# Fragility Analysis Based on Damaged Bridges during the 2021 Flood in Germany
## 1 Introduction  
Several studies have reported floods as the main causes of bridge failures worldwide [1, 2, 3]. In addition, human-induced catchment modifications masked climate change, resulting in further difficulties predicting flood scenarios [4, 5, 6]. Although catastrophic floods often trigger risk-aversion behaviors by implementing virtuous management strategies [7], the same comes at a high societal and economical cost [8]. It is estimated that more than 120 million people worldwide are affected by floods each year, making it the most threatening natural hazard [9]. The vulnerability of society to floods highly depends on coping capacity, which is tightly linked to wealth indicators. Worldwide flood vulnerability research highlights that at the present climate change rate, inequalities among low and high-income countries will increase [10]. Concerning the European context, data from RisklayerCATDAT reported that climate-related events are responsible for 80% of economic losses among those caused by natural hazards in Europe [11]. The highest economic damage per square kilometer occurred in Switzerland (\(\sim\)400 k EUR/km\({}^{2}\)) and Germany and Italy (\(\sim\)300 k EUR/km\({}^{2}\)). Of these, Germany and Switzerland had 37% of losses covered by insurance companies, while Italy had only 6%. Delegating the economic risk to insurance companies can be cost-effective for a faster recovery [12]. It is therefore of paramount importance to assess the economic risk of infrastructure facing extreme events [13]. Of these assets, bridges represent one of the most vulnerable elements [14]. Recently, failure scenarios were studied and systematized for small bridges in case of extreme events such as floods [15]. However, the performance of bridges against varying flooding scenarios is usually unknown, as the design is typically carried out on a deterministic basis [16]. On the contrary, fragility curves link the expected damage to a range of hazard intensities [17]. Subsequently, thanks to damage-loss equations, the financial aspect can be associated with the hazard intensity [18]. Therefore, fragility curves represent a milestone to financial risk assessment of structures [19; 20; 21]. The existing literature covers flood fragility curves for bridges mainly through analytical approaches and often in combination with earthquake hazards [22; 23; 24]. Nevertheless, empirical fragilities are limited to hurricane events due to the considerable number of damaged bridges and respective financial losses, motivating the interest of stakeholders [25; 26]. Indeed, empirical studies concerning flood fragility curves focused on hurricane events [27; 28; 29; 30; 31]. To the authors best knowledge, flood fragility curves based on actual failures are not available for riverine bridges in mainland Europe. The need for empirical relationships is motivated through a learning process built upon evidence of damaged bridges. In addition, the results can be used to validate existing analytical models. Bridge owner records and post-disaster surveys improve the quality of available data, while a flood with hundreds of damaged structures ensures statistical quality [32]. The database of damaged bridges is thereby discretized in order to search for correlations between bridge features and the damage level. Nevertheless, reducing bridge collapse rates is a challenge for practitioners, as causes and mechanisms have specific features linked to each structure and its location [33]. Significantly, statistical techniques on a collapsed portfolio of bridges indicated that age, design enhancement and maintenance practices failed to reduce collapse rates against floods [34]. Therefore, further research is still needed on bridge failure mechanisms, including overlooked phenomena such as hydraulic force and driftwood clogging scenarios. The gap extends also to the fragility analysis, as flood received less attention in comparison to seismic hazards due to the complex dimension of implicated variables [35].