The Pressure Ratio in the Theory of Bin Pressures

Abstract

The pressure ratio K0 is assumed to be a constant in the theory developed by Janssen for determining the pressures imparted by a granular material to its container. Recently it was shown that K0 can be defined less restrictively as the ratio of the perimeter average of the horizontal stress acting on the vertical wall of the container to the cross-sectional average of the vertical stress in the granular material at the same depth in the container. Three results concerning K0 are presented in this paper. First, it is shown that the essential result of Janssen, namely that the vertical and horizontal stresses have a constant bound at great depths, also holds in the case when the bulk density and the pressure, ratio are bounded by linear functions of the average vertical stress. Second, it is shown that a formula relating K0 to the Poisson’s ratio of the granular material is not correct, in general. Third, bounds on K0 are obtained using the Mohr-Coulomb yield condition for the granular material.