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Bagnold velocity profile for steady-state dense granular chute flow with base slip

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Abstract

The three-halves Bagnold profile for granular flow down an incline, assuming no-slip at the base, is a generally accepted velocity profile that applies in many instances. In the intermediate dense regime, the material behaviour resembles a Bingham fluid and the widely accepted friction model - μ(I) rheology originally defined within the realms of visco-plasticity applies. Here for steady-state dense granular flow, we derive a generalization of the Bagnold profile which applies to the above- mentioned inter-particle friction approach, for which the Navier slip boundary condition applies at the base, and the Bagnold profile is included as a special case. We extend the Bagnold profile for a Navier slip base and we provide an expression for the slip length ℓ which demonstrates the dependence on the fundamental physical constants appearing in the μ(I) framework. The given velocity profile provides a simple formula that captures the major flow characteristics of dense granular chute flow.

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Acknowledgements

JMH gratefully acknowledges the hospitality and the financial support provided by the Institute of Geotechnical Engineering, University of Natural Resources and Life Sciences, Vienna, during which time this work was initiated. DB wishes to acknowledge the financial support provided by a grant from the Otto Pregl Foundation for Fundamental Geotechnical Research in Vienna, Austria and the logistical support provided by the Indian Institute of Technology Delhi, India.

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Authors and Affiliations

  1. School of Information Technology and Mathematical Sciences, University of South Australia, Adelaide, Australia

    James M. Hill

  2. Department of Civil Engineering, Indian Institute of Technology Delhi, Delhi, India

    Debayan Bhattacharya

  3. University of Natural Resources and Life Sciences, Vienna, Austria

    Debayan Bhattacharya

  4. Institute of Geotechnical Engineering, University of Natural Resources and Life Sciences, Vienna, Austria

    Wei Wu

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  1. James M. Hill
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  2. Debayan Bhattacharya
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Correspondence to Debayan Bhattacharya.

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Hill, J.M., Bhattacharya, D. & Wu, W. Bagnold velocity profile for steady-state dense granular chute flow with base slip. Rheol Acta 61, 207–214 (2022). https://doi.org/10.1007/s00397-021-01308-x

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