Abstract

Rockfall fragmentation is a very complex phenomenon that is still poorly understood and modelled. Being able to adequately model fragmentation of impacting blocks, including change of shape, size, and energy after breakage, is essential to be able to predict realistic trajectories and design effective mitigation measures. In order to develop an accurate predictive model for rockfall fragmentation, it is necessary to better understand the fragmentation process and its likely outcomes. A novel model was recently proposed by the authors 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 survival probability is described as a Weibull function whose two parameters (shape parameter -m- and scale parameter - critical kinetic energy) are predicted by the model. 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. This paper presents a sensitivity analysis on the parameters which influence the prediction of the critical kinetic energy.

Introduction

Rockfall research has made considerable progress since the early 1980s, particularly in terms of design of protection structures and of rockfall trajectory modelling. The latter is a key step in the design of rockfall protection measurements and hazard assessment, as it provides information on possible block trajectories and impact energy. After a rockfall event, fragmentation of rock blocks is often observed [1]. Rock fragmentation upon impact is a still poorly understood aspect of rockfall and it is not accurately modeled because the current state of knowledge on the topic is deficient. Undoubtedly, it is a complex phenomenon which can be influenced by many factors such as rock strength, block shape, presence and properties of discontinuities, stiffness of the ground and impact conditions [5]. In recent years, Corominas and co-workers significantly contributed to modelling fragmentation in rockfall engineering with two fragmentation models. The first one is a "Rockfall Fractal Fragmentation Method" (RFFM) [8] to obtain the rockfall block size distribution (RBSD) from in situ block size distribution (IBSD). The second model is a GIS-based software, called RockGIS, that can stochastically simulate fragmentation [11]-[12]. Although this model represents a significant progress in fragmentation modeling, it relies on several assumptions and, in particular, a survival probability of the rock block upon impact must be assumed between 0 and 1 allowing a percentage of blocks to survive despite having reached a certain breakage energy threshold. As far as the authors know, there is scant experimental data about survival probability at impact, its relation to impact energy and to material properties. The authors [13] have recently proposed a model to predict the survival probability (SP) of brittle spheres upon impact from the statistical distribution of material parameters obtained by quasi-static Brazilian tests. This paper briefly recalls the model and presents a sensitivity analysis, in order to assess the effect that parameter uncertainty may have on the prediction of the survival probability.

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