In this work, we propose a two layer depth-averaged model to describe the propagation up to the deposition of granular avalanches. The model is derived in Cartesian coordinates under the assumption of long wave approximation. The two layers are supposed to follow to different flow regimes. A friction-collisional beaviour is assumed in the upper layer, while a purely frictional behaviour holds in the lower one. The model is numerically integrated through using a finite volume scheme. Since the resulting PDE system is only conditionally hyperbolic, a special treatment, involving the addition of an extra momentum flux across the interface between the layers, is implemented in the numerical scheme. The key features of this approach are illustrated by some numerical tests
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