# Fragility Analysis Based on Damaged Bridges during the 2021 Flood in Germany
## 2 Materials and Methods
### Bridge Database  
The affected bridges are located in two federal states: Rhineland-Palatinate (RLP) and North Rhine-Westphalia (NRW). According to the database of federal bridges in Germany, there are about 0.045 bridges over watercourses per square kilometer in NRW and 0.040 in RLP. This encompasses nearly 1500 bridges managed by the federal road authority in NRW and approximately 800 in RLP; however, it was not possible to determine the number of locally managed ones. The presented database comprised 250 bridges, including a vast majority of locally managed structures. In addition, culverts were not included in the database. Given the mentioned spatial pattern of rainfall, just 32% of the structures were located in NRW, while the remaining 67% were located in RLP. Of these, 99 bridges (60% of the total) spanned the Ahr river. Therefore, the present analysis concentrated on this watercourse. In Figure 4, the accumulated precipitation was overlayed with the kernel density of the 250 damaged bridges. Consequently, the spatial correlation between the magnitude of the weather event and the damaged bridges was highlighted. The information on each asset was collected through a dedicated survey and integrated by incorporating additional data such as location, missing bridge features and cross-sectional elevation through 5 m and 1 m DEMs [58,59]. Then, a survey campaign took place to investigate details on failure mechanisms, collecting measurements and photographic material as per Figures 5 and 6. Specifically, two main types of failures were recognized: those due to scour and those caused by hydraulic force. In both cases, debris clogging exacerbated those phenomena. Figure 3: Debris damming in Eichenbach, tributary of the Ahr river: (**a**) lengths of carried wood logs of up to 15 m; (**b**) average diameter of carried logs (17 cm). Pictures taken by the first author. Scour is the erosion of soil from riverbed and riverbanks in the proximity of bridge foundations due to water flow. It is caused by the local hydraulic interaction between the structure and the streambed material. As scour depth increases, the lateral resistance of the soil supporting the structure diminishes, inducing foundation settling [3]. The survey campaign revealed the occurrence of different scour types in the Ahr river, including long-term riverbed degradation, local scour and contraction scour. Figure 5a shows a pit scour hole due to the 2021 flood event. The average depth of those pits is about 60 cm. A factor that contributes to the formation of these holes is soil erodibility, confirmed by the soil shrinkage at the bottom of the pit due to clay presence. These holes usually deepen and widen over time, becoming a significant concern for the bridge's structural safety. It is therefore essential to monitor the structures affected by that type of damage, preventing the scour from reaching its critical depth. This can be achieved via SHM (structural health monitoring), as innovations on the subject are increasingly applied to scour monitoring as well as during emergency management [60, 61, 62]. Figure 5b depicts the rightmost pier of the St. Nepomuk Bridge, also shown in Figure 5c, a masonry arch bridge built in the XVIII century. The bridge partially collapsed during the 2021 event due to scour in the approach fill, leaving the arch horizontal thrust unbalanced, causing its collapse. The bridge is also affected by scour on the instream piers, as seen in Figure 5b. As can be seen from this figure, the pier was built with a shallow foundation directly placed on riverbed stones. A scour depth of 70 cm was measured, although the erosion also affected the pier itself. Indeed, the aging mortar used for the bridge crushed easily under finger pressure. However, the overall scour condition of the  
Figure 4: Spatial kernel density estimation of damaged bridges (blue to red dots). The Ahr valley was the most affected area.