## 4 Case Study  
A concrete bridge (Figure 2) built in 2011 years and detected in 2023 years in Huizhou was taken as an example to explain the effectiveness of the method improved in this paper. The water-to-cement ratio is 0.55. The cement is ordinary silicate cement. The concrete strength is more than 30 MPa. With the test, the thickness of concrete cover \(c\) followed the normal distribution, with the statistical results shown in Table 1. The sample drilled powder concrete at different depths of 0-10 mm, 10-20 mm, 20-40 mm, 40-60 mm, and 60-80 mm, respectively. The chloride ion content in the concrete powder samples could be obtained by the potential titration method, as listed in Figure 3. The mean value of the calculated value of chloride ion content at different depths of 5 mm, 15 mm, 30 mm, 50 mm, and 70 mm were 0.171, 0016, 0.0001, 0, and 0 (% of the concrete mass) (plate); 0.126, 0.012, 0.0001, 0, and 0 (% of the concrete mass) (Beam); 0.222, 0.088, 0.020, 0.0001, and 0 (% of the concrete mass) (column in atmospheric area); 0.289, 0.114, 0.026, 0.0002, and 0 (% of the concrete mass) (column in water level change area); 0.435, 0.172, 0.039, 0.0003, and 0 (% of the concrete mass) (column in splash zone); and 0.702, 0.278, 0.063, 0.0005, and 0 (% of the  
chloride ion concentration was highly discrete. The prior distribution of \(C_{cr}\) value here was selected according to [PERSON]'s recommendations [31], with the conversion to follow the normal distribution mean of 0.1% of the concrete mass and a COV of 0.2. The mean of the prior corrosion probability of reinforcement \(\mu^{\prime}_{P_{cur}(t_{0})}\) using 12 years was calculated with Formula (14). The corrosion detection sample results are shown in Table 3. The test samples were selected for half-cell potential detected samples, and the corrosion samples were the HCP (half-cell potential) level (mV) \(<-350\) mV samples. With the Formula (17), the mean value and the standard deviation of the posterior probability density function of the corrosion probability \(f^{\prime\prime}(p_{\text{cor}}|H)\) as \(\mu^{\prime\prime}_{P_{cur}(t_{0})}\) and \(\sigma^{\prime\prime}_{P_{cur}(t_{0})}\) were calculated. Then, the updated mean value of the critical chloride concentration \(\mu^{\prime\prime}_{C_{cr}}\) is listed in Table 3. According to Table 3, for different positions, the mean update result of the critical chloride ion was significantly different from the initial value of 0.1. The critical chloride ion concentrations before and after the update are shown in Figure 4. For different structural components with different inspection results, the critical chloride ion concentrations after the update varied greatly. For plates and beams, the updated critical chloride ion concentration was much lower than the theoretical value of 0.1, which was 0.076 and 0.064. For the column, the updated critical chloride ion concentration was about 1.67-4.33 times the theoretical value, indicating a significant updating effect. The traditional assessment method, which uses a consistent critical chloride ion concentration, can lead to significant assessment errors. The assessment results after the update are relatively accurate. With the updated critical chloride concentration model, the corrosion probabilities are plotted in Figure 5. Figure 5 also provides the corrosion probabilities before updating (using actual concrete cover thickness, surface chloride ion concentration, and diffusion coefficient obtained through detection) for comparison. According to Figure 5, it can be seen that the corrosion probability in concrete structures calculated using the updated model differs significantly from the original theoretical model. The updating method of durability models based on actual detection results provided in this article is of great significance. Figure 4: The critical chloride ion concentrations before and after the update.