  We revisit the problem of the stress distribution in a frictional sandpile
under gravity, equipped with a new numerical model of granular assemblies with
both normal and tangential (frictional) inter-granular forces. Numerical
simulations allow a determination of the spatial dependence of all the
components of the stress field as a function of systems size, the coefficient
of static friction and the frictional interaction with the bottom surface. Our
study clearly demonstrates that interaction with the bottom surface plays a
crucial role in the formation of a pressure dip under the apex of a granular
pile. Basic to the theory of sandpiles are assumptions about the form of
scaling solutions and constitutive relations for cohesive-less hard grains for
which no typical scale is available. We find that these constitutive relations
must be modified; moreover for smaller friction coefficients and smaller piles
these scaling assumptions break down in the bulk of the sandpile due to the
presence of length scales that must be carefully identified. After identifying
the crucial scale we provide a predictive theory to when scaling solutions are
expected to break down. At the bottom of the pile the scaling assumption always
breaks, due to the different interactions with the bottom surface. The
consequences for measurable quantities like the pressure distribution and shear
stress at the bottom of the pile are discussed. For example one can have a
transition from no dip in the base-pressure to a dip at the center of the pile
as a function of the system size.
