For open pit mine slopes cut in discontinuous rock masses, bench instabilities often influence overall pit slope geometries. Potential failure modes are identified by evaluating how mapped structural orientations interact in a given pit sector. Mapped data are also used to estimate statistical distributions and spatial correlations of pertinent characteristics of discontinuity sets that comprise the potential failure modes. Shear strengths along anticipated sloping surfaces can be statistically estimated by laboratory direct shear tests of rock specimens that contain natural discontinuities. These statistical parameters are input to probabilistic stability analyses that produce probabilities of retaining various bench widths, results which are used to generate slope design charts for each analyzed pit sector. Such charts provide probabilistic parameters useful in designing the overall slope, including the expected median retained bench width and the probability of a bench being undercut by failures of underlying benches.
Slope instabilities of open pit mines cut in discontinuous rock masses are primarily controlled by geologic structures because displacements occur along surfaces of weakness. Typically, there are two scales of potential failures, those associated with major structures (such as faults, lithologic contacts, or other features with lengths comparable to the size of the study area) and those associated with more numerous, smaller structures (such as joints, foliations, and bedding planes). Major structures have lengths great enough to affect overall pit slope stability. In contrast, the smaller, more numerous structures usually have lengths less than 10 m and, consequently, they influence the stability of benches because bench heights commonly range from 12 to 20 m (this range reflects mining operational constraints or equipment capabilities). Engineering analyses of potential slope failures associated with major structures have been developed in theory and used in practice (for example, Hoek and Bray, 1977). However, an open pit mine slope designed by these methods alone may be prone to unanticipated instabilities caused by bench failures. Numerous small structures comprise multiple potential failure modes that affect bench stability, which, in turn, has a direct influence on the overall slope angle that can be attained. Consequently, mapped discontinuity data should be used to analyze bench stability in a probabilistic manner, and the results should assist in the selection of overall slope angles. Bench failures are much more likely to occur near the crest because structure lengths sufficient to allow failures are shorter near the crest and, thus, have higher probabilities of occurrence. This phenomenon is observed in operating mines, and a valid probabilistic bench stability analysis would be expected to provide similar types of results. Therefore, results from such an analysis should include the probabilities of retaining various bench widths after all anticipated failures have occurred.
ANALYSIS OF DISCONTINUITY DATA
The most common discontinuities in rock are fractures, which include both joints (along which there has been no displacement) and faults (along which there has been displacement). Fracture characteristics such as orientation, spacing, and length are random variables that can be modeled by statistical distributions estimated from mapping data (Call and others, 1976).