Granular elasticity:: Stress distributions in silos and under point loads

An elastic-strain-stress relation, the result of granular elasticity as introduced in the preceding paper, is employed here to calculate the stress distribution (a) in cylindrical silos and (b) under point loads assuming uniform density. In silos, the ratio k(J) between the horizontal and vertical stress is found to be constant (as conjectured by Janssen) and given as k(J)=1-sin phi (with phi the Coulomb yield angle), in agreement with a construction industry standard usually referred to as the Jaky formula. Next, the stress distribution at the bottom of a granular layer exposed to a point force at its top is calculated. The results include both vertical and oblique point forces, which agree well with simulations and experiments using rainlike preparation. Moreover, the stress distribution of a sheared granular layer exposed to the same point force is calculated and again found in agreement with given data.