Reports On Technological Research - Extreme Value Statistics Improve Forecasts Of Rock Behavior

In general, many problems relating to the exploitation of mineral deposits are probabilistic in nature. This derives from the fact that the geologic universe is inherently random. Probability theory and statistics have been found useful for forecasting the behavior of natural events that occur in the geologic universe. The objective of this paper is to outline the application of the theory of extremes to this forecasting problem. Consider the design of an underground structure or the design of a rock slope. The initial step is the formulation of the various possible structural actions which result from the geometry of the layout. For a given structural model, various intensities of behavior are possible depending upon the load, deformation, and material characteristic spectra, respectively. Of popular interest to mining people is the failure behavior or condition. A necessary feature of the analysis is the rupture strength of the material. Information on the rupture strength is derived from testing either in situ or in the laboratory and the usual outcome is a variation in the test results. This variation is overcome by constructing a frequency distribution of rupture strengths, and then determining a measure of central tendency and variability. The main feature of interest in the analysis is the failure characteristic and its percentage chance of occurrence. Hence, one is naturally led to examine those areas of a distribution curve which are termed the tails. The statistical concepts which can most efficiently handle such areas are contained within extreme value statistics.