Practical Considerations For The Application Of A Survival Probability Model For Rockfall

Abstract

Rockfall fragmentation is a common and very complex phenomenon that is still inadequately understood and rarely modelled. When falling rock blocks break upon impact, their shape and size change and the kinetic energy is distributed amongst fragments. To efficiently design mitigation measures, it is necessary to adequately account for fragmentation when modelling rockfall trajectories. To do so, a better understanding of the fragmentation process, its occurrence and its likely outcomes is needed. The authors have recently proposed a novel model which can predict the survival probability (SP) of brittle spheres upon impact from the statistical distribution of material parameters, obtained by standard quasi- static tests (Brazilian tests and unconfined compression tests). The model predicts two Weibull parameters (shape parameter -m- and scale parameter – critical kinetic energy) that are used to define the SP. The model is based on theoretically-derived (from Hertzian contact theory) conversion factors used to transform the critical work required to fail disc samples in quasi-static indirect tension into the critical kinetic energy to cause failure of spheres at impact in vertical drop tests. The objective of this paper is to provide some practical insights into this model in relation of the analysis of the Brazilian test results and the number of Brazilian tests required to achieve an acceptable prediction. A first analysis highlights the importance of distribution of forces required to break the specimens in Brazilian tests and a common statistical based outlier removal methodology was applied to reduce the experimental error associated with the operator. After eliminating the outlier data, the quality of prediction is improved and, in particular, the influence of the specimen diameter used in Brazilian compressions to derive the model input parameter is significantly reduced. This latter point implies that the size effect is adequately captured. The second analysis reveals the highest variability for batches with low number of tests and a progressive reduction as the number of sampled test increases. Based on these results, it is suggested to use at least 30 Brazilian tests and remove outliers using the simple statistical approach presented in the paper.