## 3 Results and Discussion  
The results of applying the deterioration data in Table 6 and the HI derivation procedure shown in Figure 6 are illustrated in Figure 7. The HI curve represents the trend of deriving the CHI and BHI using only the deterioration models derived in Section 2.2 without specifying a particular bridge. This curve can be derived by defining \(\Delta A^{(i)}_{scaled}\) as zero in Equation (3) and then calculating the HI for each service year. It indicates the HI change trend estimated from the deterioration information of RC slab bridges in urban areas. To compare this curve with the HIs of the case study bridges, the accuracy was derived using the following equation, and it exceeded 93% for all cases:  
\[Accuracy=\frac{1}{n}\sum_{1}^{n}\lvert HI_{case}-HI_{curve}\rvert \tag{6}\]  
where \(HI_{case}\) denotes the HI for the case study bridges, \(HI_{curve}\) denotes the HI obtained from the HI curve of Seoul without inspection data, and \(n\) denotes the number of \(HI_{case}\).  
The results of our case study provided several insights. First, the alignment of the HI curves and trends for the case-study bridges suggests that the deterioration models outlined in Section 2.2 accurately reflect the specific deterioration characteristics of urban areas. Consequently, bridge maintenance managers can estimate the performance degradation based on the bridge location even if detailed inspection information is unavailable. Second, the HI-based evaluation method can effectively visualize the extent of performance degradation. Significant deviations in the HIs of the bridges below the HI curve indicate higher levels of performance degradation compared with the regional average, whereas steep HI changes represent rapid increases in deterioration. For instance, in Figure 7d, the results for Bridge A exemplify the former, whereas those for Bridge F exemplify the latter; these results can be used to make informed maintenance decisions. Bridge A requires more immediate attention than the other bridges owing to safety concerns, whereas Bridge F requires proactive measures to prevent further deterioration. Third, analyzing the HI of individual components can help identify targets for focused management. As shown in Figure 7c, the pier of Bridge A has a particularly low HI, indicating a high level of deterioration, whereas that of Bridge F decreases rapidly. This suggests that, during inspections, the deterioration factors of piers in these bridges should be closely examined, and the necessary repairs should be conducted.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Bridge** & **Service Year** & **Component** & **Microcracks** & **Macrocracks** & **Crazing** & **Material Defects** & **Efflorescence** & **Leakage** & **Rebar Exposure** \\ \hline \multirow{8}{*}{F} & \multirow{2}{*}{25} & Slab & 59.40 & 2.50 & 0.00 & 3.87 & 7.01 & 0.00 & 0.02 \\  & & Abtment & 21.40 & 0.00 & 0.00 & 3.19 & 0.00 & 15.00 & 0.00 \\  & & Pier & 18.90 & 0.00 & 0.00 & 3.67 & 0.00 & 0.00 & 0.00 \\ \hline \multirow{8}{*}{F} & \multirow{2}{*}{27} & Slab & 58.50 & 3.00 & 0.00 & 3.87 & 0.41 & 0.00 & 0.00 \\  & & & 21.70 & 0.00 & 0.00 & 6.54 & 0.00 & 0.87 & 0.10 \\  & & Pier & 17.20 & 0.60 & 0.00 & 7.02 & 0.00 & 0.00 & 0.00 \\ \hline \multirow{8}{*}{F} & \multirow{2}{*}{29} & Slab & 22.60 & 1.50 & 0.00 & 48.00 & 0.25 & 0.00 & 0.00 \\  & & & 0.00 & 0.00 & 0.00 & 7.14 & 0.00 & 0.57 & 0.00 \\  & & Pier & 0.00 & 0.00 & 0.00 & 6.20 & 0.00 & 0.00 & 0.00 \\ \hline \multirow{8}{*}{28} & Slab & 35.80 & 0.00 & 1.50 & 82.19 & 0.01 & 0.00 & 0.00 \\  & & 10.50 & 5.20 & 1.40 & 10.01 & 0.00 & 3.24 & 0.00 \\ \cline{1-1}  & & Pier & 13.70 & 0.00 & 0.00 & 4.42 & 0.00 & 0.00 & 1.00 \\ \hline \multirow{8}{*}{30} & Slab & 24.50 & 0.00 & 31.50 & 32.48 & 0.08 & 0.00 & 0.00 \\ \cline{1-1}  & & 35.70 & 12.70 & 1.40 & 10.12 & 0.06 & 2.20 & 0.00 \\ \cline{1-1}  & & Pier & 55.80 & 0.00 & 0.00 & 1.75 & 0.00 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._