A theoretical analysis shows that electrical conductivity along fractures in a saturated porous rock is a function of many factors: fluid and rock conductivities, initial fracture aperture and contact area, fracture surface geometry (asperity height distribution and tip curvature), elastic moduli of the rock, and confining pressure or normal stress acting across the fracture. The conductivity in the fracture plane decreases approximately in proportion to log pressure, but the conductivity is influenced by the increased contact area, and hence flow-path tortuosity, along the fracture surface at elevated pressures. Electrical conductivity in fractures is more affected by flow-path tortuosity than is permeability.
The dependence on pressure was tested using laboratory measurements of conductivity through split cores containing ground, saw-cut surfaces in a variety of rocks under confining pressures to 200 MPa. The conductivity decreased approximately in proportion to log pressure (there was little effect of increased contact area, and hence tortuosity), which suggests that the contact area may not exceed a few percent of the total apparent area. Measurements of gas permeability through the same split cores showed that when the asperity deformation remained largely elastic, permeability and conductivity had a power of 3 relationship. When asperity collapse occurred, as in a dolomitic marble, the powerlaw relation no longer held; permeability decreased more rapidly under pressure than did conductivity. The different influences of porosity and flow aperture may account for the different behaviors of the two transport properties. The theory suggests a number of ways in which fracture parameters may be extracted from field data. Some of the methods rely on the scale dependence and pressure dependence of the fractured-rock conductivity; other methods require correlating between different physical properties, such as seismic velocity, which are influenced by the presence of fractures.