# Fragility Analysis Based on Damaged Bridges during the 2021 Flood in Germany
## 3 Results  
The data were clustered in two different ways: based on the deck building material and based on the typology. For the first cluster, lightweight structures, such as those made of steel and wood, were separated from heavier structures, typically built with concrete or masonry. Wood and steel decks were considered together as evidence indicating similar failure modes (i.e., deck dragging and uplift). Then, by using the same principle, concrete and masonry bridges were also considered together. Therefore, the term \"lightweight\" (LWY) structures was used to indicate steel and wooden decks, and \"heavy\" (HVY) structures represented those built with masonry and concrete. The nomenclature was kept in Figures 11 and 12. Concerning the failure mechanisms, scour typologies were grouped into a single mechanism, in accordance with Figure 5, with the purpose of separating those from the mechanisms caused by hydrodynamic dragging and uplift (i.e., hydraulic force), as seen in Figure 6.  
The chart in Figure 11 shows the probability severe damage in both lightweight and heavy decks for the two failure modes. Scoured bridges exhibited higher probabilities of being damaged in both lightweight and heavy decks, compared to the hydraulic force failure mode. Nevertheless, the behavior was similar for both damage mechanisms when the deck was not overtopped (\(h^{**}<1\)). This confirmed that such damage was not influenced by the deck material but by other factors associated with different failure mechanisms, such as the scouring of instream piles. For \(h^{**}>1\), there were differences among lightweight and heavy decks under scour, but these were still minor when uncertainties were included (i.e., 5% and 95% confidence intervals) and are not represented in Figure 11 for the sake of clarity but are shown together with the velocity as IM in Figure 10.  
Figure 10: Confidence intervals for the moderate and severe damage states. Velocity data considering only arch bridges. The 95% confidence intervals are highlighted together with the mean value of the fitted distribution. Indeed, when the confidence bands (5-95%) are included, the biggest difference between scour and hydrodynamic mechanisms was observed for heavy decks in the overtopping interval (\(h^{**}>1\)). Thus, heavy decks had less probability of being severely damaged at high water stages compared to when scour occurred. The same also happened for lightweight decks, but the curves overlap when considering the confidence bands. Differences also existed when damage caused by high water stages were considered. As  
Figure 11: Fragility curves for severely damaged heavy (HVY) and lightweight (LWY) bridge decks under scour and hydraulic force (Hydr.) scenarios. Figure 12: Fragility curves for heavy bridges (HVY) under scour and hydraulic force (Hydr.) scenarios accounting for all the damage levels. expected, lightweight decks exhibited greater probabilities of being severely damaged compared to the heavier ones. When slight and moderate damage levels were considered, there were only heavy decks, as seen in Figure 12. Hence, lightweight structures exhibited only severe damage, as they were less robust to hydraulic force. Consequently, Figure 12 shows sequential damage states for heavy decks only, subjected to the same failure mechanisms. As expected, the behavior for heavy decks under scour was more severe than that under the hydraulic force damage mechanism. At low water stages, slight damage was more likely to occur. The damage level was also a function of debris carried by the flow, but the lack of data did not allow us to assess the impact of this factor on the fragility model. Another result concerned the lack of slight damage under scour events. This confirmed that erosion is a moderate to severe problem for heavy decks.