Connectivity of joint networks with power law length distributions

Over the range of fracture spatial densities commonly observed in the field, existing effective medium models for network connectivity yield inconsistent results because the connectivity depends on both the density and length distribution of the joints. Field observations indicate that joint lengths often follow a power law length distribution. Requiring the frequency of joint lengths to decrease with increasing length and the total area of the joints to be finite suggests approximate upper and lower bounds on the power law exponent which are consistent with observed distributions. The appropriate relationship between connectivity and density is investigated numerically. Results motivate a new measure of fracture intensity, the effective fracture density, and the development of a new approach toward a closed-form prediction of connectivity using measurable parameters. Although limited, model predictions compare favorably to the conductivities of networks simulated using a geomechanical model and observed in the field.