## 2 Background
### United States  
In the United States, there are various approaches to assess the condition of the bridge. For example, the California Department of Transportation defines BHI based on Equation (4). This index varies from 0 for the worst bridge condition to 100 for the healthiest bridge condition [21].  
\[\text{BHI}=\{\sum(\text{CEV})/\sum(\text{TEV})\}\times 100, \tag{4}\]  
where BHI is bridge health index, \(\text{CEV}\) is current element value, and TEV is total element value.  
CEV and TEV can be calculated according to the following equations [21]:  
\[\text{CEV}=\sum(\text{QCS}_{\text{i}}\times\text{WF}_{\text{i}})\times\text{ FC}, \tag{5}\]  
\[\text{TEV}=\text{TEQ}\times\text{FC}, \tag{6}\]  
where TEQ is total element quantity, FC is failure costs of element, \(\text{QCS}_{\text{i}}\) is quantity in condition state i, and WF is weight factor.  
In the United States, transportation departments report a set of data called national bridge inspection (NBI). Based on the physical condition of the bridge, the bridge is assigned a score in the range of 0 to 9 [22]. The assessment procedure is presented in Table 5.  
The US departments of transportation often use a computer program to assess bridge conditions. This program is based on Equation (7) [22].  
\[\text{SR}=\text{S}_{1}+\text{S}_{2}+\text{S}_{3}-\text{S}_{4}, \tag{7}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Rate** & **DI** & **Description** \\ \hline A & 0 \(\leq\) DI \(<\) 0.13 & Perfect \\ B & 0.13 \(\leq\) DI \(<\) 0.26 & Minor problem in secondary elements \\ C & 0.26 \(\leq\) DI \(<\) 0.49 & Minor problem in primary elements \\ D & 0.49 \(\leq\) DI \(<\) 0.79 & Problem in primary elements \\ E & 0.79 \(\leq\) DI & Serious problem in primary elements \\ \hline \hline \end{tabular}
\end{table}
Table 4: Assessment of bridge condition in Korea.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Rate** & **State** & **Description** \\ \hline
9 & Excellent & A new bridge \\
8 & Very good & No problems noted \\
7 & Good & Some minor problems \\
6 & Satisfactory & Structural elements show some minor deterioration \\
5 & Fair & All primary structural elements are sound but may have minor \\  & & section loss, deterioration, spalling or scour \\
4 & Poor & Advanced section loss, deterioration, spalling, scour \\  & & Loss of section, etc., has affected primary structural components; \\
3 & Serious & Local failures are possible. Fatigue cracks in steel or shear cracks in concrete may be present \\  & & & Advanced deterioration of primary structural elements. Fatigue \\
2 & Critical & cracks in steel or shear cracks in concrete may be present or scour \\  & & may have removed structural support. Unless closely monitored it \\  & & may be necessary to close the bridge until corrective action is taken \\  & & Major deterioration or loss of section in critical structural \\
1 & Imminent failure & components or obvious vertical or horizontal movement affecting \\  & & structural stability. Bridge is closed to traffic but corrective action \\  & & may allow it to be returned to light service \\
0 & Failed & Out of service. Beyond corrective action \\ \hline \hline \end{tabular}
\end{table}
Table 5: Assessment of bridge condition based on NBI.  
where SR is Sufficiency rating, S1 is the parameter related to structural safety, S2 is the parameter related to bridge serviceability and functionality, S3 is the parameter related to user requirements, and S4 is the parameter related to reductive coefficients based on structure type and traffic safety.  
SR indicates the bridge sufficiency to remain in service, where SR has a maximum rating of 100%, indicating complete bridge sufficiency, and a minimum rating of 0%, indicating complete bridge deficiency. The parameters S1, S2, S3, and S4 have weight importance of 55%, 30%, 15%, and 13%, respectively. FHWA uses SR to allocate rebuilding funds so that [22]:  
* If SR < 50, the bridge is eligible for replacement;
* If 50 < SR < 80, the bridge is eligible for rehabilitation.