A Probabilistic Theoretical Framework to Consistently Assess Rockfall Hazard

Arthur F. Rossignol (), Rémy Martin (), Maddalena Marchelli (), Didier Hantz (), Nicolas Eckert () and Franck Bourrier ()
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Arthur F. Rossignol: AgroParisTech, X - École polytechnique - IP Paris - Institut Polytechnique de Paris
Rémy Martin: ONF-RTM - Agence RTM Alpes du Nord - ONF - Office National des Forêts
Maddalena Marchelli: Polito - Politecnico di Torino = Polytechnic of Turin
Didier Hantz: ISTerre - Institut des Sciences de la Terre - IRD - Institut de Recherche pour le Développement - INSU - CNRS - Institut national des sciences de l'Univers - USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc - CNRS - Centre National de la Recherche Scientifique - Université Gustave Eiffel - Fédération OSUG - Observatoire des Sciences de l'Univers de Grenoble - UGA - Université Grenoble Alpes
Nicolas Eckert: IGE - Institut des Géosciences de l’Environnement - IRD - Institut de Recherche pour le Développement - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Fédération OSUG - Observatoire des Sciences de l'Univers de Grenoble - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes
Franck Bourrier: IGE - Institut des Géosciences de l’Environnement - IRD - Institut de Recherche pour le Développement - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Fédération OSUG - Observatoire des Sciences de l'Univers de Grenoble - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes

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Abstract: Rockfalls constitute a major challenge in mountainous territories, as they might seriously jeopardize both human life and infrastructure. Consequently, the quantitative assessment of rockfall hazard has become an effective tool for informing stakeholders and allowing for appropriate risk management and mitigation. Various quantitative methods have been developed to date, but they often differ in their underlying hypotheses and models for the stochastic processes that govern rockfall phenomena. Some methods, however, introduce approximations to simplify formulations, and this can affect the accuracy of hazard quantification. In this article, we present a probabilistic theoretical framework to consistently assess rockfall hazard, by means of a reach-probability field over a given time period. Building upon previous works and leveraging results from probability theory, we derive a general formula for the reach probability that accommodates multiple heterogeneous rockfall sources and their associated volumes. This approach is predicated on theoretical assumptions regarding the rockfall occurrence over time and the propagation of blocks over space, as well as the uncertainty about the block volumes released from each rockfall source. Through the completeness of the hazard assessment in terms of uncertainties accounted for, our methodology supports both classical source representations (localized and diffuse) and aims to provide a practical tool for operational purposes. The framework is especially well suited for carrying out hazard modeling based on block-trajectory simulations over gridded spatial terrains, and we demonstrate its practical utility through a synthetic and a real case study. Finally, we discuss various aspects of the methodology, covering its advantages and limitations, within the broader context of rockfall hazard modeling.

Keywords: Rockfall; Quantitative hazard assessment; Reach probability; Propagation probability; Departure probability; Rock-trajectory simulation (search for similar items in EconPapers)
Date: 2026-11-08
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