Friction-dependent rheology of dry granular systems

Teng Man, Pei Zhang, Zhuan Ge, Sergio A. Galindo-Torres, Kimberly M. Hill

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6 Scopus citations


Understanding the rheology of granular assemblies is important for natural and engineering systems, but the relationship between inter-particle friction (or microscopic friction) and macroscopic friction is still not well understood. In this study, using the discrete element method (DEM) with spherical particles and realistic contact laws, we investigate the mechanics of granular systems with a wide range of inter-particle frictional coefficients and aim to establish a friction-dependent rheology for dry granular flows. The corresponding results show that increasing inter-particle friction dramatically increases the effective frictional coefficient, μeff, while decreasing the solid fraction of the system and increasing the transitional inertial number that marks the division of quasi-static regimes and intermediate flow regimes. We further propose a new dimensionless number, ℳ, as a ratio between the inertial effect and frictional effect, which is similar to the effective aspect ratio in granular column collapses, and unifies the influence of inter-particle friction with the inertial number. We then establish a relationship between ℳ and the dimensionless granular temperature, Θ, to further universalize the influence of inter-particle frictions. Such study can broaden the application of the μ(I) rheology in natural and engineering systems and help establish a more general constitutive model for complex granular systems. [Figure not available: see fulltext.].

Original languageEnglish (US)
Article number722191
JournalActa Mechanica Sinica/Lixue Xuebao
Issue number1
StatePublished - Jan 2023
Externally publishedYes

Bibliographical note

Funding Information:
This study was funded by the WHO Special Programme for Research and Training in Tropical Diseases (TDR) Postdoctoral Fellowship programme in Implementation Research. The TDR had no role in the design, data collection, analysis, and interpretation of data for this study.

Funding Information:
This work was supported by the General Program of the National Natural Science Foundation of China (Grant No. 12172305) and Westlake University. The authors would like to thank the Westlake High-Performance Computing Center for computational resources and related assistance, and thank Prof. Ling Li from Westlake University and Prof. Herbert Huppert from the University of Cambridge for helpful discussions related to this study.

Publisher Copyright:
© 2022, The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature.


  • Discrete element method
  • Friction
  • Granular materials
  • Rheology


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