Stress distributions in highly frictional granular heaps

Abstract

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. Mathematics Subject Classification (2000). 73B10, 73B99, 73Q05.

Experimental Study of Stockpiles of Iron Ore Fines

“…In an attempt to formulate an analytical solution to the stockpile problem [1], it posits a theoretical stockpile made up of two regions, an outer plastic region in which the material is found in limit equilibrium and an elastic inner region in which the material is found to be in equilibrium ( Figure 2). Numerical results show that, for a stockpile standing entirely on limit equilibrium, the problem's equations can only be solved when the friction angle is 90˚, so it can be assumed that not all of the stockpile material is in limit equilibrium.…”

“…Continuum medium mechanics applied to granular environments [1] sheds light on working out a solution to the Mohr-Coulomb criterion from basic equilibrium equations:…”

“…The manner in which the material is disposed of affects the central minimum stress value. This stress could be reproduced by the occasional deposition of the material above the material stockpile, and this minimum would disappear if the stockpile was made up of consecutive horizontal layers [1].…”

“…The first part briefly addresses the state of the art where the authors emphasize the mechanics of granular materials and an article focusing on geotechnical granular materials. The second part shows the solution to the equation developed by [1] applied to the geometry of iron ore stockpiles. The study of stress variation using a scale model is performed.…”

“…The study of stress variation using a scale model is performed. The comparison of the stress variation with the analytical solution [1] is commented. The third part shows an iron ore stockpile study highlighting stress distribution by formulating discrete elements.…”