Rock-shape and its role in rockfall dynamics

Abstract

Rockfall threaten infrastructure and people throughout the world. Estimating the runout dynamics of rockfall is commonly performed using models, providing fundamental data for hazard management and mitigation design. Modelling rockfall is made challenging by the complexity of rock-ground impacts. Much research has focused on empirical impact laws that bundle the rock-ground impact into a single parameter, but this approach fails to capture characteristics associated with the impact configuration and, in particular, the effects of rock-shape. While it is apparent that particular geological settings produce characteristic rock-shapes, and that different rock-shapes may produce characteristic runout dynamics, these aspects of rockfall are poorly understood.

This study has focused on investigating the mechanics behind the notion that different rock-shapes produce characteristic runout dynamics and trajectories. The study combines field data on rockfall runout, trajectory and dynamics, laboratory analogue testing in controlled conditions, and numerical modelling of the influence of rock-shape. Initially rock-shape, deposition patterns and rockfall dynamics were documented at rockfall sites in Switzerland and New Zealand. This informed a detailed study of individual rock-ground impacts on planar slopes in which laboratory-scale and numerical rockfall experiments were combined to isolate the role of rock-shape on runout. Innovatively, the physical experiments captured the dynamics of impacts and runout paths using high speed video tracking and a sensor bundle with accelerometers and gyroscopes. Numerical experiments were performed using a 3-D rigid-body rockfall model that considers rock-shape, and has allowed the variability of rockfall behaviour to be explored beyond the limitations of physical experimentation.

The main findings of the study were on understanding rockfall-ground impacts, the influence of rock-shape on rockfall dynamics, and influence of rock sphericity. By measuring velocity, rotational speed, impact and runout character, it has been possible to quantify the variability of individual rock-ground impacts as a function of rock-shape. Investigation of single rebounds reveals that if classical restitution coefficients are applied, values greater than unity are common and rebounds are highly variable regardless of constant contact parameters. It is shown that this variability is rooted in the inherent differences in the magnitudes of the principal moment of inertia of a rock body brought about by rock-shape. Any departure from a perfect sphere induces increased range and variability in rock-ground rebound characteristics. In addition to the popular description of a rock bouncing down slope, rebounds involve the pinning of an exterior edge point on the rock, creating a moment arm which effectively levers the rock into ballistic trajectory as it rotates. Observations reveal that the angle of the impact configuration plays a key role in the resulting rebound, whereby low angles produce highly arched rebounds, while large impact angles produce low flat rebounds. The type of rebound produced has a strong bearing on the mobility of the rocks and their ability to maintain motion over a long runout. The mobility of rocks is also shown to be related to rotation, which is governed by the differences in the principal inertial axes as a function of rock-shape. Angular velocity measurements about each principal inertial axis indicate that rocks have a tendency to seek rotation about the axis of largest inertia, as the most stable state. Rotations about intermediate and small axes of inertia and transitions between rotational axes are shown to be unstable and responsible for the dispersive nature of runout trajectories, which are inherent characteristics of different rock-shapes.

The findings of this research demonstrate the importance of rock-shape in rockfall runout dynamics and illustrate how it is essential that the rock-shape is included in rockfall modelling approaches if the variability of rockfall behaviour is to be simulated.