Crack aperture and hydraulic conductivity tensors for cracked crystalline rock masses

Abstract

A hydraulic conductivity tensor for a cracked crystalline rock mass was formulated in closed form as a function of the following parameters: 1) the mean and standard deviation in a lognormal distribution of crack apertures, 2) the number of hydraulically conductive cracks intersected by a scanline per unit length and correction term depending on the scanline direction, 3) the fabric tensor determined by the statistical distribution of unit vectors normal to the crack surfaces, and 4) the in-situ stress state. A key point is that all these parameters can be determined in actual fields by analysing the data obtained from conventional field surveys. Using the data previously reported, the mean values of some involved parameters were suggested for crystalline rock masses to give a useable equation in fields. The number of conductive cracks intersected by a scanline is the only remaining variable for estimating the hydraulic conductivity at a given site and varies from site to site due to geological histories and situations. To do this, however, we needed one crucial assumption that the hydraulically conductive cracks could be identified as “open” or “distinct” on images taken by a borehole TV camera. The proposed equation agrees well with the depth-dependent hydraulic conductivities at four sites in Japan, USA, and Canada. One exception was also reported at a site in Japan, where the granite matrix was critically weathered, and hence, cracks were no longer the major flow paths.