Applications of the cluster statistics

Abstract

Applying cluster statistics of percolation theory to a cumulative local resistance distribution allows the calculation of the distribution of controlling, or bottleneck, resistances that govern flow over continuously connected paths from one side of a finite system to the other. The scale dependence of the distribution of hydraulic conductivity values can thus be obtained. When applied to a problem with significant anisotropy, it is possible to generate an expected variability of hydraulic conductivity measurements as a function of spatial scale for a given suite of geological parameters. In Chap. 10 parameters were identified that could produce the observed scale dependence of the median hydraulic conductivity value for approximately 700 experiments conducted in fractured media. In this chapter, it is shown that the same parameters also generate the variability in the individual units in which the experiments were performed. © 2014 Springer International Publishing Switzerland.