Bayesian stochastic modeling of a spherical rock bouncing on a coarse soil

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.