Connectivity of joint networks with power law length distributions

Abstract

Abstract. 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. [1997, 1998] but extend this previous work in several respects. We redefine and analyze the connectivity of the network to reflect the conductive properties of the network rather than just the probability that it percolates. Furthermore, 2661

Modeling of Groundwater Flow and Radionuclide Transport at the Climax Mine sub-CAU, Nevada Test Site

“…The presence of a power-law decay trend where α is less than 2 indicates that fracture lengths are scale invariant and that a "characteristic" length scale is undefined for fractures at the Climax stock. This observation is consistent with other studies of natural fracture networks where power-law distributions are commonly assigned to fracture length and α is thought to range between 1 and 3 (e.g., Bour and Davy, 1997;Renshaw, 1999;Bonnet et al, 2001). …”

Hydrogeologic Characterization of Fractured Rock Masses Intended for Disposal of Radioactive Waste

“…Fracture density is highly dependent on the distribution of fracture lengths in a model domain where the density at the percolation threshold increases with increasing values of a (Darcel et al, 2003;Reeves et al, 2008b;Renshaw, 1999). This will become apparent in the fracture network examples in the next section.…”

“…with a power law exponent, a, that ranges between 1 and 3 in natural fracture networks (Bonnet et al, 2001;Bour & Davy, 1997;1999;Renshaw, 1999). C is a constant based on l min and a.…”

Percolation-theory and fuzzy rule-based probability estimation of fault leakage at geologic carbon sequestration sites

“…Studies on the connectivity of faults include both faults with constant length (Balberg et al 1984(Balberg et al , 1991Gueguen and Dienes 1989;Stauffer and Aharony 1992) and faults with a power-law distribution Davy 1997, 1998;Renshaw 1999). Here, we will adopt some results from the study of Bour and Davy (1997) to find the critical density of a fault system.…”