Simulation of scree‐slope dynamics: investigating the distribution of debris avalanche events in an idealized two‐dimensional model

Abstract

ABSTRACTWe present a two‐dimensional model of the development of scree slopes using the discrete‐element method. We concentrate on the dynamics of the accumulating debris at the cliff foot rather than on the failure modes of the cliff‐face or shape of the underlying rock surface. The evolution of this unconsolidated material is intermittent and systematically changing over time, with an early high disturbance regime, dominated by a characteristic event size (where 65% of particles in the debris are in motion to some extent), replaced at later times by many shallow slides interspersed with infrequent large events that involve motion through almost the full scree depth. These large slides lead to a stratigraphy in which the layers of material are stretched almost horizontal near the base of the slope. The scree surface thus shows a gradient in age with most recent rock‐fall close to the cliff and the oldest rock‐fall debris outcropping at the foot. The final surface slope tends to show little curvature, and the final mean slope is well correlated with the angle of internal friction of the particles, although the change is very small over a wide range of friction angles [final slope (in degrees relative to horizontal) ~ 0.043 × internal friction angle + 17.49, with a correlation coefficient of 0.89, p‐value 0.0001]. Some weak size‐segregation of the debris is found, but this seems to have little to do with individual particles bounding down the slope. The shape of the rock core agrees largely with the analytic forms given by Fisher–Lehmann and Bakker–Le Heux expressions, but the original simple Fisher quadratic can give the best fit. Overall the evolution shows a remarkable insensitivity to the model parameters, suggesting that the controls on dry scree‐slope evolution are primarily geometric in character. Copyright © 2014 John Wiley & Sons, Ltd.