Micromechanics of vortices in granular media: connection to shear bands and implications for continuum modelling of failure in geomaterials

Authors

  • Antoinette Tordesillas,

    Corresponding author
    1. Department of Mathematics & Statistics, The University of Melbourne, Parkville VIC 3010, Australia
    2. School of Earth Sciences, The University of Melbourne, Parkville VIC 3010, Australia
    3. Melbourne Energy Institute, The University of Melbourne, Parkville VIC 3010, Australia
    • Correspondence to: Antoinette Tordesillas, Department of Mathematics & Statistics, The University of Melbourne, Parkville VIC 3010, Australia.

      E-mail: atordesi@unimelb.edu.au

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  • Sebastian Pucilowski,

    1. Department of Mathematics & Statistics, The University of Melbourne, Parkville VIC 3010, Australia
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  • David M. Walker,

    1. Department of Mathematics & Statistics, The University of Melbourne, Parkville VIC 3010, Australia
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  • John F. Peters,

    1. Geotechnical Laboratory, U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, U.S.A.
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  • Laura E. Walizer

    1. Geotechnical Laboratory, U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, U.S.A.
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SUMMARY

Recent analysis of data from triaxial tests on sand and discrete element simulations indicate the final pattern of failure is encoded in grain motions during the nascent stages of loading. We study vortices that are evident from grain displacements at the start of loading and bear a direct mathematical connection to boundary conditions, uniform continuum strain and shear bands. Motions of three grains in mutual contact, that is, 3-cycles, manifest vortices. In the initial stages of loading, 3-cycles initiate a rotation around a region Ω* where the shear band ultimately develops. This bias sets a course in 3-cycle evolution, determining where they will more likely collapse. A multiscale spatial analysis of 3-cycle temporal evolution provides quantitative evidence that the most stable, persistent 3-cycles degrade preferentially in Ω*, until essentially depleted when the shear band is fully formed. The transition towards a clustered distribution of persistent 3-cycles occurs early in the loading history—and coincides with the persistent localisation of vortices in Ω*. In 3D samples, no evidence of spatial clustering in persistent 3-cycle deaths is found in samples undergoing diffuse failure, while early clustering manifests in a sample that ultimately failed by strain localisation. This study not only delivered insights into the possible structural origins of vortices in dense granular systems but also a tool for the early detection of the mode of failure—localised versus diffuse—a sample will ultimately undergo. Copyright © 2014 John Wiley & Sons, Ltd.

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