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The three-halves Bagnold profile for granular flow down an incline, assuming no-slip at the base, is a generally accepted velocity profile that applies in many instances. In the intermediate dense regime, the material behaviour resembles a Bingham fluid and the widely accepted friction model - μ(I) rheology originally defined within the realms of visco-plasticity applies. Here for steady-state dense granular flow, we derive a generalization of the Bagnold profile which applies to the above- mentioned inter-particle friction approach, for which the Navier slip boundary condition applies at the base, and the Bagnold profile is included as a special case. We extend the Bagnold profile for a Navier slip base and we provide an expression for the slip length ℓ which demonstrates the dependence on the fundamental physical constants appearing in the μ(I) framework. The given velocity profile provides a simple formula that captures the major flow characteristics of dense granular chute flow. [ABSTRACT FROM AUTHOR]

In this paper we exploit the fact that dense granular flow down an inclined chute exhibits a simple scaling property. This implies that the fundamental governing partial differential equation admits similarity profiles which are applicable to any general friction law μ (I) of the material irrespective of the particular functional form under consideration, where μ (I) is a function of the dimensionless parameter, called the inertial number I. We adopt a widely accepted constitutive model describing the material response that draws its original inspiration from the realms of classical visco-plasticity. The governing steady-state similarity solutions are however applicable for any friction law describing dense granular media. These steady-state solutions embody the key aspects of dense granular flow down an inclined chute that find wide usage in various industrial applications and will further aid in modelling natural geophysical phenomenon. We provide steady-state analytical solutions for some special cases and we emphasize the importance of similarity solutions as a benchmark standard for various numerical studies concerning the complex material behaviour of dense granular flows. [ABSTRACT FROM AUTHOR]