Associate Professor Klaus Thoeni

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%.

This paper presents a new methodology for estimating the expected energies and first impact distances at the base of a rock cliff, subject to the geometry and properties of the cliff and the representative block being known. The method is based on a sensitivity analysis, conducted by means of kinematic simulations and carried out for a large range of input parameters and their combinations, taking into account the uncertainty associated with their estimate. The proposed approach is validated by comparing predictions to experimental data and shows great potential for a quick qualitative hazard assessment.

This paper investigates the factors affecting the shear strength of granular materials by means of the tilt box test. The test involves the titling of a specifically designed split-box and measuring the angle at which the upper half of the box slides off. This angle can be interpreted as the peak friction angle of the sample for a low stress state. Experimental tests and numerical analyses using the Discrete Element Method (DEM) are carried out and compared. The study is carried out for two different materials, a rounded and an angular aggregate. It is shown that rolling resistance is needed to match the experimental results if only spheres are used but this is not the case for non-spherical particles. © 2015 Taylor & Francis Group, London.

This work consists of a preliminary numerical study on the impact behaviour of rock blocks on muckpiles using the Discrete Element Method (DEM). A contact law using a linear hysteresis model for normal contacts and a Mohr-Coulomb model for tangential contacts is used. In addition, two dissipative laws are introduced consisting of a moment transfer law and normal viscous damping law. One of the aims of this study is to investigate if the contact law enables a realistic modelling of the rebound characteristics of a block during impact on a muckpile. A parametric study is carried out in order to investigate the influence of the constitutive model parameters and the presence of clumps. Numerical predictions are compared to experimental results. It is shown that clumps in the muckpile are essential to reproduce realistic results. © 2015 Taylor & Francis Group, London.

This paper presents a discrete modelling approach which allows the simulation of rockfalls behind drapery systems. The falling rock is represented by a rigid assembly of spheres whereas the slope is represented by triangular elements. Energy dissipation during impact on the slope is considered via friction and viscous damping. The drapery is represented by a set of spherical particles which interact remotely. The numerical model is used to investigate the efficiency of a drapery system. Various simulations with two different block sizes are performed and the numerical predictions of simulations with drapery are compared to simulations without drapery in order to assess the performance of the protection system.