Dr Davide Guccione

Rockfall is a natural hazard that needs to be rigorously managed along all the major road and railways transport networks by identifying the most appropriate mitigation measures. There has been significant progress in rockfall modelling and rockfall protection systems in recent years but there remains one aspect that is not very well understood and quite challenging to account for in the design of rockfall protection structures, namely the fragmentation of falling blocks upon impact. Rocks often break up upon impact, which leads to a change in size, shape and energy of falling blocks, parameters that affect the design of the protective structures. Before being able to incorporate fragmentation into predictive trajectory models, it is required to better understand the fragmentation process and its likely outcome (number, volume of fragments and their trajectories). To that aim, an innovative experimental setup was developed at the University of Newcastle (Australia) to study rock fragmentation upon impact. The setup was designed to perform controlled vertical drop tests and record the following impact parameters: impact force, impulse, impact duration, velocities (of the block before impact and its fragment after impact) and all components of energy, pre and post impact. Six views (four high-speed cameras and two mirrors) are used for an accurate reconstruction of the 3D trajectory of blocks and fragments, in translation and rotation. This paper presents the validation of the setup via two series of drop tests using mortar spheres. Attention was focused on the evaluation of impact force and impulse from load cells placed under the impacted surface, tracking of translational and rotational velocity and the computation of total kinetic energy (before and after impact) and all components of energy dissipation. The results confirm that the experimental setup and the approach developed can be used to obtain impact force, impulse and to compute the energy balance during the impact and fragmentation and conduct advanced fragmentation testing.

Fragmentation of rocks upon impact during rockfall is a phenomenon that is poorly understood, scarcely researched and difficult to predict. However, to adequately predict the outcomes of rockfall events, it is essential to know whether a given block is likely to fragment given the impact conditions and what will be the outcome of the fragmentation process; that is, the number, size and trajectory of fragments. To date, there is no model or data that can be used to fully answer these questions. This paper presents the first theoretical model that can predict the fragmentation survival probability of brittle spherical blocks upon dynamic impact (i.e. drop tests) from the statistical distribution of material properties, determined from a range of standard quasi-static tests. Considering that survival probabilities tend to follow a Weibull distribution, the model focuses on predicting the two Weibull parameters, commonly known as the shape parameter (m) and the scale parameter (here, the critical kinetic energy). The model is based on theoretically-derived conversion factors used to turn 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 drop tests. The mechanistic conversion factors specifically account for the shape and size of the specimens tested and the increase of strength under dynamic loading (strain rate effect). Three series of drop tests were conducted (on spheres of three different diameters) and complemented by extensive material characterisation testing in order to validate the novel predictive model. The variability of material properties was characterised, and it was found that the material strength found by the characterisation tests generally follows a Weibull form, but the survival probability distribution of the drop tests seems to be linear. The predicted conversion factors were first compared against their experimental counterparts before validating the prediction of survival probability of the spheres upon dynamic impact (in drop tests). It was found that it is possible to predict the survival probability of artificial rock of three different diameters (50 mm, 75 mm, 100 mm) and two different strengths upon impact solely from the statistical information coming from Brazilian tests and with an average relative error of less than 9%.