A new constitutive law for dense granular flows

In many geophysical or industrial applications involving flows of grains, a continuum description would be of considerable help, for example in predicting natural hazards or in designing industrial processes. However, constitutive equations for dry granular flows are still matter of debates 1-10. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated) 11. For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for the collisional rapid flows 12 , and soil mechanics for slow plastic flows 13. The intermediate dense regime, where the granular material flows like a liquid, still lacks unified view and has motivated many studies the last decade 14. The main characteristics of granular liquids are the existence of a yield criterion, i.e. the flow is not possible below a critical shear stress, and a complex shear rate dependence when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids like Bingham fluids. Inspired by this analogy and recent numerical 15,16 and experimental works 17-19 , we propose here a new constitutive relation for dense granular flows. We then test our three-dimensional (3D) model by carrying out experiments of granular flows on a pile between rough sidewalls, where a complex 3D flow pattern develops. We show that, without any fit parameter, the model gives quantitative predictions for the flow shape and velocity profiles. These new results support the idea that a simple visco-plastic approach can capture quantitatively granular flows properties and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.