Vectorial Cellular Automaton for the Stress in Granular Media

We introduce a simple cellular automaton to model the force distribution in a gravity-loaded granular medium. Two test cases are considered: the sand heap, and the silo geometry. The model gives results consistent with established observations. For the heap, the normal stress on the base plane displays a pronounced depression underneath the apex. In the silo geometry, the model reproduces the correct scaling for the approach to a stationary (depth-independent) stress state.