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

Granular Matter, Jun 2017

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.

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

Granular Matter Influence of packing density and stress on the dynamic response of granular materials Masahide Otsubo 0 1 Catherine O'Sullivan 0 1 Kevin J. Hanley 0 1 Way Way Sim 0 1 0 Atkins , The Hub, 500 Park Avenue, Aztec West, Almondsbury, Bristol BS32 4RZ , UK 1 Department of Civil and Environmental Engineering, Imperial College London , London SW7 2AZ , UK 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 Discrete-element modelling; Dynamics; Elasticity; Waves; Filtering; Eigenmode analysis - 2 Institute for Infrastructure and Environment, School of Engineering, The University of Edinburgh, Edinburgh EH9 3JL, UK 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. 1 Introduction Investigations of the nature of wave propagation through granular materials provide essential material properties and are often conducted for engineering applications. For example, the velocity of the propagating wave can be related to the small-strain stiffness of granular materials and is important in geophysics, geotechnical engineering and fundamental research into granular materials [ 1–3 ]. In these dynamic geophysics tests, the wave velocity can be obtained using either time domain techniques (e.g. [ 4,5 ]) or frequency domain techniques (e.g. [ 6–9 ]). This paper explores whether additional information, i.e. in addition to the elastic stiffness parameters, can be obtained about the tested samples by relatively simple analyses of the received signal. A testing scenario is considered which involves a controlled disturbance to generate an inserted signal at one sample boundary and monitoring of the received signal at another sample boundary. Two research questions are considered here: 1. Granular materials act as a low-pass filter to seismic (stress) or acoustic waves. Santamarina and Aloufi [ 10 ] and Santamarina et al. [ 11 ] related the maximum transmitted frequency ( flow− pass ) and the associated wavelength (λlow− pass ) to particle size, while Mouraille and Luding [ 12 ] related λlow− pass to the layer spacing. In their analysis of bender element tests and simulations, O’Donovan et al. [ 13 ] found that the relationship between particle size and flow− pass differs from that proposed by Santamarina and Aloufi [ 10 ] and Santamarina et al. [ 11 ]. Data presented in O’Donovan [ 14 ] indicates that flow− pass varies with confining pressure in randomly packed monodisperse materials. Lawney and Luding [ 15 ] examined a 1-D chain of spheres and observed that a narrower band of frequencies is transmitted when there is a variation in the sphere masses, in comparison with the case of perfectly uniform spheres. At a given stress and void ratio, the contact model also alters the frequency limit [ 16 ]. 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. 2. The study also examines whether comparison of inserted and received signals in the frequency (...truncated)


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Masahide Otsubo, Catherine O’Sullivan, Kevin J. Hanley, Way Way Sim. Influence of packing density and stress on the dynamic response of granular materials, Granular Matter, 2017, pp. 50, Volume 19, Issue 3, DOI: 10.1007/s10035-017-0729-2