Forces on bins: The effect of random friction

The q model of Coppersmith et al. @Phys. Rev. E 53, 4673 ~1996!# has renewed interest in understanding the forces generated along the walls and at the bottom of a silo filled with a granular material. Fluctuations in the mean stress have been characterized for the q model, and related to experimental work on stress chains. The classical engineering approach to bin loads follows from Janssen’s analysis @Z. Ver. Dtsch. Ing. 39, 1045 ~1895!#, predicting a saturation of stress, as a function of depth, in a tall silo. In this paper we reexamine the Janssen theory, introducing randomness into the important parameters in the theory. The Janssen analysis relies on assumptions not met in practice. For this reason, we numerically solve the partial differential equations governing the equilibrium of forces in a bin, again including randomness in parameters. We show that the most important of these parameters is a coefficient of friction at the wall of the bin. This random friction model combines some features of fluctuations as seen in experiments, with a classical continuum mechanics approach to describing granular materials. @S1063-651X~98!03003-7#