manuscript No. (will be inserted by the editor) Closure Relations for Shallow Granular Flows from Particle Simulations

Abstract The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute with varying basal roughness, thickness and inclination. We observe three major regimes: arresting flows, steady uniform flows and ac-celerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed: for small inclinations the flow can be highly energetic and strongly layered in depth; where-as, for large inclinations it can be non-uniform and oscillat-ing. For steady uniform flows, depth profiles of density, ve-locity and stress are obtained using an improved coarse-graining method, which provides accurate statistics even at the base of the flow. A shallow-layer model for granular flows is completed with macro-scale closure relations ob-tained from micro-scale DPM simulations of steady flows. We obtain functional relations for effective basal friction, shape factor, mean density, and the normal stress anisotropy as functions of layer thickness, flow velocity and basal rough-ness