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A random Cantor set as a measure of the statistical homogeneity of fractured rock masses

This study addresses the applicability of the exponent of a power-law scaling model, as an index of the statistical homogeneity of fractured rock masses. We systematically examine the capability of a random Cantor set, Dc, to quantify the combined effect of fracture density and size distribution on fracture networks. Total 129 two-dimensional fracture configurations were generated, based on different combinations of fracture size distribution and fracture density. The Dc for each generated fracture network system was calculated using the random Cantor dust method. We found that the standard deviation of trace length has no effect on the calculated Dc, and the estimated Dc increases with the total density and/or mean trace length. To explore the field applicability of this study, we investigated the statistical homogeneity of a fractured rock mass of the Upper Devonian Grosmont Formation in Alberta, Canada. The results clearly show that the methodologies given in this study are capable of determining the statistical homogeneity of fractured rock masses.