The influence of density variation of a granular pile on the pressure distribution at its bottom

We report that when the density at the centre of a cohesionless granular pile is slightly smaller than the density at its sides, such that the elastic strength at the centre is evidently smaller than the strength at the sides, the pressure distribution under the pile will show a dip at the centre. For the conical (or wedge-shaped) piles formed by slowly pouring grains from a point (or a line), the small density variation may be due to the phenomenon that the pile is slightly tapped by the down-rolling grains along the pile surfaces. The computation shows that the observed pressure distribution can be well reproduced by the elastic theory with a spatial-varying bulk modulus.