MONTE CARLO SIMULATION OF 3-D BLOCK POPULATIONS TO CHARACTERIZE BOREHOLE AND OUTCROP SAMPLING BIAS

Accurate estimation of 3-D block volumes and size distributions from 1-D borehole data or 2-D outcrop maps poses a significant problem in many engineering geologic projects, particularly those involving block-in-matrix materials (bimrocks) such as melanges and tills. Borehole data and outcrop maps will always produce biased estimates of the true block size distribution, and superficial consideration of the problem suggests that 1-D or 2-D sampling will consistently underestimate 3-D block volumes and sizes. Monte Carlo simulations of block populations cut by virtual outcrop faces or pierced by virtual boreholes, however, suggest the bias is more complicated than simple underestimation. If the blocks are spherical but randomly positioned relative to a 2-D sampling plane, the bias will always be towards consistent underestimation of block volumes and sizes. In a slightly more complicated situation where the blocks are of uniform size but ellipsoidal rather than spherical, the sampling bias can lead to significant under- or overestimation of block volumes and sizes depending on the aspect ratios and orientations of the blocks relative to the sampling line or plane. The amount of bias can be reduced if geologic information can constrain block orientation uncertainty, for example by knowing the angular relationship between an outcrop face and the average orientation of blocks in a block-in-matrix material with a well-developed fabric. Generation of apparent block sizes from a realistic non-uniform parent size distribution, for example a Pareto distribution of fractured block diameters, adds an additional layer of complexity to the problem. In such a case, the engineering geologist must try to understand the nature of an apparent block distribution that is the non-unique product of an underlying true block size distribution and the sampling bias. The implication for engineering geology practice is that naïve estimates of block volumes and size distributions from even the most carefully obtained borehole or outcrop data are more likely to be seriously wrong than they are to be nearly correct if sampling bias is not taken into account.