Surface elastic waves in granular media under gravity

TL;DR

This paper investigates surface elastic waves in granular media under gravity, revealing localized Rayleigh-like waves influenced by non-linear Hertz contacts and comparing theoretical predictions with field measurements.

Contribution

It introduces an elastic model accounting for non-linearity and yielding in granular matter, predicting surface wave modes and their dispersion characteristics.

Findings

Existence of surface-localized waves similar to Rayleigh waves.

Discrete modes corresponding to sagittal and transverse waveguides.

Wave speeds align with field measurements on sand dunes.

Abstract

Due to the non-linearity of Hertzian contacts, the speed of sound $c$ in granular matter is expected to increase with pressure as $P^{1/6}$. A static layer of grains under gravity is thus stratified so that bulk waves are refracted toward the surface. We investigate wave propagation in the framework of an elastic description taking into account the main features of granular matter: non-linearity between stress and strain and existence of a yielding transition. We show in this context the existence of waves localised at the free surface --~like Rayleigh waves~-- but with a wave guide effect related to the non-linear Hertz contact. The dispersion relationship shows a discrete number of modes which correspond to modes localized in the sagittal plane but also to transverse modes. The propagation speed of these waves is finally compared to recent measurements performed in the field, at the surface of a sand dune.