Rat-hole stress profiles for shear-index granular materials

Summary

The formation of stable circular and almost vertical cylindrical holes in stockpiles and hoppers is a familiar phenomena in granular material industries and is often the cause of serious disruption to the industry. These holes are referred to as “rat-holes” and the precise conditions under which they may form or the stability of an existing rat-hole are two issues which have yet to be properly resolved in the literature. We do not address these issues here, but for an existing rat-hole, and assuming a shear-index granular material, we determine the limiting stress profiles. Existing theory applies only to the Coulomb-Mohr yield function. A shear-index granular material is one for which failure due to frictional slip between particles, occurs when the shear and normal components of stress τ and σ satisfy the so called Warren Spring equation (vτv/C)ⁿ=1−(σ/t), wherec, t andn are positive constants which are referred to as the cohesion, tensile strength and shear-index respectively, and the known numerical values of the shear-index indicate that for certain materialsn lies between the values 1 and 2. The valuen=1 corresponds to the standard Coulomb-Mohr yield function while the valuen=2 permits some further analytical investigation, and stress profiles for these two values constitute bounds for those shear-index materials for which 1<n<2.