Rockfall analysis considering coefficients of restitution based on three-dimensional sphere discontinuous deformation analysis

Collisions are the most complex part of rockfall movement processes and significantly affect the scope and movement distance of rockfall hazards. An accurate analysis of collisions is helpful for obtaining reliable rockfall trajectories. In this study, the energy loss during collision is characterized by normal and tangential coefficients of restitution (COR), and the rockfall collision and motion processes are simulated via numerical methods. Contact theory and a method for calculating COR are considered for three-dimensional sphere discontinuous deformation analysis (SDDA) to simulate collisions during rockfall movement. A detailed calibration method is proposed to obtain the critical parameter “contact yield stress” of the normal COR (NCOR). Through parameter sensitivity analysis, the inherent velocity loss in SDDA is investigated, and correction strategies are proposed. Additionally, the effects of the material, incident angle, and impact velocity on COR are studied, and the fundamental reasons for the change in COR caused by various factors are discussed. Finally, based on the topography of a high and steep dangerous rock slope in the Wulong area of Chongqing, China, rockfall motion in complex terrain was simulated, and the simulation results were compared with the traces of rockfall left behind and stopping area in the field. The results show that the SDDA considering COR can simulate the collision process of rockfall movement, which has important practical value for rockfall risk assessment.