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The spatial and temporal quantification of rockfall frequency remains a major challenge in mountain environments, especially also in terms of rockfall management. Approaches that have been used traditionally to quantify rockfall frequency include historical records, remote sensing, or in situ monitoring, but have been shown repeatedly to suffer from a lack of completeness or to rely on rather short time series (of a few years) that are, in addition, limited to small areas. As such, they normally cannot meet the stringent requirements of hazard and risk analyses. Here, we propose a new procedure coupling field analysis of rockfall deposits in mitigation structures and growth disturbances in tree-ring series with three-dimensional (3D), process-based rockfall modeling to estimate rockfall frequencies for individual cliff compartments. This procedure has been tested on a slope in the Swiss Alps (La Fory, Sembrancher VS), where rockfall triggered from a 38 hm $$^{2}$$ cliff to threaten a 1-km-long section of the road to the Grand St. Bernard tunnel and the local railway line. Based on 84 rockfall deposits retrieved from 420-m-long protection barrier and growth disturbances in trees over the 1994–2017 period, we estimate rockfall hazard to between 0.043 and 0.348 events yr $$^{-1}$$ at various locations on the slope. In total, we used 68,680,000 rockfall simulations to translate hazard values into rockfall frequencies at the cliff level. Converging release frequencies between tree-ring analyses (0.99–1.35 events yr $$^{-1}$$ hm $$^{-2}$$ ) and values obtained from deposits in the protection barrier (0.82 events yr $$^{-1}$$ hm $$^{-2}$$ ) confirm the reliability of our procedure. Despite remaining limitations, our approach enables precise quantification of rockfall release frequency in a holistic and reproducible manner both in space (a few hm $$^{2}$$ ) and time (several decades), and thus yields the data needed for hazard and risk mapping. We therefore recommend, where applicable, to include this procedure in future rockfall management strategies.

International audience; Rockfall propagation models are routinely used for the quantitative assessment of rockfall hazard. Their capacities and limitations remain difficult to assess due to the limited amount of exhaustive experimental data at the slope scale. This article presents experiments of block propagation performedin a quarry located in Authume (France). This study site was chosen for its complexity, related with the presence of topographical discontinuities and ofconfigurations promoting block rolling. A total of more than one hundred blocks were released on two propagation paths. The propagation of the blockswas assessed by measuring the block stopping points as well as their kinematics at specific locations of the paths, called evaluation screens. Significant variability of the stopping points and of the block kinematics at the evaluation screens was observed and preferential transit and deposit zones were highlighted. The analysis of the results showed predominant effect of topography, in particular that related to topographical discontinuities. Significant influence of local and small scale parameters (e.g. block orientation, local topography) was also highlighted. These conclusions are of particular interest for researchers or practitioners who would like to assess the relevance of propagation modelling tools considering this complex study site. In this configuration, the quality of block propagation simulations should notably rely on the accuracy of digital terrain models, and on the integration of local conditions effects using physically based approaches.

The paper presents a new approach to assess the effecctiveness of rockfall protection barriers, accounting for the wide variety of impact conditions observed on natural sites. This approach makes use of meta-models, considering a widely used rockfall barrier type and was developed from on FE simulation results. Six input parameters relevant to the block impact conditions have been considered. Two meta-models were developed concerning the barrier capability either of stopping the block or in reducing its kinetic energy. The outcome of the parameters range on the meta-model accuracy has been also investigated. The results of the study reveal that the meta-models are effective in reproducing with accuracy the response of the barrier to any impact conditions, providing a formidable tool to support the design of these structures. Furthermore, allowing to accommodate the effects of the impact conditions on the prediction of the block–barrier interaction, the approach can be successfully used in combination with rockfall trajectory simulation tools to improve rockfall quantitative hazard assessment and optimise rockfall mitigation strategies.

International audience; The objective of this research was to use numerical models based on mechanical approaches to improve the integration of the protective role of forests against rockfall into block propagation models. A model based on the Discrete Element Method (DEM) was developed to take into account the complex mechanical processes involved during the impact of a block on a tree. This modelling approach requires the definition of many input parameters and cannot be directly integrated into block propagation models. A global sensitivity analysis identified the leading parameters of the block kinematics after impact (i.e. block energy reduction, trajectory changes and rotational velocity): the impact velocity, the tree diameter and the impact point horizontal location (i.e. eccentricity). Comparisons with the previous experimental and numerical studies of block impacts on trees demonstrated the applicability of the DEM model and showed some of the limitations of earlier approaches. Our sensitivity analysis highlights the significant influence of the impact velocity on the reduction of the block's kinetic energy. Previous approaches usually also focus on parameters such as impact height, impact vertical incidence and tree species, whose importance is only minor according to the present results. This suggests that the integration of forest effects into block propagation models could be both improved and simplified. The DEM model can also be used as an alternative to classical approaches for the integration of forest effects by directly coupling it with block propagation models. This direct coupling only requires the additional definition of the location and the diameter of each tree. Indeed, the input parameters related to the mechanical properties of the stem and the block/stem interaction in the DEM model can be set to average values because they are not leading parameters. The other input parameters are already defined or calculated in the block propagation model.