Fractal Dimension and Rock Quality Charts

Abstract

Fractal dimension is proposed as a useful parameter for characterizing the irregular fragmentation within a rock mass leading to a new empirical rock quality chart and classification. A new algorithm is developed which can be easily implemented provided that intact length measurements are available along a borehole core or scanline on fresh cut rock surfaces. During the application of the algorithm, total recoverable intact length and their number are calculated for a given set of reference lengths. In general, the total recoverable intact length decreases as longer reference lengths are considered and their plot on arithmetic paper yields a line with negative slope. This plot is referred to as the Rock Quality Chart (RQC) and the slope of the regression straight line is adopted as the rock quality index. The smaller the slope, the better becomes the rock quality. It is also possible to obtain probable maximum block sizes from a relevant RQC. On the other hand, the plot of reference lengths versus their number along a scanline also yields a straight line but on log-log paper with negative slope, S. Accordingly, the fractal dimension, D, for the scanline concerned is defined as 1-S. The significance of the fractal dimension in rock quality descriptions is explained in detail. Both concepts of rock quality charts and fractal dimensions are applied to some scanline measurements already available in the literature.