Stress distributions in highly frictional granular heaps

The practice of storing granular materials in stock piles occurs throughout the world in many industrial situations. As a result, there is much interest in predicting the stress distribution within a stock pile. In 1981, it was suggested from experimental work that the peak force at the base does not occur directly beneath the vertex of the pile, but at some intermediate point resulting in a ring of maximum pressure. With this in mind, any analytical solution pertaining to this problem has the potential to provide useful insight into this phenomenon. Here, we propose to utilize some recently determined exact parametric solutions of the governing equations for the continuum mechanical theory of granular materials for two and three-dimensional stock piles. These solutions are valid provided sin φ = 1, where φ is the angle of internal friction, and we term such materials as “highly frictional”. We note that there exists materials possessing angles of internal friction around 60 to 65 degrees, resulting in values of sin φ equal to around 0.87 to 0.91. Further, the exact solutions presented here are potentially the leading terms in a perturbation solution for granular materials for which 1- sin φ is close to zero. The model assumes that the stock pile is composed of two regions, namely an inner rigid region and an outer yield region. The exact parametric solution is applied to the outer yield region, and the solution is extended continuously into the inner rigid region. The results presented here extend previous work of the authors to the case of highly frictional granular solids.