We present simulations of static 2D piles made of almost monodisperse spheres. With this simplified model we reproduce different former theoretical predictions which were based on the assumption of a homogeneous contact network in the whole pile and perfectly rigid particles.
One fact is that arching and the so called dip in the vertical stress at the bottom are not neccessarily due to solid friction [11, 14]. If the contact network varies as a function of the position in the pile we observe stresses different from the theoretical predictions based on a regular network. If we observe arching the orientation of the stress tensor is fixed, at least in the outer part, and the contact network is symmetric to the center but not translation invariant. The orientation of the major principal axis and the ratio of the two eigenvalues of the stress tensor are correlated with the structure of the contact network. We observe diamond lattices, either vertical or tilted by 60 degrees outward from the center, if the major principal stress is almost vertical or tilted outwards respectively. But if the major and minor principal axis are comparable in magnitude we observe a triangular lattice, i.e. all possible contacts closed, rather than a diamond lattice. Together with the tilted contact network, i.e. strongly tilted principal axis, we evidence in some cases arching and a small vertical stress under the center of the pile. If the contact network is tilted outwards, stresses are preferentially propagated outwards, what may be regarded as a reason for arching and for the dip.
Varying the size of the particles randomly, we find that already tiny polydispersities destroy the regular contact network. Due to the small fluctuations in particle size the particles are still positioned on a triangular lattice even when the contacts are randomly open. In the case of a random network we also find the so called stress chains, i.e. selected paths of large stresses, and the stress fluctuations are larger or of the order of the mean stress. The stress chains - or better the stress network - is also disordered. When averaging over many realizations of the stress network we get a dip in the vertical stress at the bottom if the size fluctuations are large enough. Thus we observe a similar stress distribution at the bottom as obtained by a cellular automaton model based on a random opening of contacts.
Since we are able to find most of the phenomenology, expected in a sandpile, already in an oversimplified regular model system, we conclude that the role of the contact network (or the fabric) is eminent. However, friction and small polydispersity may play a different role in more general situations with physical sandpiles.
As an extention of our model we started more realistic simulations with a nonlinear Hertz contact law [21], with solid friction, and also with nonspherical particles [27]. The effect of those more realistic interaction laws has to be elaborated and also threedimensional examinations should be performed.