A REVISED FORM OF THE BERGMARK-ROOS EQUATION FOR DESCRIBING THE GRAVITY FLOW OF BROKEN ROCK

Abstract

The proper design of underground mines using caving methods such as block caving or sublevel caving requires a good understanding of how broken rock flows under the influence of gravity. To date, the mathematical equation that best describes the shape of the extraction drawbody is given by the Bergmark-Roos Equation. The derivation of the Bergmark-Roos Equation is reviewed and a revised version of the equation is developed which accounts for a non-zero opening width. Equations for the area, volume, and maximum width of the drawbody for a given extraction height are developed for both the original and modified forms of the Bergmark-Roos Equation. The equations derived can be used to evaluate existing mine layouts as well as in the design of new mining geometries.