Exact Solutions for Nonlocal Steady Fully Developed Debris Flows Down Inclines
Publication: Journal of Engineering Mechanics
Volume 146, Issue 4
Abstract
Exact solutions for steady fully developed dry granular and saturated granular–liquid mixture flows down rough inclined planes are presented with an emphasis on nonlocal effects. The particle rheology of both dry granular and saturated granular–liquid mixtures is described by a recently developed nonlocal granular fluidity (NGF) model. The fluid rheology of a saturated granular–liquid mixture is represented by the eddy viscosity, and the contacting forces between the fluid and grains are drag and buoyancy forces. The problems are then reduced to solving the resulting partial differential equations (PDEs). Closed-form solutions for the critical stopping layer height of dry granular and saturated granular–liquid mixtures are derived by analytically solving the linearized equations of the NGF model. Moreover, exact solutions for velocity profiles are acquired by solving the coupled equations with a PDE solver.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant/Award Nos. 51978105 and 51922024), the Chongqing Research Program of Basic Research and Frontier Technology (Grant/Award No. cstc2017jcyjAX0261), and the Fundamental Research Funds for the Central Universities (2018CDQYTM0045).
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 4 • April 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Aug 7, 2019
Accepted: Nov 4, 2019
Published online: Feb 13, 2020
Published in print: Apr 1, 2020
Discussion open until: Jul 13, 2020
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