Sand piles do not have a perfectly conical shape as
suggested by the
concept of the angle of repose but
have as we found at the bottom a logarithmic tail which is due
to some simple similarity argument.
The figure shows an
experimental heap (polenta). In addition to the analytical shape
we also see the straight line that defines the angle of
repose. For more details
see the paper
published with Juanjo Alonso in Phys. Rev. Lett. 76 (1996) 4911-4914.
Similarly one can obtain the shape in a two dimensional silo
published in Comptes Rendus de l'Academie des Sciences Paris,
Vol.326, Serie IIb, p.61-67 (1998) with Yan Grasselli:
Its relation to the angle of repose and the dependence on the
filling procedure for silos and heaps was systematically
studied in 2-d Hele Shaw cells in the
paper published in Europ.J.Phys. B, Vol.10, p.673-679 (1999).
With Oron Gadi and
we made a model
to explain the shapes of Yan Grasselli's two-dimensional heaps as
published in Granular Matter Vol.2, p.97-100 (2000).
Three dimensional heaps under the impact of particles
falling from a certain height form craters which were
measured in the
paper published in Granular Matter Vol.3, p.201-204 (2001)
Comparison with experiments made at the University of Habana
are given in a
preprint having the following figures:
For other papers with Stefano Zapperi see also