Characterization of base roughness for granular chute flows

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, Ra, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of Ra is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as Ra increases. Critical values of Ra are identified for the construction of a nonslip base at various angles of inclination.