Surface stability of granular systems under horizontal and vertical vibration: the applicability of a coefficient of friction

We investigate the conditions under which the surface of a granular pile becomes unstable to vibrations. Three stability boundaries are identified, which depend upon the relative phase of the driving forces and the angle of the prepared slope. The experimental findings can be interpreted within the context of a Coulomb friction model and used to define an effective coefficient of friction. For up-hill motion we find that the coefficient of friction depends strongly on the slope angle and that, in general, it requires less vibration to transport grains uphill than would be otherwise expected.