On the Influence of Sampling Scale on the In Situ Block Size Distribution

The modelling of discontinuities in rock mass is undertaken with different measurement techniques and used to determine the in situ block size distribution (IBSD). Two monitoring techniques are employed: televiewer logging of boreholes and photogrammetry of highwall faces in a quarry bench; televiewer performs at the borehole diameter scale, while photogrammetry surveys at the entire bench scale. Ground sampling distances were, respectively, about 1 and 8.5 mm. The discontinuities are modelled as a stochastic discrete fracture network (DFN), with the number of discontinuities used in the simulation calibrated by the intensity per unit length (P10) on the televiewer data, or by the fracture density (P21) on the photogrammetry data, leading to different fracture networks. From the discontinuity network models, the IBSDs are calculated and discussed as function of the sampling scale (i.e. televiewer or photogrammetry data source) and of the fracture density. The goal is to compare the results from both techniques for rock mass structural characterization, to assess their limitations and shortcomings, and to show their potential complementarity at different sampling scales. The televiewer data provides smaller block sizes than the photogrammetry, following the higher number of fractures observed in the former. All volumetric distributions obtained are extremely well represented by Gamma with a power law tail distribution. Despite different location parameters, it is particularly remarkable that all distributions present very similar Gamma shape parameters. The constant log–log slopes of the tails provide evidence of multi-scale validity and a scaling invariant structure (more than two orders of magnitude) of discontinuities of the rock mass. The IBSDs and the scale effect are discussed in the light of the fragment size distributions from blasts carried out in the area characterized.