Unconfined flow of granular avalanches along a partly curved surface. I. Theory.R. GREVE, T. KOCH and K. HUTTER AbstractThis paper deals with threedimensional gravity driven free surface flows of piles of granular materials along bottom profiles that are weakly curved in the downward direction and plane in the lateral direction. We present in detail a threedimensional extension of the twodimensional SavageHutter model for such granular avalanches. In this extended model, the avalanche is described as a threedimensional incompressible continuum obeying a Coulomb dry friction law at the base and a MohrCoulomb plastic yield criterion in the interior. Based on this, the balance laws of mass and linear momentum and kinematic and stress boundary conditions at the free surface and the base are used to derive depthaveraged dynamic equations that describe the temporal evolution of the height and the depthaveraged horizontal velocity components as functions of position and time. A computation is performed for a pile of granular material with an initial spherical cap geometry moving down an inclined plane. Proceedings of the Royal Society London A 445 (1924), 399413 (1994). 
