On the cubic law and variably saturated flow through discrete open rough-walled discontinuities

Abstract

Fracture flow is fairly well documented with the widespread application of, for instance, the cubic law and assumed smooth parallel plate model. Geometrical intricacies such as aperture, roughness and infill do however significantly influence the validity of the cubic law with even its application to smooth parallel systems being contestable. Rock mechanical discontinuity surveys provide valuable information regarding the discontinuity geometry that can likely contribute to the evaluation of flow through individual fractures with variable properties. The hydraulic aperture is available for the transmission of flow, while normal and shear stresses alter discontinuity properties over time. In this, numerous advances have been made to better accommodate deviations of natural discontinuity geometry to that of smooth parallel plates and at partial saturation. The paper addresses these advances and details conditions under which the cubic law, even in local form, fails to adequately estimate the hydraulic properties. The role of roughness in open discontinuities is addressed in particular, as contact areas and high amplitude roughness cause most extensive deviation from the cubic law. Aperture of open fractures still governs hydraulic properties, but inertial forces control flow in very rough fractures, in which instances the applicability of the cubic law should be revisited. Open questions are finally posed, assessment of which will contribute significantly to the understanding of flow through individual discontinuities as well as fracture networks.