Electrical conductivity of fractured media: A computational study of the self-consistent method

Effective medium theory can be used to link conductivity estimationmethods with prior knowledge about the distributionof fractures in the investigated geological structure. In the literature,little work has been presented on assessing the accuracyof effective medium approximations for dense networksof finite-sized fractures. We present here a systematic computationalstudy, comparing the conductivity predictions ofthe popular self-consistent method with results from numericalfinite-element simulations. Our results show that the selfconsistentmethod is accurate within acceptable error boundsfor a range of parameter values, in some cases even beyondthe percolation limit. We also compare the percolation thresholdspredicted by self-consistent theory with the thresholds obtainedby a numerical percolation algorithm. For the cases wehave studied, the percolation thresholds agree to a remarkabledegree