A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway)

[1] Fracture patterns are characterized by a complex geometry which involves a large length distribution and nonhomogeneous density distributions. Here we address the issue of the modeling of this complex geometry over scales through a first-order model providing the characterization of the number of fractures of a given length and at a given scale. We propose that the simplest model is a power law in both space and fracture length, with three main parameters: the exponent a of a power law length distribution, the fractal dimension D which fixes the scale dependence of the number of fractures, and the fracture density a. We verify the applicability of this model on seven fracture patterns mapped from the metric scale up to almost the kilometric scale in the Hornelen basin. The model efficiently describes fracture network properties at all scales with a single set of parameters. For the Hornelen fracture networks we found a simple relationship between basic exponents, a = D + 1, implying that the fracture network is self-similar. Through this analysis, we present different methodological developments for deriving the basic exponents a and D and for verifying the consistency of the model. Overall, the main methodological development is about the normalization of the measurements made from different scales of observation. Finally, we discuss both the limitations and the uses of such a model for analyzing the hydraulic and mechanical properties of fracture networks.