Fractures change mechanical properties of rock masses, which can be a concern for many rock-engineering applications like underground repository and support design, slope stability or mine caving. We propose to calculate, for typical hard rock conditions, the link between elastic properties and the complete fracture network system through its relevant geometrical properties. We show that the resulting effective properties depend on stress regime, fracture size and orientation. We finally apply the model to site statistical DFN models defined from investigations led in Scandinavia for future underground storage of spent nuclear fuel. For these geological conditions, we show that rock mass effective elastic properties are statistically dependent on scale. This evolution derives from the multi-scale nature of the fracture size DFN model that controls the scale evolution of the statistical occurrences of the largest fractures.

1 Introduction

Assessing effective mechanical properties of jointed rock mass is a prerequisite to many geotechnical applications. How and up to which extent DFNs control the rock mass properties are important issues addressed through both empirical approaches and theoretical and numerical approaches. The seminal papers of Griffith (1920) and Irwin (1958) acknowledge the importance of fractures in controlling the embedding rock mass properties. Analytical solutions exist for describing the stress field and displacement vector generated by a frictionless disk-shaped crack (Fabrikant et al. 1989). They can then be used to derive the effective elastic properties of crack networks with a few simplifying assumptions, like considering a uniform effect of fracture-to-fracture interactions in the fracture plane and neglecting the role of fracture intersections (see review in Kachanov (1993)). In tensile conditions, recent advances in effective elastic media improved the relation between the fracture density and the Young modulus of fractured rock (Le Goc et al. 2014). The solution writes as:

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