Small- and half-scale experimental studies of rockfall impacts on sandy slopes

In the framework of rockfall trajectory modelling, the bouncing phenomenon occurring when a rock block impacts with the slope surface is the most difficult to predict, owing to its complexity and its very limited understanding. Up to now, the rebound is commonly quantified by means of (one or) two coefficients of restitution expressing the amount of energy dissipated during impact. These restitution coefficients generally are evaluated from a rough description of the ground material, whereas other parameters likely to influence the rebound phenomenon as the characteristics of the block itself and the kinematics are often neglected. In the framework of this thesis, two experimental campaigns have been performed in laboratory to acquire a better knowledge of the impact mechanisms governing the rebound phenomenon of rock blocks on granular (sandy) slopes and to quantify the discovered dependencies. About 200 impact tests on a small scale have helped to identify first the most significant impact parameters and to qualify their influence. Further, a half-scale testing campaign has been performed to quantify these influences. The impact of a rock block on a granular material is modelled for varying impact parameters, concerning: the ground material (internal friction angle, compaction) the block (weight, radius, shape) and the kinematics (slope angle, impact direction (vertical or inclined), impact velocity). The impact process has been filmed by a high-speed camera. The analysis of the block movement before, during and after the shock allowed to gather information concerning the impact process itself (velocity and acceleration of the block, penetration into the ground material, duration of impact etc.) and to determine a criterion for which the impact process is completed. By means of this criterion, the normal (Rn), tangential (Rt) and energetic (RTE) coefficients of restitution have been evaluated for the mass centre of the block according to the most common formulations (ratio of the normal or tangential velocities respectively the total energies before and after impact). The qualitative analysis of the small and half-scale tests proves that the rebound of rock blocks as well as the coefficients of restitution commonly used to characterise the rebound depend not only on the ground characteristics (material, slope inclination), but also on parameters related to the block (weight, geometry) and the kinematics (impact velocity and angle). A thorough observation of the impacts has shown that the block motion during impact is governed by three mechanisms (penetration, sliding, rotation), acting partly antagonistically. For different impact conditions, one or another of these mechanisms is privileged, governing on his part the block motion after impact. The quantitative interpretation of the half-scale tests leads first to a proposition of formulations expressing the maximal penetration of the block into the ground material, the maximal contact force and the rotation of the block acquired during impact. Parting from these formulations and inspired by the principle of the conservation of linear momentum, expressions for the normal and tangential component of the coefficients of restitution are developed. The implementation of coefficients of restitution defined by similar formulations as the proposed ones in rockfall trajectory codes should lead to a better prediction capacity of the latter and finally to a better delineation of areas at risk by hazard maps.