  We present calculations of forces for two dimensional static sandpile 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
spring-like 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.
