Failure Properties of Fractured Rock Masses as Anisotropic Homogenized Media

Abstract

Conceived as a potential alternative to the classical design methods employed for analyzing the stability of jointed rock structures, the homogenization approach advocated in this contribution stems from the intuitive idea that, from a macroscopic point of view, a rock mass intersected by a network of joint surfaces may be perceived as a homogeneous medium. The strength criterion of the latter can be theoretically determined from the knowledge of the failure conditions of the individual constituents, namely, rock matrix and joint interfaces. It turns out that, as could be expected, this criterion is of the anisotropic cohesive frictional type, as shown by the closed-form expressions obtained in the case of two mutually orthogonal joint families. While it appears that such a homogenization concept is well suited for densely fractured rock masses, a significant “scale effect” may prevail in the case of structures involving a relatively low number of joints. It is conjectured that a possible way to capture such a scale effect, while still keeping advantage of the homogenization approach, is to adopt a description of the fractured rock mass as a Cosserat or micropolar continuum. This is achieved by proposing a formulation of the macroscopic failure condition in terms of stresses and couple stresses. Such a generalized homogenization method is then applied to a simple illustrative example.