The use of scale independent shape measures to assess open stope performance

1. IntroductionExcavation performance in bulk underground mining applica-tions, such as open stoping, is generally assessed by the ability toachieve maximum extraction with minimal dilution. The successof open stoping methods relies on the stability of large (mainlyun-reinforced) stope walls and crowns as well as on the stabilityof any exposed ﬁll masses [1]. The performance of an open stopecan therefore be judged on the actual outcome versus the plannedoutcome, in terms of the ﬁnal volume, tonnage and grade of thematerial extracted, and the timeliness of extraction, compared tothe planned design and schedule. Performance can be describedin a number of ways, from subjective qualitative terms toquantitative numbers, based on a number of parameters and/orphysical quantities. A number of quantitative measures of stopeperformance, such as ELOS [2], have been used in the past;however, some of these measures fail to adequately capturecertain geometrical aspects of over-break or under-break. Backanalysis of open stope performance is essential in the dilutioncontrol process, as an improved understanding of mechanismsallows one to check the validity of any assumptions and reﬁnegeotechnical parameters used in the design process. A number ofnew shape descriptors are introduced to improve quantiﬁcationof over-break and under-break. The methodology is illustrated ondata from two case studies.2. New methodology2.1. Excavation geometry and performanceAn analysis of the shape of a resulting excavation surface relativeto its intended design can potentially provide useful informationabout the factors inﬂuencing excavation performance. For example,ﬁnal excavation surfaces that are typiﬁed by extensive arcuateshaped over-break may indicate that the performance has beenaffected by signiﬁcant rock mass failure, whereas prismatic orpolyhedral shaped over-break may potentially indicate more struc-turally controlled rock mass failure modes. Some further examplesof over-break geometries and potential failure modes and factorsaffecting performance are presented in Table 1.2.2. Geometrical assessment of stope performanceIn an attempt to determine the relative performance of stopes,one generally compares certain geometrical parameters of theover/under-break, such as volume, area or depth. Comparison ofthese parameters can be made on individual stope wall surfacesto ascertain whether there is any differential performancebetween walls. However, the use of such parameters alone doesnot necessarily provide an adequate characterisation of thegeometry of over/under-break. In evaluating the geometry ofover/under-break one needs to consider the following aspects:location, orientation, size and shape.The ﬁrst two aspects of geometry are relatively simple toascertain. In this paper the size-and-shape aspects of over-breakare investigated with a number of quantitative measures pro-posed to describe these two geometrical aspects.2.3. Shape and sizeShape is one of the most difﬁcult parameters to measure, as itmay be deﬁned in a number of ways for various purposes, eachwith various degrees of precision [3]. The basic deﬁnition of‘‘shape’’ is provided by [4]; ‘‘Shape is all the geometrical informa-tion that remains when location, scale and rotation effects areﬁltered out from an object.’’ Essentially this means that twogeometrical objects will have the same ‘‘shape’’ if, after beingrotated, translated and re-scaled, they match perfectly. Some-times, it is also necessary to see if geometrical objects of thesame ‘‘shape’’ are of different sizes. In this case, the deﬁnition ofContents lists available at ScienceDirectjournal homepage:www.elsevier.com/locate/ijrmms