# Fragility Analysis Based on Damaged Bridges during the 2021 Flood in Germany
## 4 Discussion  
Damage reports used in this research were retrieved from local authorities, bridge condition inspections and integrated surveys in the aftermath of the 2021 flood in Germany. The intensity measure, called \(h^{**}\), was chosen based on available data as the ratio between the water stage upstream bridges and the deck elevation. Nevertheless, existing literature demonstrated the relevance of geomorphologic indicators on the bridge collapse probability, suggesting that the failure mechanism can be significatively influenced by the location and hydraulic conditions of the stream [28]. In the present work, the aggregated geomorphologic indicator used in Germany to rank rivers was tested for usage [52], but no correlation was found with the selected intensity measure. This can be attributed to the aggregation level of sub-indicators in the aforementioned metric. Therefore, the explained variance was too low to proceed further. Concerning the hydraulic model, the flood event was reconstructed by [PERSON] et al., [42] for the Ahr river (Germany) by using a 2D model calibrated on the hydrograph from LFU [52]. The damage levels were chosen based on the semantic description of the DIN 1076 bridge condition ratings [68] and the ranking method used in empirical fragility models [27; 28]. However, for the collapse event (DIN1076 rating = 4.0), the damage was classified as extensive, as opposed to HAZUS, where a collapse is represented as a complete damage [27]. This discrepancy was highlighted in Section 2.2 and is due to the classification used in the DIN1076, as within the 3.5-4.0 interval, structural, traffic and durability safety are ranked as extensively compromised. The generation of fragility curves was developed according to the FEMA P-58 method and was adapted to floods [36]. To assess the goodness of fit and manage the outliers, we employed [PERSON] test and [PERSON]'s criterion, respectively. The failures were grouped by the triggering failure mechanisms; either scour- or hydrodynamic-related force. Although the influence of clogged debris has been pointed out, it was not possible to estimate this factor due to a lack of data. Then, bridges were clustered by observing trends between failure mechanisms and the deck material, separating lightweight structures from heavier ones. Then, bridges were also categorized based on their structural topology, distinguishing beam decks from arches. The results suggested that beam bridges subjected to water overtopping experienced a higher probability of failure compared to arches, although another internal subdivision among beam bridges had to be made. Indeed, lightweight beam decks exhibited even higher vulnerability to hydraulic force compared to heavier ones. However, beam bridges tended to have a lower occurrence of damage type than arches, due to their lower blockage to the flow. Nevertheless, the real failures demonstrated that arch bridges are not likely to collapse under high hydraulic force, often reporting slight to moderate damage. It should also be pointed out that there is a disagreement among studies concerning the magnitude of hydraulic uplift on arch bridges. In order to shed light on this point, a shift towards a probabilistic approach to account for hydrodynamic actions on decks is encouraged. To this end, [PERSON] et al. [80] presented a novel methodology to compute fragility curves caused by hydraulic force and driftwood actions for varying discharges. When scour was considered the triggering mechanism, beam bridges usually collapsed, while arches reported a more robust behavior, showing moderate damage. However, beam bridges experienced lower scour-induced damage rates compared to arches. Concerning existing codes, currently, the Eurocode 1 includes a specific limit state for horizontal water thrust on decks but only during bridge construction [81]. For the in-service bridge portfolio, the safety margin is represented by a given clearance on top of the 100- or 200-year flood level.