We studied the flow of granular layers subject to vertical vibrations with amplitude a, and frequency ;For narrow gaps ;An important property of granular layers is dilatancy. When a granular layer is agitated, the grains unlock and start to flow. We measured the dilation due to the imposed vibrations. The dilation is limited to a small layer near the free surface. The height and phase of shaker dependence of the dilated layer are well-predicted by a simple model of an inelastic bouncing ball. |