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A simple analytic theory for the statistics of avalanches in sheared granular materials

Nature Physics volume 7, pages 554557 (2011) | Download Citation

Abstract

Slowly sheared granular materials at high packing fractions deform via slip avalanches with a broad range of sizes. Conventional continuum descriptions1 are not expected to apply to such highly inhomogeneous, intermittent deformations. Here, we show that it is possible to analytically compute the dynamics using a simple model that is inherently discrete. This model predicts quantities such as the avalanche size distribution, power spectra and temporal avalanche profiles as functions of the grain number fraction v and the frictional weakening ɛ. A dynamical phase diagram emerges with quasi-static avalanches at high number fractions, and more regular, fluid-like flow at lower number fractions. The predictions agree with experiments and simulations for different granular materials, motivate future experiments and provide a fresh approach to data analysis. The simplicity of the model reveals quantitative connections to plasticity and earthquake statistics.

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Acknowledgements

We thank R. Behringer, B. Chakroborty, K. Daniels, T. Earnest, J. P. Sethna and G. Tsekenis for useful discussions, and NSF DMR 03-25939 (MCC), MGA, the USC Earth Sciences Department, the UCSB Kavli Institute of Theoretical Physics, and the Aspen Center of Physics for support and hospitality.

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Affiliations

  1. Department of Physics, University of Illinois at Urbana Champaign, 1110 W. Green Street, Urbana, Illinois 61801, USA

    • Karin A. Dahmen
  2. Department of Earth Sciences, University of Southern California, Los Angeles, California 90089-0740, USA

    • Yehuda Ben-Zion
  3. 450 Las Lomas, Dr., La Habra, California 90631, USA

    • Jonathan T. Uhl

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All authors contributed extensively to the work presented in this paper.

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The authors declare no competing financial interests.

Corresponding author

Correspondence to Karin A. Dahmen.

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https://doi.org/10.1038/nphys1957

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