![]() With respect to floods and debris flows, however, vulnerability values were only given in tabular form for three classes (low, medium, high process intensity). Vulnerability functions were presented in this study for snow avalanches and rock fall processes ( Borter, 1999b). In this section, we summarise the different approaches dealing with vulnerability functions for torrent processes in chronological order.īorter (1999a) reported a comprehensive approach for risk analyses focussing mainly on gravitational mass movements in the European Alps. Fragility curves, however, generally relate the intensity of the process to the probability of exceeding certain damage states or, in the case of protection measures, states of failure ( Merz, 2006, Schultz et al., 2010). They are referred to either as vulnerability function (e.g., Fuchs et al., 2007a), vulnerability curve (e.g., Barbolini et al., 2004), damage function (e.g., FEMA, 2007) or fragility curve (e.g., Tsao et al., 2010). ![]() These functions express a mathematical relationship between the intensity of the process and the degree of loss of the elements at risk. With respect to mountain hazards, the quantification of vulnerability through the development and application of respective functional relationships has emerged within the previous two decades. Several methods to assess vulnerability have been proposed, and these assessment methods can be qualitative, semi-quantitative, or quantitative ( Fuchs et al., 2011). Vulnerability is thereby defined as the degree of loss of a given element at risk as a result from the occurrence of a natural phenomenon of a given intensity, ranging between 0 (no damage) and 1 (total loss) ( UNDRO, 1979, Fell et al., 2008). Vulnerability assessment for elements at risk (e.g., buildings located on torrent fans) is an important component in this risk-based approach ( Uzielli et al., 2008, Fuchs, 2009, Fuchs et al., 2012). The concept of risk represents a possibility to address mountain hazards and their potential consequences based on a common framework, normally referred to as risk or disaster management ( Carter, 1992, Alexander, 2000, Kienholz et al., 2004). This evolved into a risk-based approach (e.g., Kienholz et al., 2004). For decades, geohazard assessments focused on the hazard potential of mass movements and corresponding mitigation strategies ( Merz, 2006, Holub and Fuchs, 2009). The adverse effects associated with these hazards may increase due to the continued socio-economic development in some mountain regions and the possible influence of climate change on the frequency and magnitude of the hydro-geomorphic processes ( Cendrero et al., 2006, Jakob and Lambert, 2009, Keiler et al., 2010). Natural hazards, such as snow avalanches, landslides and torrent processes, pose a threat to the urban development and infrastructure in mountain areas. ![]() The method is transferable to other mountain regions if the input data needed are available. The derived vulnerability functions may be applied within the framework of risk management for mountain hazards within the European Alps. The uncertainty inherent to regression functions was quantified by the calculation of confidence bands. ![]() This comparison showed the wider applicability of the derived vulnerability functions. The final vulnerability functions were further validated with data from the Italian Alps and different vulnerability functions presented in the literature. The results suggest that there is no need to distinguish between different sediment-laden torrent processes when assessing vulnerability of residential buildings towards torrent processes. The calculation of vulnerability functions was based on a nonlinear regression approach applying cumulative distribution functions. With respect to this goal to merge different data based on different processes and building types, several statistical tests were conducted. Based on data from the Austrian Alps, we extended a vulnerability curve for residential buildings affected by fluvial sediment transport processes to other torrent processes and other building types. The vulnerability of buildings affected by torrent processes can be quantified by vulnerability functions that express a mathematical relationship between the degree of loss of individual elements at risk and the intensity of the impacting process. ![]() Vulnerability assessment for elements at risk is an important component in the framework of risk assessment. ![]()
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