Free-surface granular flows down heaps

• Published in: Journal of engineering mathematics 2008-02, Vol.60 (2), p.221-240
• Main Author: Savage, Stuart B.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Theoretical and Applied Mechanics
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-007-9141-y

The present paper extends the granular-flow constitutive model of Savage (1998 J Fluid Mech 377:1–26) to treat spherical particles. Savage accounted for both quasi-static and collisional stresses by considering: (i) strain-rate fluctuations embodied in a critical state plasticity model, as well as, (ii) individual particle velocity fluctuations modelled by granular-flow kinetic theory. In the present work, the governing equations of the kinetic theory of Jenkins (1998 In: Hermann HJ, Luding S (eds) Physics of Dry Granular Media. Kluwer Academic pp. 353–370) for identical spherical, smooth, inelastic particles are supplemented with additional quasi-static terms that have forms patterned after the corresponding terms in the equations of Savage for two-dimensional disk-like particles. The resulting equations along with side-wall and free-surface boundary conditions are applied to examine free-surface granular flow down a heap contained between two frictional vertical side walls. Width-averaged equations of motion are integrated to obtain depth profiles of mean velocity, granular temperature, solids fraction and the Savage–Jeffrey parameter. Detailed comparisons are made with particle-tracking experiments. When the gap between the vertical side walls is fairly narrow, good agreement is found between the predicted and the measured profiles of mean velocity and granular temperature.