# Performance-Based Reliability Estimates for Highway Bridges Considering Previous Inspection Data
## 3 Performance-Based Resistance Deterioration Model
### Process of Performance-Based Resistance Deterioration Modeling  
Figure 3 shows the calibration process of the standard performance degradation model and development process of the performance-based resistance deterioration model.  
Step 1 consists of calibrating the standard performance degradation model using previous inspection results. Figure 4 shows the Step 1 for calibrating the standard performance degradation model. The standard performance degradation model was calibrated via reg  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Level**} & **Crack Width** & **Surface Damage Rate** \\  & **(\(w\),mm)** & **(\(D_{s}\),\%)** \\ \hline A & \(w<0.1\) & - \\ B & \(0.1\leq w<0.3\) & \(D_{s}<2\) \\ C & \(0.3\leq w<0.5\) & \(2\leq D_{s}<10\) \\ D & \(0.5\leq w<1.0\) & \(10\leq D_{s}\) \\ E & \(1.0\leq w\) & Serious damage \\ \hline \hline \end{tabular}
\end{table}
Table 4: Condition level evaluation criteria of the reinforced concrete (RC) slab [17].  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Level**} & **Crack Width** & **Surface Damage Rate** \\  & **(\(w\),mm)** & **(\(D_{s}\),\%)** \\ \hline A & - & - \\ B & \(w<0.2\) & \(D_{s}<2\) \\ C & \(0.2\leq w<0.3\) & \(2\leq D_{s}<10\) \\ D & \(0.3\leq w<0.5\) & \(10\leq D_{s}\) \\ E & \(0.5\leq w\) & Serious damage \\ \hline \hline \end{tabular}
\end{table}
Table 5: Condition level evaluation criteria of the PSC-I girder [17].  
Figure 2: Condition level curves based on the standard performance degradation model.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Bridge Member**} & \multicolumn{10}{c}{**Year of Condition Inspection**} \\ \cline{2-13}  & **2*** & **4*** & **6*** & **8*** & **10*** & **11*** & **13*** & **15*** & **16*** & **18*** & **20*** & **21*** & **23*** & **25*** & **26*** & **28*** \\ \hline RC & With previous inspection (2-W) & A & A & A & B & B & B & B & B & B & B & C & C & C & C & C & C \\ slab & Without previous inspection (2-W/O) & - & - & - & - & - & - & - & - & - & - & C & - & - & - & C \\ \hline PSC-I & With previous inspection (2-W) & A & A & A & A & A & B & B & B & B & B & B & B & B & C & C \\ girder & Without previous inspection (2-W/O) & - & - & - & - & - & - & - & - & - & - & B & - & - & C \\ \hline \end{tabular}  
* Precision inspection, ** precision safety diagnosis.  
\end{table}
Table 7: Condition level of an RC slab and PSC-I girder (inspection type 2).  
Step 2 is the process of applying the calibrated performance degradation model to the basic model (basic deterioration model of resistance capacity) presented in Section 2. The degradation factors evaluated for the calibrated performance degradation model (Figure 5a) are then reflected in the basic resistance model (Figure 5b--1 st part). In Figure 5a no degradation is assumed for condition level A and 25% degradation is assumed for condition level E. In addition, a linear degradation model is adopted from A to E. Figure 5b shows the result of the calibrated resistance degradation model combined with the basic deterioration model of resistance capacity for up to 75 years without any repair on the deteriorated members. The performance-based resistance deterioration model developed through Steps 1 and 2 is used for the lifetime reliability analysis in Step 3 (Section 4).