Coefficients Of Restitution In The Application Of Rigid Body Impact Mechanics In Rockfall Analysis

Introduction Rockfalls occur when rocks or boulders detach from mountains or hills and tumble down. They can pose significant hazards to infrastructure such as highways, buildings, and mine open pits, and they sometimes result in personal injury or death. Prediction of rockfalls is a difficult task. Slopes that are at risk of rockfall have highly variable geometries. The location, mass, and shape of the rocks that might dislodge and fall are uncertain. Moreover, the materials that make up a slope can vary considerably from one section to another. Furthermore, the relevant material properties are usually not well known. Performing probabilistic simulations of rockfalls, combined with proper statistical analyses, has proven to be an effective and acceptable method for dealing with these difficulties [1, 2, 3]. The movements of a falling rock can be classified as freefall, bouncing, sliding, toppling, or rolling. The falling trajectory is controlled mainly by the geometry of the slope, the block shape, and the energy dissipated at each contact of the block with the slope. A rockfall model is evaluated based on its ability to efficiently predict the velocity, frequency, height of bounce, and run-out distance of falling rocks. With this information, the engineer can design remedial measures such as restraining nets and ditches. Most of the existing rockfall simulators are based on particle models that consider the falling rock as an infinitesimal particle with a mass, called the lumped mass or stereomechanical models [1, 2, 3, 4]. Other models involve hybrid methods relying on simplified assumptions. The most common hybrid methods are based on contact searching for the movement of a dimensionless object and incorporate some aspects of rigid body impact for bouncing [5, 6, 7]. There are also some rigid body models in the literature that employ simplified versions of rigid body models [8, 9]. This study applies a more sophisticated rigid body theory based on rigid body impact mechanics (RBIM), which was developed by Stronge [10, 11, 12]. The new theory captures all modes of rigid body movement. Due to the importance of the rock geometry, single impacts of ellipsoidal and prismatic rocks with rectangular cross sections are investigated. The effect of rock slenderness on rebound velocities and energies is also investigated for ellipsoidal rocks. The correspondence between the model parameters and the data from the rockfall literature data will be discussed.