Key block theory for the miner: a novel simplified method for determining block removability

Abstract

Rock falls driven by gravity cause the most injuries and deaths in the South African underground mines. Discontinuities such as joints define most rocks that are free to fall. Key block theory describes how to decide if a rock defined by joints can move into an excavated space. Key block analysis requires complex calculations and many iterations to reach such a decision. The complexity of applying key block theory restricts its routine use. Although there are several methods that address some of the shortcomings of key block theory, none address the complexity of its underlying calculations. The main drive of this research project was to find a method to judge rock block removability that is simple enough to enable the routine application of key block theory in mining. The new gravitational removability theorem described in this report satisfied the need for simplicity. A comparison between the gravitational removability method and the edge vector method on many generated blocks yielded a fair correlation in terms of removability, but less so in terms of non-removability. The definition and application of a set of calibrating geometric conditions in conjunction with the gravitational removability method resulted in a perfect accounting of all the synthetic blocks. The gravitational removability method proved effective in identifying rotational removability as well. This research report presents the new gravitational removability theorem, equations to calculate the gravitational removability number and a set of geometric conditions that allows the judgement of removability of a block with no, or minimal calculation.