ORIGINAL PAPER Empirical Model for Predicting Rockfall Trajectory Direction Pavlos Asteriou 1 • George Tsiambaos 1 Received: 19 February 2015 / Accepted: 16 July 2015 Ó Springer-Verlag Wien 2015 Abstract A methodology for the experimental investi- gation of rockfall in three-dimensional space is presented in this paper, aiming to assist on-going research of the complexity of a block’s response to impact during a rockfall. An extended laboratory investigation was con- ducted, consisting of 590 tests with cubical and spherical blocks made of an artificial material. The effects of shape, slope angle and the deviation of the post-impact trajectory are examined as a function of the pre-impact trajectory direction. Additionally, an empirical model is proposed that estimates the deviation of the post-impact trajectory as a function of the pre-impact trajectory with respect to the slope surface and the slope angle. This empirical model is validated by 192 small-scale field tests, which are also presented in this paper. Some important aspects of the three-dimensional nature of rockfall phenomena are high- lighted that have been hitherto neglected. The 3D space data provided in this study are suitable for the calibration and verification of rockfall analysis software that has become increasingly popular in design practice. Keywords Rockfall analysis  Laboratory and field tests  Deviation  Coefficient of restitution  Shape effect  Lateral dispersion 1 Introduction Rockfall is a gravitationally driven geomorphic process that occurs rapidly on steep natural or manmade slopes. It can have disastrous effects on human activities and infrastructure and therefore poses a significant natural hazard. However, due to the complex nature of the phe- nomenon, methods of analysing rockfall incorporate assumptions that can lead to oversimplifications; these will be thoroughly discussed hereafter. During a rockfall and while a block is in the air, the block moves along a parabolic path under the sole control of gravity. Because no external forces act on the block, the trajectory lies in the vertical plane. Once the block comes in contact with a slope, depending on the kinematic and geometrical conditions, it might rebound, resulting in a new parabolic trajectory. Alternate response types to rebound are rolling, sliding or a combination thereof. Once a block makes contact with a slope, deformation occurs on the slope depending on the surficial material. For low-strength materials (weathered rock, soils, debris, etc.) plastic deformation occurs that resembles a crater. On rocky slopes, the surface will remain intact without any visible impact traces, implying that deformation occurred in the elastic regime. Hereafter, only the rebound mecha- nism for rocky slopes will be considered. The rebound is the most difficult part of a trajectory to predict. It is influenced by several parameters, presented in Table 1, which cause a complex response, such that the understanding of the phenomenon is limited. In general, the post-impact part of the trajectory is calculated according to the coefficients of restitution (COR), which are overall values that are assumed to take into account all the char- acteristics of the impact and describe the change in the block’s velocity magnitude (Giani 1992). Various COR & Pavlos Asteriou paster@central.ntua.gr 1 Department of Geotechnical Engineering, School of Civil Engineering, National Technical University of Athens, 9 Iroon Polytechniou Str., 15780 Athens, Greece 123 Rock Mech Rock Eng DOI 10.1007/s00603-015-0798-7