A continuum constitutive model for cohesionless granular flows

A constitutive model is developed to represent shear granular flows of cohesionless solids. The model is based on the postulate that the friction coefficient and the solids fraction in a moving granular material are exclusive functions of the inertial number, which represents the ratio of inertial to normal stress forces. The constitutive equation obtained has the same form as a multidimensional Bingham fluid model, albeit with apparent viscosity and yield stress that depend on the vertical normal stress. The model is applied to previously published experimental results dealing with shear flows of granular beds made up of cohesionless spherical particles. The first case analyzed corresponds to a granular bed moving on top of a rotating disk. The model captures the main trends of the velocity profiles with a single adjustable parameter. The second case is a conventional Couette flow, for which the model is capable of representing the velocity and solids fraction profiles measured experimentally.