A theoretical model for the stress distribution in granular matter. III. Forces in sandpiles

Following the ideas of the two previous papers we consider the problem of a free boundary system, the sandpile. It is argued that some simple model of a sandpile is needed where the angle of repose is at least approximately understood. Such a model is of plates which when deposited on the plate pile will lie parallel to its surface. As the pile grows the information that the interior was earlier on the surface is built into an extension of the equations of the previous papers. These crude equations (which are of first order) are easily solved and the distribution of pressure at the base of the sandpile is in good agreement with what is experimentally observed (the dip in the middle arising due to arches propagating the force in the medium at an angle different to that of the angle of repose).