[Paper Review] Sound wave velocities in dry and lubricated granular packings packings: numerical simulations and experiments

Ivana Agnolin, Jean-Noël Roux+3 more|arXiv (Cornell University)|Jan 20, 2009

Granular flow and fluidized beds15 references5 citations

TL;DR

This study combines numerical simulations and experiments to show that lubricated granular packings, despite lower density, exhibit significantly higher sound wave velocities than dry packings due to a higher coordination number. The simulations reveal that preparation method—particularly lubrication—alters microstructure more than density, with coordination number being the dominant factor influencing stiffness and wave propagation, challenging assumptions that density alone determines elastic properties in granular materials.

ABSTRACT

Numerical simulations are used to investigate the origins of the different wave velocities measured in dense granular samples assembled with different methods. Glass bead packings are prepared in the lab either by pouring and vibrating the dry material in a container, or by mixing with a very small amount of a viscous lubricant. Lubricated samples, although less dense, exhibit significantly higher wave velocities for confining pressures in the 100 kPa range. Numerical predictions for elastic moduli agree much better with experimental results when the computational preparation of the samples mimics the laboratory one, albeit in a simplified manner. A plausible explanation to the laboratory observations is that the coordination number, which influences the material stiffness more than its density, is notably higher in lubricated packings.

Motivation & Objective

• To understand why lubricated granular packings exhibit higher elastic wave velocities than dry ones despite lower density.
• To investigate how different sample preparation methods (dry pouring vs. lubricated mixing) affect microstructural properties like coordination number and stiffness.
• To evaluate whether numerical simulations can accurately reproduce experimental wave velocity measurements in granular packings.
• To determine whether coordination number or density is the dominant factor influencing elastic wave velocities in dense granular materials.
• To assess the validity of simplified numerical models in capturing real laboratory preparation effects on granular microstructure and mechanical response.

Proposed method

• Numerical simulations using discrete particle dynamics to model granular packings with simplified representations of laboratory preparation methods: 'vibrated' dry (C-type), and 'lubricated' (A and B types) assemblies.
• Simulation of mechanical equilibrium under confining pressure, followed by calculation of stiffness matrix from contact network to derive elastic moduli.
• Use of the Voigt-Reuss-Hill averaging scheme to compute effective bulk (B) and shear (G) moduli from the stiffness matrix.
• Derivation of longitudinal (VP) and transverse (VS) wave velocities from moduli and mass density using standard elasticity equations: VP = √[(B + 4G/3)/ρ], VS = √[G/ρ].
• Comparison of simulated wave velocities with experimental data from ultrasonic measurements on dry (E1) and lubricated (E2) glass bead packings under varying confining pressures (30–1000 kPa).
• Analysis of coordination number and contact network structure in simulated samples to correlate microstructure with macroscopic elastic response.

Experimental results

Research questions

• RQ1 Why do lubricated granular packings exhibit higher sound wave velocities than dry packings, despite lower packing density?
• RQ2 To what extent does the sample preparation method—specifically lubrication—affect the coordination number and elastic moduli in dense granular packings?
• RQ3 Can simplified numerical simulations of laboratory preparation procedures reproduce experimental wave velocity trends in granular materials?
• RQ4 Is coordination number a more influential factor than density in determining elastic wave velocities in granular packings?
• RQ5 How do the mechanical responses of numerically simulated packings compare to experimental results across different confining pressures?

Key findings

• Lubricated packings (E2) exhibit 10–20% higher longitudinal and transverse wave velocities than dry packings (E1), despite a lower solid fraction (0.62 vs. ~0.64).
• Numerical simulations show that C-type samples (simulating dry, vibrated packing) match experimental wave velocities for dry packings (E1) much better than A-type (perfect lubrication) or B-type (imperfect lubrication) simulations.
• The higher wave velocities in lubricated packings are attributed to a higher coordination number, which enhances stiffness more than density affects it.
• Simulations reveal that coordination number is a more significant determinant of elastic wave velocity than packing density in dense granular packings.
• The study demonstrates that numerical models must replicate the preparation protocol—not just the final density—to accurately predict mechanical behavior, as coordination number is a largely independent microstructural variable.
• At low confining pressures (~100 kPa), the distinction between high- and low-coordination-number packings is critical, while at higher pressures (>1 MPa), differences between simulation types diminish, aligning with experimental trends.