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We revisit the problem of the stress distribution in a frictional sandpileunder gravity, equipped with a new numerical model of granular assemblies withboth normal and tangential (frictional) inter-granular forces. Numericalsimulations allow a determination of the spatial dependence of all thecomponents of the stress field as a function of systems size, the coefficientof static friction and the frictional interaction with the bottom surface. Ourstudy clearly demonstrates that interaction with the bottom surface plays acrucial role in the formation of a pressure dip under the apex of a granularpile. Basic to the theory of sandpiles are assumptions about the form ofscaling solutions and constitutive relations for cohesive-less hard grains forwhich no typical scale is available. We find that these constitutive relationsmust be modified; moreover for smaller friction coefficients and smaller pilesthese scaling assumptions break down in the bulk of the sandpile due to thepresence of length scales that must be carefully identified. After identifyingthe crucial scale we provide a predictive theory to when scaling solutions areexpected to break down. At the bottom of the pile the scaling assumption alwaysbreaks, due to the different interactions with the bottom surface. Theconsequences for measurable quantities like the pressure distribution and shearstress at the bottom of the pile are discussed. For example one can have atransition from no dip in the base-pressure to a dip at the center of the pileas a function of the system size.

The sandpile revisited: Computer assisted determination of constitutive relations and the breaking of scaling