Identifying uncertainty in estimates of bimrocks volumetric proportions from 2D measurements

Chaotic geological bodies composed of rock inclusions of different lithology and size enclosed in a weaker matrix are often referred to as bimrocks (block-in-matrix rocks). When dealing with these challenging and widespread geomaterials, a major concern for geopractitioners is the estimation of block content, which has been demonstrated to strongly affect the overall mechanical behaviour of bimrocks. Since the estimation of this parameter is not a simple matter, stereological principles are generally applied to infer 3D block contents from 1D or 2D measurements. However, they are often fraught with a high magnitude of error. In this study, a statistical approach was developed to determine the uncertainties associated with estimates of the 3D block proportions from 2D measurements. A Matlab code was implemented to generate heterogeneous models with a size distribution typical of bimrocks. An uncertainty factor is provided related to the size of the outcrop area investigated and the 2D block content to adjust the initial 2D estimates. It was found that a larger investigation area increases the reliability of the 2D measurements and as actual volumetric block proportion increases, the uncertainty decreases. The results obtained through this procedure were subsequently compared with previous findings from the literature concerning the uncertainty in estimates of the VBP from 1D measurements. The outcome of this comparison highlights the strength of the procedure described in this paper.