Prediction of the Angle of Repose from Materials Failure Theory

Abstract

A fundamental materials failure theory is used to predict the angle of repose for granular solids. This long-existing classical problem is now solved. The solution only requires two properties: (1) the uniaxial compressive strength of the aggregate and (2) the effective grain size. There are no adjustable parameters. When subjected to the specified gravity field, the angle of repose θ between the free surface and the horizontal datum is uniquely determined. The results are compatible with observations existing in nature and with specific cases involving materials products in granular forms. The general failure theory is specialized to the limiting case of a cohesionless materials form in order to consummate the solution to the problem. The significance of this work for all isotropic materials failure problems is assessed in the final section.