Depth-dependent hydraulic conductivity tensor for jointed granite

Abstract

Stress-dependent hydraulic conductivity tensor is formulated in a closed form on the basis of Oda's permeability tensor and Bianchi & Snow's proposal for change of the crack aperture. Using a simple cracked model, a general equation is derived to obtain the hydraulic conductivity tensor as a function of depth and the coefficient of earth pressure at rest. The general trend of the equation is consistent with the in-situ hydraulic conductivity values measured at various sites. Conductivity itself does not have any practical meaning unless the state of stress is concurrently specified. Anisotropy in the hydraulic conductivity tensor is mainly related to the state of stress given by the earth pressure coefficient rather than the crack geometry, particularly in the cases where three orthogonal sets of joints are observed. Anisotropy is magnified in two dimensions because of excessive confinement of the flow direction. Additional procedures should be performed when the results obtained from two-dimensional analyses are generalized for three-dimensional real sites. The hydraulic conductivity K0 at the earth surface and γ′H for controlling the aperture of cracks are proposed as index measures for characterizing a given site from a comprehensive point of view.