Geometric and Statistical Modeling of Fractures in the 3D Disturbed Zone of a Claystone Around a Cylindrical Gallery (Meuse-Haute Marne Underground Research Laboratory, France)

Abstract

This paper deals with the generation of rock fractures in 3D space around a cylindrical excavation (here a horizontal gallery or “drift”), based on geometric and probabilistic concepts. This research is conducted in the framework of studies on the isolation properties of a geological claystone repository for radioactive waste disposal (MeuseHaute Marne Underground Research Laboratory, France). The overall objective is to quantify equivalent “upscaled” hydro-mechanical properties of the disturbed porous rock, and to analyze the effect of fracturing on macroscale rock properties, e.g., equivalent permeability [1], mechanical stiffnesses, and hydro-mechanical couplings. The present work focuses on the mathematical and probabilistic representation of fractures, and their spatial distributions around the drift. The methodology is as follows. We use a mixed random/deterministic fracturing model, comprising: (i) a statistical set of 10 000 small planar joints with radially inhomogeneous statistics (size, aperture, and spatial density increasing near the wall), and (ii) a deterministic set of large curved “chevron” fractures, periodically spaced along the axis of the gallery according to a 3D chevron pattern (or 3D herringbone pattern). In particular, the spatial statistics of the small planar joints in 3D space were worked out using inhomogeneous Poisson process and other concepts from geometric probability. We also developed a new geometric model for the large curved chevron fractures, in terms of a deterministic parametric surface (a modified conoïd). In this short paper, some of the resulting fracture patterns are shown graphically; the interested reader may refer to [1] for other mathematical and technical details.