Hydro‐micromechanical modeling of wave propagation in saturated granular crystals

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 43; no. 5; pp. 1115 - 1139
• Main Authors: Cheng, Hongyang, Luding, Stefan, Rivas, Nicolás, Harting, Jens, Magnanimo, Vanessa
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.04.2019
• Subjects: acoustic source; Biot theory; Computational fluid dynamics; Computer simulation; Confining; Coupling; Crystals; Discrete element method; Elastic waves; Fluid flow; fluid‐solid coupling; Granular materials; Granular media; Hydrodynamics; lattice Boltzmann method; Local flow; Mathematical models; Modelling; Modulus of elasticity; Numerical prediction; P-waves; Pressure; Propagation; S waves; Shear wave velocities; Terminal velocity; Viscosity; Wave equations; Wave propagation; Waveforms; Wavelength
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2920

Summary Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro‐micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two‐way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore‐scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one‐dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face‐centered‐cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.