Sound velocity fluctuations in confined granular materials: Coarse-graining lengths and elastic heterogeneities

Abstract

We measure the consequences of elastic heterogeneities in confined granular layers using long-wavelength sound velocity determination. By progressively decreasing the coarse-graining length w, which is determined here by the sample size L, we measure the standard deviation of the longitudinal sound velocity and the packing density ϕ, normalized by their ensemble-averaged values. We find that the relative fluctuations in VL and ϕ increase when w is decreased. Importantly, we observe that decreasing the confining pressure P or using nonspherical particles leads to an important increase of the fluctuations in . We conduct simulations of sound propagation in 2D hexagonal packings with contact-stiffness disorder to mimic the inhomogeneous contact networks. The sound velocity fluctuations of coherent longitudinal waves increase either with decreasing the sample size or with increasing the elastic disorder related to confining pressure, in consistency with the experiments. Our experimental observations thus support the scenario of a pressure-dependent mesoscopic length (at ), below which the continuum elasticity breaks down, likely due to the large spatial fluctuation of the shear modulus .