Biot's theory predicts the wave velocities of a saturated poroelastic
granular medium from the elastic properties, density and geometry of its dry
solid matrix and the pore fluid, neglecting the interaction between constituent
particles and local flow. However, when the frequencies become high and the
wavelengths comparable with particle size, the details of the microstructure
start to play an important role. Here, a novel hydro-micromechanical numerical
model is proposed by coupling the lattice Boltzmann method (LBM) with the
discrete element method (DEM. The model allows to investigate the details of
the particle-fluid interaction during propagation of elastic waves While the
DEM is tracking the translational and rotational motion of each solid particle,
the LBM can resolve the pore-scale hydrodynamics. Solid and fluid phases are
two-way coupled through momentum exchange. The coupling scheme is benchmarked
with the terminal velocity of a single sphere settling in a fluid. To mimic a
pressure wave entering a saturated granular medium, an oscillating pressure
boundary condition on the fluid is implemented and benchmarked with
one-dimensional wave equations. Using a face centered cubic structure, the
effects of input waveforms and frequencies on the dispersion relations are
investigated. Finally, the wave velocities at various effective confining
pressures predicted by the numerical model are compared with with Biot's
analytical solution, and a very good agreement is found. In addition to the
pressure and shear waves, slow compressional waves are observed in the
simulations, as predicted by Biot's theory.Comment: Manuscript submitted to International Journal for Numerical and
Analytical Methods in Geomechanic