Theory and calibration of the Pierre 2 stochastic rock fall dynamics simulation program

Abstract

The use of computer models to determine rock fall hazards is increasingly common, with increasingly complex models being developed. In most practical applications, slopes potentially affected by rock falls are characterized in general terms only, thus a simpler model is desirable to reduce the parameter uncertainty. The model presented here utilizes a lumped-mass representation of the rocks. Key features are the stochastic roughness angle to represent contact geometry variability, hyperbolic restitution factors, and a stochastic shape factor, which have been developed considering impact mechanics theory. Together, these features can yield realistic results for linear and angular velocity, bounce height, runout distance, and normal restitution factors greater than one while still being easy to calibrate. The model calibration has been carried out using detailed, full-scale experiments from a talus slope in France, a hard rock quarry in Austria, and a weak bedrock and talus slope in Japan. An observed rock fall event in British Columbia was modeled as a pseudoforward analysis to demonstrate the model validity. The usefulness of the model as a design tool has been demonstrated by using the simulation results as inputs for a hypothetical barrier design application, and calculating the reliability of the design values.