A framework to account for structural damage, functional efficiency and reparation costs within the optimal design of countermeasures: Application to snow avalanche risk mitigation

In mountain areas, long-term snow avalanche risk evaluation is of paramount importance for land use planning. In avalanche-prone areas, when real estate demand is high, for instance, building protective structures may be a sensible choice for reaching a compromise between safety and development. Specifically, minimizing the risk within a quantitative framework can provide optimal defense structure configurations (size, localization, construction technology, etc.). However, existing approaches based on a proper theoretical decision-making framework still suffer from limitations making them hardly usable in practice. It is herein proposed to account for the physical, functional, and monetary dimensions of a protective measure within the assessment of total risk. Total risk, which is calculated as the mean expected loss, is quantified within a four-state system in which the failure of the dam and the failure of the dwellings to be protected are assessed with specific vulnerability relations. Bounds for the risk and subsequent optimal dam design values are quantified using minimum and maximum (min/max) functional efficiency relations of the dam. Additional assumptions regarding the functional-structural efficiency relation allow for the optimal design and corresponding minimum risk to be reached. An application is proposed with a case study from the French Alps. A comprehensive parametric study shows that the min/max bounds risk quantification is worth implementing in some cases, such as, for instance: if there is a high uncertainty of the functional efficiency of the dam, of if the assets to be protected have a monetary value. However, when the failure of the dam is unlikely to occur (due to its location or to its material resistance), it is shown that quantification of the intermediate risk without the min/max bounds approach is sufficient. In the future, the framework could be extended to many other mountain hazards (debris flows, landslides, etc.), more complex elements at risk, and even to problems going beyond the sole question of land-use planning such as traffic road regulation.