The angle of initial yield of haphazard assemblages of equal spheres in bulk

Abstract

The maximum slope angle assumed by heaped granular solids is of considerable interest in geology, geomorphology and soil mechanics, as also is the slope stability of such heaps. Representing the solids by equal spheres, we here deduce that the relationship between the maximum slope angle (angle of initial yield) and the concentration of equal spheres arranged haphazardly in bulk in the gravity field is tan Φi= k1C - k2 + A, in which Φi is the angle of initial yield, C is the fractional volume concentration, k1 and k2 are known constants depending on the properties of equal spheres in regular cubical and rhombohedral array, and A is a variable dimensionless coefficient representing frictional, electrostatic and other non-gravitational forces. This relationship is broadly confirmed by experiments using glass beads of two different narrow size ranges, though the experiments are not of a high order and accuracy. It is of interest that a natural sand, well sorted compared with other sands but still showing an approximately 1 : 4 range of sizes, also conforms to the relationship deduced for equal spheres.