Estimation of shear strength using fractals as a measure of rock fracture roughness

Researchers at the Bureau of Mines investigated the use of close-range photogrammetry and subsequent stereo digitizing to obtain data from rock fracture roughness profiles. The photogrammetric process yielded results that were acceptable but somewhat inferior to those obtained by a mechanical profilometer. On the basis of this study, further pursuit of photogrammetry as a data collection method in mining is proposed. Fractal geometry was investigated as a means of measuring the roughness of rock fracture profiled. Four fractal algorithms were used: divider method, modified divider method, box method, and spectral method. A comparison of the methods gave ambiguous results. Brown's modified divider method provided the best means of obtaining the fractal dimension. Shear strength estimates were obtained using the parameters of the modified divider method and Myers' Z2 measure. Because of differences in results when comparing the different ways of obtaining the fractal dimension, future users of fractals in studies of rock fractures are advised to cross-check their results carefully.