A hybrid approach to quantifying rockfall risk with limited knowledge: a case study in Aosta Valley

The quantification of rockfall risk along an infrastructure is a fundamental achievement for an appropriate management of mountain roads and it consists of various steps: from the identification of the sources and sizes of the potential unstable blocks, to the trajectory analysis and, finally, the quantification of the effects on the elements at risk. The degree of knowledge of the slope and the previous rockfall events provides a solid base for the calculation and a precise risk quantification can be obtained for areas of limited extent. On the contrary, when moving to areas of large extent the previous steps cannot be completely achieved and the risk has to be computed by considering the effects of the limited knowledge. To this aim, the paper details a procedure to include the effect of uncertainties into the quantification of the societal risk along a road. The proposed method is a hybrid quantitative approach that integrates elements of likelihood-based, fuzzy, and Bayesian methodologies. It is specifically designed for rockfall risk assessments over extensive areas under conditions of limited data availability. To address epistemic uncertainty, the method primarily involves assigning likelihoods to the frequency of blocks reaching the road, based on historical data, in order to estimate a range of potential risks and their associated probabilities. Aleatory uncertainty inherent in the phenomenon is handled using Monte Carlo probabilistic techniques. To explain the various steps in the analysis, the proposed approach is applied to a study case consisting of a 7.5 km long touristic road subjected to rockfall hazard in Aosta Valley, in the Northwestern Italian Alps, considering different possible traffic scenarios. It is shown that the method is suitable to determine the risk when the knowledge of the area is limited.