Sensitivity of avalanche risk to vulnerability relations

• An expanded set of vulnerability relations for RC buildings and humans inside them
• A comprehensive risk sensitivity analysis on a case study
• Risk bounds and optimal design ranges usable by engineers
• Comparison of obtained risk values with acceptable risk limits
• Return period-based zoning limits may be too optimistic.

Long-term avalanche risk assessment is of major importance in mountainous areas. Individual risk methods used for zoning and defense structure design are now gaining popularity in the effort to overcome the major drawbacks of approaches based on high return period events only. They require, for instance, precise vulnerability relations, whereas available knowledge mostly consists in coarse curves inferred from a few catastrophic events. In this paper, we first considerably expand the vulnerability curve sets in use today for reinforced concrete buildings and humans inside them. To do so, we take advantage of the results of a comprehensive reliability analysis of various building types subjected to avalanche loads, and we included humans inside buildings in our results by using different link functions. The fragility curves obtained propose refined destruction (building)/death (people) rates as a function of avalanche pressure that can be used in the risk context exactly like deterministic vulnerability curves.Second, since land use planning should be done for a reasonably large class of buildings rather than for a very precise single building type, this study shows how a comprehensive risk sensitivity to vulnerability/fragility relation analysis can be conducted. Specifically, we propose bounds and indexes for individual risk estimates and optimally designed defense structures of both theoretical (quantifying uncertainty/variability that cannot be simply expressed in a probabilistic way) and practical (minimal/maximal plausible values) aspects. This is implemented on a typical case study from the French Alps. The results show that individual risk estimates are extremely sensitive to the choice of the vulnerability/fragility relation, whereas optimal design procedures may well be more robust, in accordance with mathematical decision theory. These two outcomes are of crucial importance in practice. For example, the individual risk for buildings and people at various positions in the runout zone spreads over several orders of magnitude. For risk zoning, this suggests that the usual (tri)centennial choice may be seen as optimistic since only abscissas above the 1000-year return period are below standard risk acceptance levels with certainty according to plausible variations of human fragility. On the other hand, the optimal height of a protective dam can be more precisely determined, promoting the use of cost–benefit analyses in avalanche engineering.