Influence of packing density and stress on the dynamic response of granular materials

Abstract

Laboratory geophysics tests including bender elements and acoustic emission measure the speed of propagation of stress or sound waves in granular materials to derive elastic stiffness parameters. This contribution builds on earlier studies to assess whether the received signal characteristics can provide additional information about either the material's behaviour or the nature of the material itself. Specifically it considers the maximum frequency that the material can transmit; it also assesses whether there is a simple link between the spectrum of the received signal and the natural frequencies of the sample. Discrete element method (DEM) simulations of planar compression wave propagation were performed to generate the data for the study. Restricting consideration to uniform (monodisperse) spheres, the material fabric was varied by considering face-centred cubic lattice packings as well as random configurations with different packing densities. Supplemental analyses, in addition to the DEM simulations, were used to develop a more comprehensive understanding of the system dynamics. The assembly stiffness and mass matrices were extracted from the DEM model and these data were used in an eigenmode analysis that provided significant insight into the observed overall dynamic response. The close agreement of the wave velocities estimated using eigenmode analysis with the DEM results confirms that DEM wave propagation simulations can reliably be used to extract material stiffness data. The data show that increasing either stress or density allows higher frequencies to propagate through the media, but the low-pass wavelength is a function of packing density rather than stress level. Prior research which had hypothesised that there is a simple link between the spectrum of the received signal and the natural sample frequencies was not substantiated.

Using geophysical data to quantify stress transmission in gap-graded granular materials

“…Granular materials act as a filter to sound or stress waves (Santamarina et al, 2001;Mouraille, 2009;Lawney and Luding, 2014) so that frequencies higher than the low-pass frequency (flp) do not propagate through the material. flp is a material property that is influenced by packing density, effective stress and particle size (Otsubo et al, 2017a;Dutta et al, 2019). The frequency domain responses for the shear stresses recorded at the boundary walls for dense samples are compared in Fig.…”

“…The maximum transmitted frequency, i.e. the low-pass frequency (flp), depends on the particle size, void ratio, and the confining stress (Santamarina et al, 2001;Mouraille and Luding, 2008;Otsubo et al, 2017a;Dutta et al, 2019). No prior study has examined the phenomenon of frequency filtering and flp in the case of gapgraded materials.…”

Selecting an Appropriate Shear Plate Configuration to Measure Elastic Wave Velocities

“…The stress-wave simulation approach adopted here broadly follows that documented in Otsubo et al (2017), and key details are repeated here for clarity. To simulate the wave transmission, either the entire top cap or a portion of the top cap was excited horizontally (X-direction ( Fig.…”

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, 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.…”