Development of a viscoelastoplastic contact model for the size- and velocity-dependent normal restitution coefficient of a rock sphere upon impact

Abstract

Improved knowledge of the size and velocity dependences of the normal restitution coefficient (NCOR) is necessary for extending the NCOR laboratory results to practical rockfall trajectory analysis. Hence, a new normal impact device was developed for conducting laboratory impact tests of marble spheres under a wide range of impact velocities. Compression tests of marble spheres were also conducted. A new viscoelastoplastic contact model was proposed, and the size- and rate-dependent contact yield strength was considered for the first time. The results of compression tests demonstrate that the contact yield strength is strongly size-dependent. The size effect of the NCOR at low impact velocities is opposite that at higher impact velocities. The theoretical NCOR that was obtained from the proposed model with size- and rate-dependent strength shows satisfactory agreement with the experimental results. The complex size and velocity dependences of the NCOR are well captured by the proposed model. The theoretical results clearly demonstrate that the influence of the size on the NCOR substantially exceeds that of the impact velocity. The viscosity determines the NCOR for small marble spheres at low impact velocities, and plasticity is the dominant factor that determines the NCOR of large marble spheres at high impact velocities.