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Basal layer of granular flow down smooth and rough inclines: kinematics, slip laws and rheology

Published online by Cambridge University Press:  16 December 2025

Teng Wang Open the ORCID record for Teng Wang [Opens in a new window] ,
Lu Jing Open the ORCID record for Lu Jing [Opens in a new window] ,
C.Y. Kwok Open the ORCID record for C.Y. Kwok [Opens in a new window] ,
Yuri D. Sobral Open the ORCID record for Yuri D. Sobral [Opens in a new window] ,
Thomas Weinhart Open the ORCID record for Thomas Weinhart [Opens in a new window]  and
Anthony R. Thornton Open the ORCID record for Anthony R. Thornton [Opens in a new window]
Teng Wang
Affiliation:
Institute for Ocean Engineering, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, PR China Department of Civil Engineering, The University of Hong Kong, Hong Kong, PR China
Lu Jing*
Affiliation:
Institute for Ocean Engineering, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, PR China State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, PR China
C.Y. Kwok
Affiliation:
Department of Civil Engineering, The University of Hong Kong, Hong Kong, PR China
Yuri D. Sobral
Affiliation:
Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, 70910-900 Brasília, DF, Brazil
Thomas Weinhart
Affiliation:
Department of Thermal and Fluid Engineering, University of Twente, Enschede 7500 AE, The Netherlands
Anthony R. Thornton
Affiliation:
Department of Thermal and Fluid Engineering, University of Twente, Enschede 7500 AE, The Netherlands Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
*
Corresponding author: Lu Jing, lujing@sz.tsinghua.edu.cn
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Abstract

Granular flow down an inclined plane is ubiquitous in geophysical and industrial applications. On rough inclines, the flow exhibits Bagnold’s velocity profile and follows the so-called $\mu (I)$ local rheology. On insufficiently rough or smooth inclines, however, velocity slip occurs at the bottom and a basal layer with strong agitation emerges below the bulk, which is not predicted by the local rheology. Here, we use discrete element method simulations to study detailed dynamics of the basal layer in granular flows down both smooth and rough inclines. We control the roughness via a dimensionless parameter, $R_a$, varied systematically from 0 (flat, frictional plane) to near 1 (very rough plane). Three flow regimes are identified: a slip regime ($R_a \lesssim 0.45$) where a dilated basal layer appears, a no-slip regime ($R_a \gtrsim 0.6$) and an intermediate transition regime. In the slip regime the kinematics profiles (velocity, shear rate and granular temperature) of the basal layer strongly deviate from Bagnold’s profiles. General basal slip laws are developed that express the slip velocity as a function of the local shear rate (or granular temperature), base roughness and slope angle. Moreover, the basal layer thickness is insensitive to flow conditions but depends somewhat on the interparticle coefficient of restitution. Finally, we show that the rheological properties of the basal layer do not follow the $\mu (I)$ rheology, but are captured by Bagnold’s stress scaling and an extended kinetic theory for granular flows. Our findings can help develop more predictive granular flow models in the future.

JFM classification

Granular media: Avalanches Granular media: Dry granular material

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JFM Papers
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Journal of Fluid Mechanics , Volume 1025 , 25 December 2025 , A27
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© The Author(s), 2025. Published by Cambridge University Press

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