Rheology of two-dimensional granular chute flows at high inertial numbers

Contrary to the popular inertial number-based rheology of dense granular flows, recent studies suggest a non-monotonic variation of the effective friction coefficient $μ(I)$ with the inertial number I in plane shear flows. While the popular rheology assuming monotonic variation of $μ(I)$ with I suggests existence of an upper limit of inclination angle for steady chute flows, the non-monotonic variation suggests the possibility of two different flow states for chute flows at a given inclination angle. In this work, we perform DEM simulations of chute flow of frictional inelastic disks and show that steady, fully developed flows are possible at inclinations much higher than those predicted from the monotonic $μ−I$ rheology. We observe steady flows up to inertial number $I≈2$ and find non-monotonic variation of the effective friction at high inertial numbers for chute flow of disks. The flows at high inertial numbers exhibit a constant density bulk region supported on top of a very dilute energetic basal layer of particles. We show that, in addition to a modified effective friction law that accounts for the non-monotonic variation of $μ(I)$ and the dilatancy law relating the solids fraction $ϕ$ with I, the rheological description also needs to account for the stress anisotropy by means of a normal stress difference law. By accounting for the presence of the normal stress difference, we also establish that only a single flow state is possible at any given inclination angle despite the non-monotonic variation of the effective friction coefficient.