The influence of packing structure and interparticle forces on ultrasound transmission in granular media

Abstract

Ultrasound propagation through externally stressed, disordered granular materials was experimentally and numerically investigated. Experiments employed piezoelectric transducers to excite and detect longitudinal ultrasound waves of various frequencies traveling through randomly packed sapphire spheres subjected to uniaxial compression. The experiments featured in situ X-ray tomography and diffraction measurements of contact fabric, particle kinematics, average per-particle stress tensors, and interparticle forces. The experimentally measured packing configuration and inferred interparticle forces at different sample stresses were used to construct spring networks characterized by Hessian and damping matrices. The ultrasound responses of these network were simulated to investigate the origins of wave velocity, acoustic paths, dispersion, and attenuation. Results revealed that both packing structure and interparticle force heterogeneity played an important role in controlling wave velocity and dispersion, while packing structure alone quantitatively explained most of the observed wave attenuation. This research provides insight into time- and frequency-domain features of wave propagation in randomly packed granular materials, shedding light on the fundamental mechanisms controlling wave velocities, dispersion, and attenuation in such systems.

Challenges and opportunities in measuring time-resolved force chain evolution in 3D granular materials

“…Despite the differences in compliance, wave speeds, and dimensionality, 2D photoelasticity studies have revealed the role of force chain statistics and fluctuations on mechanical properties [20], stick-slip [24], dynamic penetration and compaction [13,14,25], and electrical and mechanical wave transmission [6,8]. A benefit of studies employing 2D photoelastic and rubber discs is that measurements can be made over very short timescales using high-speed imaging.…”

“…Granular materials play prominent roles in landslides, avalanches, earthquakes, and river-bed mass transport, as well as in the pharmaceutical, food, and mineral processing industries [1][2][3]. The statistics, fluctuations, and organization of force chainsinter-particle forces with magnitudes greater than the average in a cohesion-less material -have been linked to: material stresses [4]; electrical and mechanical energy transport [5][6][7][8]; mechanical failure via particle fracture and inter-particle slip [9,10]; mechanical failure of confining vessels due to stress concentrations [11]; stick-slip on granular fault gouge [12]; hot spot formation during compaction of energetic powders [13]; the dynamics of intruders penetrating granular beds [14]. However, measuring time-resolved 3D force chain evolution at timescales relevant to these and other applications remains a challenge due to technological limitations and the difficulty of such experiments.…”

Propagation and attenuation of pulses driven by low velocity normal impacts in granular media

“…Hertzian (or Hertz-Mindlin) contact theory underlies estimates for the nature of sound propagation in granular media (e.g., Gómez et al 2012;van den Wildenberg et al 2013) and development of a continuum model, denoted an effective medium theory (e.g., Goddard 1990;Johnson et al 2000). In granular systems, broadening and attenuation of seismic or acoustic pulses may be intrinsically related (Langlois and Jia, 2015;O'Donovan et al, 2016;Zhai et al, 2020).…”

Stress and force measurement uncertainties in 3D granular materials

“…Techniques for determining interparticle forces include those leveraging photoelastic discs [1], compliant grains imaged with X-ray tomography [2], intra-particle speckle patterns combined with digital image correlation [3], and sand grains analyzed with X-ray computed tomography (XRCT) and 3D X-ray di↵raction (3DXRD) [4]. The combination of XRCT and 3DXRD has been used in natural and synthetic particle packs to study stress distributions [5], particle fracture mechanics [6], energy dissipation [7], and wave propagation [8]. Although prior work has described sources of experimental uncertainties in stresses and inferred forces [9,10], limited work has systematically examined uncertainty propagation.…”