Characterization and reconstruction of a rock fracture surface by geostatistics

It is well understood that, in studying the mechanical and hydromechanical behaviour of rock joints, their morphology must be taken into account. A geostatistical approach has been developed for characterizing the morphology of fracture surfaces at a decimetre scale. This allows the analysis of the spatial variability of elevations, and their first and second derivatives, with the intention of producing a model that gives a numerical three‐dimensional (3D) representation of the lower and upper surfaces of the fracture. Two samples (I and II) located close together were cored across a natural fracture. The experimental data are the elevations recorded along profiles (using recording steps of 0.5 and 0.02 mm, respectively, for the samples I and II). The goal of this study is to model the surface topography of sample I, so getting estimates for elevations at each node of a square grid whose mesh size will be, for mechanical purposes, no larger than the recording step. Since the fracture surface within the sample core is not strictly horizontal, geostatistical methods are applied to residuals of elevations of sample I. Further, since structural information is necessary at very low scale, theoretical models of variograms of elevations, first and second derivatives are fitted using data of both that sample I and sample II. The geostatistical reconstructions are computed using kriging and conditional simulation methods. In order to validate these reconstructions, variograms and distributions of experimental data are compared with variograms and distributions of the fitted data. Copyright © 2002 John Wiley & Sons, Ltd.