Exact calculation of force networks in granular piles

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Abstract
We present calculations of forces for two-dimensional static sand pile models. Using a symbolic calculation software we obtain exact results for several different orientations of the lattice and for different types of supporting surfaces. The model is simple, supposing spherical, identical, rigid particles on a regular triangular lattice, without friction and with unilateral springlike contacts. Special attention is given to the stress tensor and pressure on the base of the pile. We show that orientation of the lattice and the characteristics of the supporting surface have a strong influence on the physical properties of the pile. Our results agree well with numerical simulations done on similar systems and show, in some specific cases, a dip, i.e., a depression under the apex of the pile. We also estimate that the algorithm we have developed can be easily adapted to other configurations and models of granulates and can be used in other physical cases where piecewise linear systems are encountered.