# Fragility Analysis Based on Damaged Bridges during the 2021 Flood in Germany
## 3 Results
An important aspect is that when these bridges are overtopped (\(h^{**}=1\)), there is an 80% probability of observing a moderate to severe damage in case of scour, while the probability reduces to 36% in cases of water thrust, as a damage mechanism is triggered. Considering damage levels, the probability that scour caused a moderate damage is 33% (hydrodynamic loads is therefore 67%), while for a severe damage the probability rises to 78%, leaving hydrodynamic loads with a probability of causing the remaining 22% of occurrences. For the second cluster, beam structures, including trusses and box-girders, were separated from arch bridges. Figures 13 and 14 present the results for beam and arch bridges, respectively. By looking at Figure 13, it is shown that among beam bridges, moderate damage is missing. Then, combining the fragilities for bridge material and typology, it was identified that the moderate damage for heavy decks in Figure 12 only occurs in arch bridges. A common feature among the results is the severity of the scour mechanism, which led to higher damage probabilities for a given \(h^{**}\). Figure 13: Fragility curves for beam bridges under scour and hydraulic force (Hydr.) mechanisms. Another observation concerns the absence of arch failures due to hydraulic force mechanism, as per Figure 14. Then, the severe damage caused by hydraulic force in Figure 12 is attributable to beam bridges. This opens up a major issue on whether arch bridges do experience collapse due to water thrust, and which hydraulic force component (drag or uplift) causes the most damage. While for the dragging action there is agreement among studies and data, concerning the uplift component, the studies by [PERSON] et al. [74] and [PERSON], [PERSON] [75] are in disagreement with those of [PERSON] [76], [PERSON] et al., [77], [PERSON] et al., [57] and [PERSON] [78]. Indeed, [PERSON] et al. and [PERSON], [PERSON] and [PERSON] suggested a positive uplift mechanism for the arch, called upthrust, while flume experiments on hydrodynamic forces on bridge decks from the other authors reported negative uplift coefficients for most of the submergence ratios encountered in floods. However, the dynamic effect is mitigated by the Archimedes' thrust, which may eventually become predominant at higher submergence ratios, because of less negative dynamic uplift at higher water stages. The collected evidence from the bridges damaged in the 2021 flood in Germany are compatible with a positive drag and a negative uplift, as none of the arch bridges exhibited the failure mechanism described in [PERSON] et al. but instead suffered damage due to the combined effect of wood clogging and drag force. In this regard, the main problem is the high blockage of an arch against the flow, resulting in considerable drag, contributing to the removal of backfill and leaving the arch itself standing against the flow [79]. In addition, the impact of hydraulic force against the intrados often causes slight damage, i.e., masonry and mortar detachments, exposed rebars and parapets, among others. This phenomenon is shown in Figure 14, where slight damage occurred in partially submerged arch bridges, \(h^{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text{\text{\text{\  
Nevertheless, beam bridges tend to suffer less damage from hydraulic force, due to their lower blockages against the flow. Regarding scour, it was observed that arch bridges suffered moderate and severe damage, while beam decks only experienced the latter. However, in terms of more severe damage, scour in arch bridges is more serious than in beam decks, as the damage probability rapidly increases once the bridge is overtopped. One can therefore conclude that arch bridges are more prone to scour and debris clogging, although their structural behavior is more robust than beam bridges, which is confirmed by the presence of a moderate damage level.