Field Determination of the Three-Dimensional Hydraulic Conductivity Tensor of Anisotropic Media: 2. Methodology and Application to Fractured Rocks

TLDR: In this paper, the results of cross-hole tests conducted in anisotropic porous or fractured media are analyzed graphically, where the injection and monitoring intervals are short relative to the distance between them.

Abstract: The analytical solutions developed in the first paper can be used to interpret the results of cross-hole tests conducted in anisotropic porous or fractured media. In the particular case where the injection and monitoring intervals are short relative to the distance between them, the test results can be analyzed graphically. From the transient variation of hydraulic head in a given monitoring interval, one can determine the directional hydraulic diffusivity, Kd(e)/Ss, and the quantity D/Ss, by curve matching. (Here Kd(e) is directional hydraulic conductivity parallel to the unit vector, e, pointing from the injection to the monitoring interval, Ss is specific storage, and D is the determinant of the hydraulic conductivity tensor, K.) The principal values and directions of K, together with Ss, can then be evaluated by fitting an ellipsoid to the square roots of the directional diffusivities. Ideally, six directional measurements are required. In practice, a larger number of measurements is often necessary to enable fitting an ellipsoid to the data by least squares. If the computed [Kd(e)/ss]½ values fluctuate so severely that a meaningful least squares fit is not possible, one has a direct indication that the subsurface does not behave as a uniform anisotropic medium on the scale of the test. Test results from a granitic rock near Oracle in southern Arizona are presented to illustrate how the method works for fractured rocks. At the site, the Oracle granite is shown to respond as a near-uniform, anisotropic medium, the hydraulic conductivity of which is strongly controlled by the orientations of major fracture sets. The cross-hole test results are shown to be consistent with the results of more than 100 single-hole packer tests conducted at the site.