Coefficient of restitution and rotational motions of rockfall impacts

Abstract

Abstract This paper presents experimentally obtained results for the coefficient of restitution for spherical boulders impacting on rock slopes. Plaster modeling material is used for casting both the boulders and slopes. It is observed that the normal component of the coefficient of restitution ( R n ) increases with the slope angle α , which agrees with Wu's observations (Trans. Res. Rec. 1–5 (1985) 1031). However, there appears to be no clear correlation between the tangential component of the coefficient of restitution ( R t ) and the slope angle α . When the ratio of the resultant velocities and the ratio of the kinetic energies before and after impacts are used to define the coefficient of restitution (i.e. R V and R E ), a very clear increasing trend in the coefficient of restitution with α is observed. When all data are plotted onto the R t − R n space, our laboratory data fall into the rock slope regime proposed by Fornaro et al. (In: D.G. Price (Ed.), Proceedings of the Sixth International Congress IAEG, Amsterdam, Balkema, Rotterdam, 1990, p. 2173) and also agree with those data gleaned from literature. In addition, the rotational kinetic energy E r , induced at each impact, increases with the slope angle α , achieves a maximum at about α =40°, before decreasing again to a negligible value at α =70°. A simple theoretical model is proposed to explain this observation based on the locking between the boulder and the slope during impact. The α -dependence of E r differs from the recommendation by the Japanese Railway Association that the induced rotational energy is about 10% of that of the translational kinetic energy.