A survey of some mathematical results for highly frictional granular materials
Recently the authors have exploited the notion of a highly frictional granular material to derive analytical solutions for certain problems. Generally, we use the term highly frictional granular material to refer to those materials which possess an angle of internal friction such that the trigonometric sine of the angle of internal friction is close to unity. There are many granular materials for which this is the case, such as black and brown coal and limestone powder. For such materials formal perturbation solutions can be derived for which the zeroth-order solution corresponds to an angle of internal friction precisely equal to 90 ◦ , while the full perturbation solution applies to a larger range of angles of internal friction. In this paper, we present a survey of the ideas and the theory underlying highly frictional granular materials and catalogue the major solution types which are available for such materials. We illustrate some of the recent results obtained by using these analytical solutions to model the problems of determining the stress and velocity distributions in a gravity flow hopper, and the stress profiles beneath a stockpile and within a stable rat-hole.