Multiple scattering effects in water saturated beads

Abstract

Ultrasonic measurements have been used to study the propagation of longitudinal waves in systems comprised of unconsolidated glass and Plexiglas spherical beads saturated with water. In each sample there is roughly a 20% spread in the sphere diameters. The mean diameters vary between 100 and 500 μm. In every sample the porosity is about 38%. We find that the measured velocity dispersion and attenuation are in generally good agreement with the results of multiple scattering calculations based on the quasicrystalline approximation. In these calculations, the average sphere diameter and porosity of the samples are modeled in terms of the radial (i.e., two site) distribution function, and the scattering properties of the individual spheres are treated exactly. Surprisingly, we find that the properties of the glass and Plexiglas bead samples are remarkably similar. This is true in spite of the fact that the elastic properties of the two materials are quite different. At the lowest frequencies, we show that essentially equal sound speeds for the glass and Plexiglas systems can be understood on the basis of the Biot theory.