-W), and 2.78 (\(P_{f}=2.7\times 10^{-3}\)) for the calibrated model (2-W). When compared with the basic model, the standard model showed an increase in the probability of failure by 2.4 times, the calibrated model (1-W) by 3.4 times, and the  
Figure 6: Calibration of the performance degradation model of the RC slab. Figure 7: Calibration of the performance degradation model of the PSC-I girder. calibrated model (2-W) by 2.2 times. These results suggest that inspection results affect the reliability analysis of the bridge. Based on the service lifespan of 75 years, the calibrated model (1-W) with normal traffic characteristics had a reliability of 3.02 (\(P_{f}=1.3\times 10^{-3}\)) in a mild corrosion environment, 2.63 (\(P_{f}=4.2\times 10^{-3}\)) in a normal corrosion environment, and 2.13 (\(P_{f}=1.7\times 10^{-2}\)) in a severe corrosion environment. These results show that, given the same traffic characteristics, the reliability of bridges is influenced by different degrees of corrosive environments. Figure 8: Reliability degradation under light traffic characteristics (with previous inspection). Figure 9: Reliability degradation under normal traffic characteristics (with previous inspection). Figures 11-13 show the analyzed reliabilities of the PSC-I girder bridges based on a 75-year service lifespan with only one or two inspection results (in cases where there are insufficient or no previous inspection data). The calibrated model (1-W/O) reflects the calibrated degradation model, whose condition level declined more quickly than that of the standard degradation model. The calibrated model (2-W/O) reflects the calibrated degradation model, whose condition level declined more slowly than that of the standard degradation model. Figure 11: Reliability degradation under light traffic characteristics (without previous inspection). Figure 10: Reliability degradation under heavy traffic characteristics (with previous inspection).