Granular Flows in the Elastic Limit

  1. William McCaffrey,
  2. Ben Kneller and
  3. Jeff Peakall
  1. C. S. Campbell

Published Online: 17 MAR 2009

DOI: 10.1002/9781444304275.ch6

Particulate Gravity Currents

Particulate Gravity Currents

How to Cite

Campbell, C. S. (2001) Granular Flows in the Elastic Limit, in Particulate Gravity Currents (eds W. McCaffrey, B. Kneller and J. Peakall), Blackwell Publishing Ltd., Oxford, UK. doi: 10.1002/9781444304275.ch6

Editor Information

  1. School of Earth Sciences, University of Leeds, Leeds, LS2 9JT, West Yorkshire, UK

Author Information

  1. Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA

Publication History

  1. Published Online: 17 MAR 2009
  2. Published Print: 24 APR 2001

ISBN Information

Print ISBN: 9780632059218

Online ISBN: 9781444304275



  • granular flows in elastic limit;
  • recent computer simulation studies into rheological behaviour of granular materials between the quasi-static and rapid-flow regime;
  • Young's modulus of bulk material - particles proportional to stiffness;
  • elastic granular flows;
  • stresses scaling with interparticle stiffness indicating forces supported by networks of particles in intimate contact;
  • intermediate range of granular flow lying between rapid flow and quasi-static limit at large concentrations and small shear rates


This chapter describes recent computer simulation studies into the rheological behaviour of granular materials in the regime that lies between the quasi-static and rapid-flow regime. This study was a result of studies of landslides, hopper flows and the ‘phase change’ (i.e. the change between solid-like and fluid-like behaviour) all of which indicated that the shear-to-normal stress ratio (the effective friction coefficient for the material) increased with shear rate. The results presented herein account for those observations by demonstrating that the stress ratio varies with a dimensionless parameter created by scaling the shear rate with the stiffness of the interparticle contacts. The results indicate that in dense regimes, the stresses themselves scale with the stiffness indicating that they are generated by the elastic response of particle networks. Such speculation is supported by studies that show that the normal stresses are strongly dependent on the interparticle friction coefficient which affects the ability of internal elastic particle structures to support load. Finally, estimates are made of the regions of particle concentration for which the elasticity of the material is important.