FORCES ON BINS - THE EFFECT OF RANDOM FRICTION

The q model of Coppersmith et al. [Phys. Rev. E 53, 4673 (1996)] has r enewed interest in understanding the forces generated along the walls and at the bottom of a silo filled with a granular material. Fluctuati ons in the mean stress have been characterized for the q model, and re lated 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 functi on of depth, in a tall silo. In this paper we reexamine the Janssen th eory, introducing randomness into the important parameters in the theo ry. The Janssen analysis relies on assumptions not met in practice. Fo r this reason, we numerically solve the partial differential equations governing the equilibrium of forces in a bin, again including randomn ess in parameters. We show that the most important of these parameters is a coefficient of friction at the wall of the bin. This random fric tion model combines some features of fluctuations as seen in experimen ts, with a classical continuum mechanics approach to describing granul ar materials.