b.
With the parallel plate assumption, the conductivity of a single
under normal loading was investigated by Witherspoon et al. (1980) performing flow tests on artificially induced tension fractures. A friction factor ‘‘f’’ was introduced and included the ideal cubic law in order to take the roughness effect into consideration. They reported that f P 1 in the case of roughness and it varied from 1.04 to 1.65 in their study. This friction factor was found very successful to account for the effects of deviations from the ideal cubic law concept due to roughness. Interestingly, this range of ‘‘f’’ is reminiscent of the surface fractal dimension that was measured in the past (Develi and Babadagli, 1998) and used in the present study.
Further studies were based on stochastic description of the roughness and modelling flow in such fracture systems by gridding them with assigned fracture apertures (Neuzil and Tracy, 1981; Brown and Scholz, 1985a;