Elastic wave propagation in dry granular media: Effects of probing characteristics and stress history

Abstract

Elastic wave propagation provides a noninvasive way to probe granular materials. The discrete element method using particle configuration as input, allows a micromechanical interpretation on the acoustic response of a given granular system. This paper compares static and dynamic numerical probing methods, from which wave velocities are either deduced from elastic moduli or extracted from the time/frequency-domain signals. The dependence of wave velocities on key characteristics, i.e., perturbation magnitude and direction for static probing, and maximum travel distance and inserted signals for dynamic probing, is investigated. It is found that processing the frequency-domain signals obtained from dynamic probing leads to reproducible wave velocities at all wavenumbers, irrespective of the perturbation characteristics, whereas the maximum travel distance and input signals for the time domain analysis have to be carefully chosen, so as to obtain the same long-wavelength limits as from the frequency domain. Static and dynamic probes are applied to calibrated representative volumes of glass beads, subjected to cyclic oedometric compression.Although the perturbation magnitudes are selected to reveal only the elastic moduli, the deduced wave velocities are consistently lower than the long-wavelength limits at various stress states, and thus sensitive to sample size. While the static probes investigate the influence of stress history on modulus degradation, dynamic probing offers insights about how dispersion relations evolve during cyclic compression. Interestingly, immediately after each load reversal the incremental behavior is reversibly elastoplastic, until it becomes truly elastic with further unload/reload. With repeating unload/reload, the P-or S-wave dispersion relations become increasingly scalable with respect to their long-wavelength limits.

DEM simulation of anisotropic granular materials: elastic and inelastic behavior

“…In all cases examined, increments larger than 10 −4 produces a non-linear regime, more evident in case of anisotropy, in which the response depends on the amplitude of incremental strain ( [19,36,37]). Moreover, in the regime of deformation where the inelastic stiffness is defined, when anisotropy develops, the aggregate exhibits the loss of the major symmetry in the macroscopic stiffness, A 13 ≠ A 31 .…”

“…[7,8] or as indicator for localization [9]. Several approaches have been used to investigate elasticity numerically, e.g., dynamical unloading probes [10][11][12], response envelope [13][14][15], stiffness matrix [16,17], wave propagation [4,18,19], depending on the specific focus and final goal. In particular, procedures (and often conclusions) diverge if the interest is on "pure" elasticity at very small strains or an elasto-plastic framework.…”

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

“…Extensive research has been conducted using mathematical, numerical, and experimental tools to elucidate ultrasound wave behavior in granular materials in both the time and frequency domains. Some phenomena that have previously been studied include stress-dependent velocity scaling ( 8 , 12 ), frequency filtering ( 8 , 13 , 14 ), wave dispersion ( 15 – 18 ), band gaps ( 8 , 13 , 19 ), rotational waves ( 17 , 20 – 22 ), wave focusing ( 23 ), and wave scattering ( 20 , 21 , 24 , 25 ).…”

“…Frictional contact loss, viscoelastic/viscous contact dissipation, wave scattering, and material damping have been assumed to be responsible for wave attenuation ( 25 , 35 , 42 , 43 ). Local contact damping has been incorporated in discrete element simulations ( 18 , 35 , 44 – 46 ), enabling analysis of the energy dissipation during wave propagation. Additionally, a stiffness matrix incorporating all particle contacts of a granular packing has been used to build a lattice-based model to examine the wave attenuation and scattering for 2D granular systems ( 20 , 21 , 47 ).…”

Hydro‐micromechanical modeling of wave propagation in saturated granular crystals

“…The acoustic source at the pressure boundary aims to simulate the propagation of acoustic waves from a viscous fluid to a saturated granular medium. Alternatively, the wave can be agitated by perturbing the solid phase at a given position, 11,58,59 with an interparticle force slightly bigger than elsewhere, eg, between the boundary particles fixed in space and their neighbors. The resulting unbalanced forces on the neighboring spheres, in turn, induce a mechanical impulse propagating into the granular packing.…”