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.
Highlights
Investigations of the nature of wave propagation through granular materials provide essential material properties and are often conducted for engineering applications
As discussed in O’Sullivan and Bray [24] and Otsubo et al [25], the particles in a Discrete element method (DEM) simulation are analogous to the nodes in a finite element model, while the contacts are roughly equivalent to the elements
This conceptual model of a granular material is used in implicit discrete element method formulations such as the particulate form of discontinuous deformation analysis (DDA) as outlined in [26,27,28]
Summary
Investigations of the nature of wave propagation through granular materials provide essential material properties and are often conducted for engineering applications. A better understanding of the material characteristics that determine flow−pass would enable us to assess whether measurement of flow−pass in laboratory seismic tests can provide useful information about how to characterise the material In addressing these issues here, the influence of confining stress and void ratio on flow−pass and λlow−pass are discussed. Alvarado and Coop [17] proposed that the frequencies of fundamental vibration modes can be identified from the local maxima of the ratio of the Fourier transforms of the received and inserted signals They based their hypothesis on a simple analysis of a single degree of freedom system. Agreement between the results of the three methods serves as a verification that each model formulation is reasonable and has been correctly implemented
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