We report on direct measurements of the basal force components for granular material flowing down a smooth incline. We investigate granular flows for a large range of inclination angles from $\theta =13.4^{\circ }$ to 83.6° and various gate openings of the chute. We find that the effective basal friction coefficient ${\mu }_B$, obtained from the ratio of the longitudinal force to the normal one, exhibits a systematic increase with increasing slope angle and a significant weakening with increasing particle holdup $H$ (the depth-integrated particle volume fraction). At low angles, the basal friction is slightly less than or equal to tanθ. The deviation from tanθ can be interpreted as a contribution from the sidewall to the overall friction. At larger angles, the basal friction ${\mu }_B$ saturates at an asymptotic value that is dependent on the gate opening of the chute. Importantly, our data confirm the outcomes of recent discrete numerical simulations. First, for steady and fully developed flows as well as for moderately accelerated ones, the variation of the basal friction can be captured through a unique dimensionless number, the Froude number Fr, defined as $\mathrm{Fr}=\overline{U}/{\left(gH\cos \theta \right)}^{1/2}$, where $\overline{U}$ is the mean flow velocity. Second, the mean velocity scales with the particle holdup $H$ with a power exponent close to $\frac{1}{4}$, contrasting with the Bagnold scaling $\left(\overline{U}\sim H^{3/2}\right)$.

• Received 16 February 2021
• Accepted 30 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042905