On drawbody shapes: From Bergmark–Roos to kinematic models

The geometrical locus defined by the initial location of the fragments that are recovered from an extraction point in underground mining, after a given operation, is commonly named “drawbody”. A brief review of drawbody shapes in flat-bottomed hoppers is proposed. The Bergmark–Roos hypothesis is discussed and it is shown that when the continuity equation is considered, particle density increases with time and when moving toward the hopper aperture. Drawbody shapes are calculated for flows predicted from a plasticity approach, as well as from a kinematic model. Applications to complex configurations in which the flow is produced by two drawpoints, either in simultaneous or sequential extractions, are discussed in some detail. In particular, the extracted zone is calculated exactly and its dependence on distance between drawpoints is investigated. The knowledge of such locus should prove valuable when optimizing ore recovery in mining processes.