Non-parametric three-dimensional discrete fracture network modelling from fracture mapping data

Abstract

Rock masses usually include discontinuities in the form of fractures or joints, which in general are critical in determining the mechanical or flow properties of the rock mass at the engineering scale. Recent advances in computing power have made it possible to represent these fractures explicitly in a rock mass model. However, in practice, three-dimensional fracture systems are impossible to measure, and the best available alternative is either to map fractures in drill cores (one-dimensional) or on exposed rock surfaces (two-dimensional). The construction of a three-dimensional fracture system that is representative of reality then becomes a very challenging inverse problem, as this is essentially a relationship of one reality corresponding to many possibilities. Most existing approaches start with assumptions about the distribution of measured features, perform a series of bias corrections and then use some further assumptions and stereological analysis to establish the three-dimensional fracture model. The usual practice is to focus on particular aspects (parameters) of the three-dimensional fracture model which can easily produce a biased representation of the real fracture system. In this paper, a non-parametric systematic optimisation framework is described which can help construct a more realistic three-dimensional fracture model that best matches the statistics of the fracture mapping data. No bias correction is necessary in this approach provided the sampling of the fracture model is consistent with that used in the data collection. The framework can also be used to assess the uncertainty of the fracture model, which is an important, but often neglected, component of modelling in existing approaches. In addition, this non-parametric approach is also flexible and can deal with data from different sources (e.g., different sampling planes at different orientations, mixtures of plane and borehole sampling). This is a significant advantage over existing approaches as different data sources often display different statistical characteristics even for the same fracture set. The Stripa Mine dataset is used to demonstrate the application of the proposed method.