# Fragility Analysis Based on Damaged Bridges during the 2021 Flood in Germany
## 2 Materials and Methods
### Damage Categories and Bridge Condition Rating  
The German Standard DIN 1076 regulates structural and traffic security of road infrastructures, with emphasis on the inspection and analysis of bridges, tunnels and culverts [67]. Each damage type is assessed and rated, justifying the reduction in structural safety, durability and/or traffic safety. In addition, guidelines support analysts in determining bridge condition ratings, with a grading system ranging from 1 to 4, including one decimal place [68]. The best condition possible for a structure is 1, while 4 is attributed to collapsed structures. The scale is not linear, thus for example, a structure rated 2.0 is not twice as safe as one rated 4.0. Under the same logic, the decimal point at threshold bounds should not be considered as a slight increment, i.e., when increasing a score from 3.4 to 3.5, the damage should be significantly different. The classification follows the scheme displayed in Table 1.  
In the database of bridges damaged in the 2021 flood, many structures were inspected by qualified surveyors in the aftermath of the event. However, for some structures, unfortunately those data were not available. For most of these bridges, other types of documentation was found, such as pictures and damage reports. To solve the issue of having quantitative information for one part of the database and qualitative information for the other part, expert opinion was employed to homogenize the two scales. A minority of structures did not have enough data to work with and were therefore not included. As bridge ratings were semantically described, the process of attributing categories was facilitated, considering also the detailed description included in the DIN 1076, which was briefly recapped in Table 1. To balance granularity and accuracy, four damage categories were created:  
1. undamaged--D1;
2. slightly damaged--D2;
3. moderately damaged--D3;
4. extensively damaged--D4. The categories differ from HAZUS ones, which are slight, moderate, extensive and complete damage [27]. This discrepancy is mainly due to the different rating system associated with the structures. Indeed, the German bridge condition rating based on DIN1076 differs from that of the NBI (National Bridge Inventory) [68]. Therefore, the present categories were chosen according to HAZUS-based classification, which is employed in the existing literature on empirical fragility curves issued for bridges [28; 29]. This choice was made in an attempt to facilitate further comparisons at research level but also maintaining a rigorous approach when following the damage levels reported in Table 1, which are described in the German standard DIN1076 [68]. Therefore, the only difference to the HAZUS classification system concerned structural collapse (German rating = 4.0), which \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rating** & **Structural Safety** & **Traffic Safety** & **Durability** \\ \hline
1.0–1.4 & Not compromised & Not compromised & Not compromised \\
1.5–1.9 & Not compromised & Not compromised & Can be compromised in the long-term \\
2.0–2.4 & Not compromised & Not compromised & Can be compromised in the medium-term \\
2.5–2.9 & Not compromised & Can be compromised & Can be compromised \\
3.0–3.4 & Is compromised & Is compromised & Extensively compromised \\
3.5–4.0 & Extensively compromised & Extensively compromised \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definitions of bridge condition ratings according to DIN 1076 [68]. was associated with the complete damage reported in HAZUS but was included in the extensive damage category in DIN1076, given that the rating spans between 3.5 and 4.0, as per Table 1. Both in the USA and Germany, ratings are given by qualified experts. From this perspective, the condition rating is based on experts' judgment on the safety domain boundary, which is linked to failure mechanisms.