The propagation of a mechanical impulse in a granular medium

An experimental study has been made of the propagation of a low-amplitude mechanical impulse in a granular medium. The response of granular matter to an applied impulse is primarily governed by the behaviour of the contacts between its constituent particles. The contact behaviour depends on the existing static load on the bed, on the history of previous loading, and on the characteristics of the applied impulse. A procedure has been developed to enable beds with a consistent and reproducible initial state to be deposited and prepared, thus permitting a certain isolation of the effects of loading history. Measurements of the variation of velocity of propagation and attenuation of transmitted impulses with applied static load, impulse duration and intensity, and distance of propagation, have been made on beds of four size fractions of dry sub-angular sand, and comparative experiments performed on beds of common salt and silicon carbide. The velocity of propagation of the impulse is found to vary with the static load raised to some power. The experimental values of this exponent are close to the one-sixth power dependence predicted by Hertz contact theory, but the results show systematic departures from this value related to the size fraction of material. The magnitude of the received impulse is found to decay exponentially with distance, at constant static load, yielding a distance attenuation factor. The magnitude and direction of the variation of this attenuation factor with static load is observed to depend in an involved manner on the particle size fraction and the impulse duration. Literature relating to the deposition and packing of granular media, the effects of applied stress and vibration, wave propagation, and theoretical analyses of the mechanics of granular matter, has been reviewed. The contact theory of Hertz, as developed in particular by Mindlin, forms the basis of an analysis of the observed phenomena.