Effects of the impact angle on the coefficient of restitution in rockfall analysis based on a medium-scale laboratory test

The reliability of a computer program simulating rockfall trajectory depends on the ascertainment of reasonable values for the coefficients of restitution, which typically vary with the kinematic parameters and terrain conditions. The effects of the impact angle with respect to the slope on the coefficients of restitution have been identified and studied using small-scale laboratory tests. To investigate whether the existing conclusion based on small-scale laboratory tests is valid when the test scale changes as well as the role of rotation in the effect of the impact angle on the coefficients of restitution, this study performed a medium-scale laboratory test using spherical limestone polyhedrons to impact concrete slabs. Free-fall tests are conducted, and the velocities before and after the impact are obtained by a 3-D motion capture system. The comparison of results between our test and the existing small-scale tests verified that several general laws occur when accounting for the effect of the impact angle, regardless of the test scales and conditions. Increasing the impact angle will induce reductions in the normal coefficient of restitution Rn, the kinematic coefficient of restitution Rv and the kinetic energy coefficient of restitution RE, whereas it will lead to increases in the tangential coefficient of restitution Rt. The rotation plays an important role in the effect of the impact angle. A higher percentage of kinetic energy converted to rotational energy always induces a higher normal coefficient of restitution Rn and a lower tangential coefficient of restitution Rt. As the impact angle decreases, the ratio between the rebound angle β and the impact angle α increases, and the percentage of kinetic energy dissipated in rotation as the collision became higher. Considering that the effect of block shape and the detailed impact orientations are not involved in the present study, the test results are valid for trajectory simulation codes based on a lumped-mass model and can be referenced in the trajectory predication of spherical rocks impacting hard surfaces using a rigid body model.