Pierre3D: a 3D stochastic rockfall simulator based on random ground roughness and hyperbolic restitution factors

Abstract

The use of dynamic computational methods has become indispensable for addressing problems related to rockfall hazard. Although a number of models with various degrees of complexity are available, model parameters are rarely calibrated against observations from rockfall experiments. A major difficulty lies in reproducing the apparent randomness of the impact process related to both ground and block irregularities. Calibration of rigorous methods capable of explicitly modeling trajectories and impact physics of irregular blocks is difficult, as parameter spaces become too vast and the quality of model input and observation data are insufficient. The model presented here returns to the simple “lumped-mass” approach and simulates the characteristic randomness of rockfall impact as a stochastic process. Despite similarities to existing approaches, the model presented here incorporates several novel concepts: (i) ground roughness and particle roughness are represented as a random change of slope angle at impact; (ii) lateral deviations of rebound direction from the trajectory plane at impact are similarly accounted for by perturbing the ground orientation laterally, thus inducing scatter of run-out directions; and (iii) a hyperbolic relationship connects restitution factors to impact deformation energy. With these features, the model is capable of realistically accounting for the influence of particle mass on dynamic behaviour. The model only requires four input parameters, rendering it flexible for calibration against observed datasets. In this study, we calibrate the model against observations from the rockfall test site at Vaujany in France. The model is able to reproduce observed distributions of velocity, jump heights, and runout at observation points. In addition, the spatial distribution of the trajectories and landing points has been successfully simulated. Different parameter sets have been used for different ground materials such as an avalanche channel, a forest road, and a talus cone. Further calibration of the new model against a range of field datasets is essential. This study is part of an extensive calibration program that is still in progress at this first presentation of the method, and focuses on fine-tuning the details of the stochastic process implemented both in two-dimensional (2D) and three-dimensional (3D) versions of the model.