Granular Matter

, Volume 14, Issue 4, pp 531–552 | Cite as

Closure relations for shallow granular flows from particle simulations

  • Thomas Weinhart
  • Anthony R. Thornton
  • Stefan Luding
  • Onno Bokhove
Open Access
Original Paper


The discrete particle method (DPM) is used to model granular flows down an inclined chute with varying basal roughness, thickness and inclination. We observe three major regimes: arresting flows, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed: for small inclinations the flow can be highly energetic and strongly layered in depth; whereas, for large inclinations it can be non-uniform and oscillating. For steady uniform flows, depth profiles of density, velocity and stress are obtained using an improved coarse-graining method, which provides accurate statistics even at the base of the flow. A shallow-layer model for granular flows is completed with macro-scale closure relations obtained from micro-scale DPM simulations of steady flows. We obtain functional relations for effective basal friction, velocity shape factor, mean density, and the normal stress anisotropy as functions of layer thickness, flow velocity and basal roughness.


Discrete particle method Coarse graining Granular chute flow Depth-averaging Shallow-layer equations 



The authors would like to thank the Institute of Mechanics, Processes and Control, Twente (IMPACT) for the primary financial support of this work as part of the research program “Superdispersed multiphase flows”. The DPM simulations performed for this paper are undertaken in Mercury-DPM, which was initially developed within this IMPACT program. It is primarily developed by T. Weinhart, A. R. Thornton and D. Krijgsman as a joint project between the Multi ScaleMechanics (Mechanical Engineering) and the Mathematics of Computational Science (Applied Mathematics) groups at theUniversity of Twente. We also thank the NWO VICI grant 10828 and the DFG project SPP1482 B12 for financial support.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Thomas Weinhart
    • 1
    • 2
  • Anthony R. Thornton
    • 1
    • 2
  • Stefan Luding
    • 1
  • Onno Bokhove
    • 2
  1. 1.Multiscale Mechanics, Department of Mechanical EngineeringUniversity of TwenteEnschedeThe Netherlands
  2. 2.Numerical Analysis and Computation Mechanics, Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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