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A theoretical formulation of dilatation/contraction for continuum modelling of granular flows

Published online by Cambridge University Press:  20 April 2021

Huabin Shi Open the ORCID record for Huabin Shi [Opens in a new window] ,
Ping Dong Open the ORCID record for Ping Dong [Opens in a new window] ,
Xiping Yu Open the ORCID record for Xiping Yu [Opens in a new window]  and
Yan Zhou Open the ORCID record for Yan Zhou [Opens in a new window]
Huabin Shi*
Affiliation:
State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental Engineering, University of Macau, Avenida da Universidade, Taipa, Macao, China
Ping Dong
Affiliation:
School of Engineering, University of Liverpool, Brownlow Hill, LiverpoolL69 3GH, United Kingdom
Xiping Yu
Affiliation:
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing100084, China
Yan Zhou
Affiliation:
School of Engineering, University of Liverpool, Brownlow Hill, LiverpoolL69 3GH, United Kingdom
*
†Email address for correspondence: [email protected]
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Abstract

Shear dilatation/contraction of granular materials has long been recognized as an important process in granular flows but a comprehensive theoretical description of this process for a wide range of shear rates is not yet available. In this paper, a theoretical formulation of dilatation/contraction is proposed for continuum modelling of granular flows, in which the dilatation/contraction effects consist of a frictional component, which results from the rearrangement of enduring-contact force chains among particles, and a collisional component, which arises from inter-grain collisions. In this formulation, a frictional solid pressure, which considers the rearrangement of contact force chains under shear deformation, is proposed for the frictional dilatation/contraction, while well-established rheological laws are adopted for the collisional inter-grain pressure to account for the collisional dilatancy effect. The proposed formulation is first verified analytically by describing the shear-weakening behaviour of granular samples in a torsional shear rheometer and by capturing the incipient failure of both dry and immersed granular slopes. The proposed dilatation/contraction formulation is then further validated numerically by integrating it into a two-fluid continuum model and applying the model to study the collapse of submerged granular columns, in which the dilatation/contraction plays a critical role.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A56
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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