Anomalous dispersion and attenuation in models of fluid-saturated granular packings

Motivated by the acoustic properties of marine sediments, we use discrete-element method (DEM) simulations to study wave propagation in fluid-saturated granular packings. Existing theories, including the Biot-Stoll (B-S) and Viscous Grain Shearing (VGS) models, are widely used in marine acoustics and across geosciences. However, there are certain features of experimental data that these theories cannot explain, at least without ad hoc modifications using complex and experimentally untestable loss mechanisms (e.g., squirt flow). Granular packings commonly exhibit emergent mechanical properties, including an excess of low-frequency modes and non-affine local grain motion in response to external forcing, but the B-S and VGS models do not explicitly consider the granular packing structure. We perform DEM simulations of waves propagating in granular packings, using linearized forces between particles (i.e., springs and dashpots), and demonstrate that the disordered packing structure leads to anomalous scaling laws for the frequency dependence of wave speed and attenuation that (1) agree with prevalent freatures of large experimental data sets and (2) arise directly from the granular packing structure. We connect these anomalous scaling laws to non-affine grain motion as well as to the excess low-frequency modes that are known to exist in granular packings. Our work suggests that wave propagation through a fluid-saturated granular packing may be primarily explained using the mechanical properties of granular packings.