Elastic waves generated by impact and vibration in confined granular media

Abstract

Observational data of asteroids can be explained by considering them as an agglomerate of granular material. Understanding the mechanical properties of these objects is relevant for many scientific reasons: space missions design, evaluation of impact threats to our planet, and understanding the nature of asteroids and their implication in the origin of the solar system. In-situ measurements of mechanical properties require complex and costly space missions. Here a laboratory-scale characterization of wave propagation in granular media is presented using a novel experimental setup as well as numerical simulations. The pressure inside an asteroid is still a matter of debate, but it definitely presents a pressure gradient towards the interior. This is why impact characterization needs to be performed as a function of the confining pressure. Our experimental setup allows for the simultaneous measurement of the external confining pressure, internal pressure, total strain, and acceleration in a 50 cm side squared box filled up with a billion grains. We study the propagation of impact-generated and shaker-born seismic body waves in the 500 Hz range. Through subsequent compression-relaxation cycles, it was observed that the granular media behaves on average like a solid with a constant elastic modulus during each compression. Effective medium theory (EMT) for granular media explains the data at low pressure. After each compression-relaxation cycle, the elastic modulus increases, and a high hysteresis is observed: relaxation shows a more complex behavior than compression. We show that seismic waves generated by both impact and vibration travels at the pressure wave speed. Thanks to a numerical model, we measure a strong wave attenuation α ∼ 3.4 Np/m. We found that the wave speed increases with the confining pressure with a p1/2 dependency, in disagreement with theoretical models that predicts a shallower dependency. The dependency of the elasticity with the confining pressure can be explained by a modified EMT model with a coordination number proportional to the pressure, or equivalently by a mesoscopic nonlinear model based on third-order nonlinear elastic energy. The interpretation of these models is a deep reorganization in the particle contact network.