Mitigation effects of trees on rockfall hazards: does rock shape matter?

Abstract

Does rock shape matter to the mitigation effects of trees on rockfall hazards? This question must be resolved in order to better quantify the protective role of mountain forests against rockfall. To probe this question, we investigate a single rock-tree interaction using non-smooth, hard-contact mechanics that allows us to consider rock shape at impact. The interaction of equant shaped rocks with cylinder-like tree stems is modeled. The equant shaped rocks are close to spherical but have a certain shape variability governed by the rock’s surface area ratio and aspect ratio. This work serves as an important follow-up study to the existing investigations from Toe et al. (Landslides 14: 1603-1614, 2017), where the effects of trees on block propagation are numerically investigated using spherical shaped rocks. The objective of our simulations is to understand how and to what extent, shape will influence energy dissipation and trajectory change. The primary results include: surface area ratio plays a more important role than aspect ratio in determining the rock’s post-impact dynamics. The primary parameters governing the rock kinematics after impact (i.e., block’s energy reduction, reflected rotational speed, and trajectory change) are impact velocity, impact eccentricity, and the tree stem diameter. The latter observation aligns well with previous findings and suggests that the shape factors, at least for nearly spherical rocks, can be integrated into the current block propagation models. However, from a statistical viewpoint, the anisotropic distribution of mass and hence the asymmetric moment of inertia of non-spherical rocks leads to stronger or weaker spin effects compared to mass- and volume-equivalent spheres. Apparently, the rotational motion of an irregular object serves as a kinetic energy reservoir leading to subsequent rock-tree impacts, and therefore significant differences in energy loss and trajectory in comparison to spherical shaped rocks. This effect must be further investigated using elongated and flattened blocks and underscores the importance of measuring rockfall rotation in experimental investigations.