Scaling of fracture connectivity in geological formations

A new method to quantify fracture network connectivity is developed and applied to analyze two classical examples of fault and joint networks in natural geological formations. The connectivity measure accounts for the scaling properties of fracture networks, which are controlled by the power law length distribution exponent a, the fractal dimension D and the fracture density. The connectivity behavior of fracture patterns depends on the scale of measurement, for a < D + 1, but is independent of scale for a > D + 1. Analysis of the San Andreas fault system shows that a < D + 1 and that the connectivity threshold is reached only at a critical length scale. In contrast, for a typical sandstone joint pattern, a approximate to D + 1, which is on the cusp where the connectivity threshold is highly sensitive to the minimum fracture length in the system.