The role of block shape and slenderness in the preliminary estimation of rockfall propagation

Among the wide range of variables that influence the falling process of blocks during a rockfall event, the shape of the block often plays a crucial role. Spherical-like blocks typically reach longer runout distances while elongated and plate volumes stop earlier. Nevertheless, with reference to runout modelling and hazard analyses, the shape of the block was disregarded for very long time until the last two decades when more rigorous rockfall models were developed. Nowadays fully 3D rigid body models and particle-based ones can take into account different and complex aspects related to block geometry and size (e.g. shape, change of shape, slenderness, fragmentation, etc.) when in site-specific applications are addressed. On the other hand, when the rockfall analysis is extended over large areas, simplified runout models can be used for preliminary, quick analyses, aimed at highlighting the most critical zones of the area. In this case, the variables that influence the rockfall process should be included in the analysis in equivalent terms. Among these simplified models, the Cone Method allows to reduce the runout phase to an equivalent sliding motion of the block along an inclined plane. The inclination of this plane with respect to the horizontal plane (i.e. the energy angle ) can be related to both block and slope properties of the real rockfall case. The authors of this paper developed a methodology for the estimation of the energy angle as a function of the condition of the site under analysis (characteristics of the blocks and the slope), to be used for preliminary forecasting analyses at medium-small scales. To this aim, a series of parametric analyses have been carried out to quantify the role of each variable on the energy angle. In this paper, the role of block shape and slenderness (i.e. the ratio between the height and the width of the rock block) is analysed via several propagation analyses carried out on simplified synthetic slopes by using the fully 3D RAMMS::ROCKFALL model. The results were finally statistically treated in terms of energy angles in order to take into account the variability of rockfall trajectories and provide a contribution for the estimation of the parameters within preliminary analyses based on the Cone Method.