Abstract
Abstract. Trajectory analysis models are increasingly used for rockfall hazard mapping. However, classical approaches only partially account for the variability of the trajectories. In this paper, a general formulation using a Taylor series expansion is proposed for the quantification of the relative importance of the different processes that explain the variability of the reflected velocity vector after bouncing. A stochastic bouncing model is obtained using a statistical analysis of a large numerical data set. Estimation is performed using hierarchical Bayesian modeling schemes. The model introduces information on the coupling of the reflected and incident velocity vectors, which satisfactorily expresses the mechanisms associated with boulder bouncing. The approach proposed is detailed in the case of the impact of a spherical boulder on a coarse soil, with special focus on the influence of soil particles' geometrical configuration near the impact point and kinematic parameters of the rock before bouncing. The results show that a first-order expansion is sufficient for the case studied and emphasize the predominant role of the local soil properties on the reflected velocity vector's variability. The proposed model is compared with classical approaches and the interest for rockfall hazard assessment of reliable stochastic bouncing models in trajectory simulations is illustrated with a simple case study.
Highlights
Trajectory simulation models classically use Digital Elevation Models that define the topography, and geographic information systems that provide information on the rockfall sources and the spatial distribution of the parameters neces-sary to calculate the bouncing of the falling rocks at each point of the study site
A generalized velocity vector V composed of a normal-to-soil-surface velocity component vy, a tangential-to-soil-surface velocity component vx – both expressed at the gravity center of the falling rock – and a rotational velocity ω properly describes the kinematic parameters of the boulder: V = vx vy Rbω t where Rb is the mean radius of the boulder
The use of large data sets from numerical impact simulations and of Bayesian modeling schemes has led to the definition of a stochastic bouncing model in the context of the impact of a spherical projectile on a coarse soil
Summary
Trajectory simulation models classically use Digital Elevation Models that define the topography, and geographic information systems that provide information on the rockfall sources and the spatial distribution of the parameters neces-sary to calculate the bouncing of the falling rocks at each point of the study site. The models classically used for bouncing calculations are based on restitution coefficients that express the dependence of the kinematic parameters of the rock after impact (reflected kinematic parameters) on the kinematic parameters of the rock before impact (incident kinematic parameters). Experimental studies have proved the complexity of simulating this dependence by means of reasonably simple mechanical models (Wu, 1985; Bozzolo and Pamini, 1986; Chau et al, 1998; Ushiro et al, 2000; Chau et al, 2002; Heidenreich, 2004). Deterministic prediction of boulder bouncing remains highly speculative because the available information on the mechanical and geometrical properties of the soil and the boulder is not sufficient. The spatial distributions of the parameters of the bouncing model integrated into the geographic information system result from a field survey which, for practical reasons, cannot be exhaustive. As for many physical processes in the field of natural hazards, it seems impossible to predict the bouncing deterministically
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