The scaling of hydraulic conductivity in rock fracture zones

Beyond the scale of a few meters, fracture traces as viewed on aerial photographs represent fracture zones. Thus for bulk fractured rock permeability, the hydraulic properties of fracture zones are important. Here, observations on joint zones in sandstones from western Norway are used to build a quantitative model relating joint zone length and effective hydraulic conductivity. Using simple rules for hydraulic conductors in series and parallel applied to joint zone geometry, the 'effective' hydraulic aperture (the aperture of a single parallel-walled channel that conducts the same flow) is estimated for 72 joint zones of known length. A power law relation between trace length, l, and effective hydraulic aperture, b(e), with an effective exponent of around 0.27 is found which may extend to kin scales. This exponent contrasts with values of 0.5 to 2.0 reported for veins.