Percolation Theory: A Model For Rock Fracture?

Abstract

Recent theoretical advances have confirmed the status of the so-called ‘scaling relations’ for percolation theory. On this pretext, their implications for the treatment of rock fracture are re-examined. Comparison between predicted and observed b-values suggest that classical percolation may be a less appropriate model than had been anticipated. Directed variants, such as first-passage, oriented and invasion percolation, may prove more successful, but at present little firm theoretical knowledge exists concerning their cluster properties. At the present time the simpler branching process appears to offer as effective a model as any for rock fracture. Major ambiguities of interpretation prevent any clear conclusions from being drawn.