Intermittency of Rock Fractured Surfaces: A Power Law

Abstract

Roughness of rock fractured surfaces is one of the most important factors controlling fluid flow in rock masses. Roughness quantification is of prime importance for modelling the flow of ground waters as well as reservoir fluid mechanics. In this study, with the aid of high-resolution 3D X-ray CT scanning and image processing techniques, the roughness of four different rock types is reconstructed with a resolution of 16.5 microns. Moreover, the correlation and structure functions are used to analyse height fluctuations as well as statistical intermittency of the studied rock fractured surfaces. It is observed that at length scales smaller than a critical length scale, fractures surfaces are correlated and show multifractality. Monofractals are neither intermittent nor correlated; hence, a meaningful link between statistical intermittency and the correlation function of multifractals is expected. However, a model that considers this relationship and predicts multifractal spectra of disordered systems is still missing. A simple power law that can exactly forecast the multiscaling spectrum of rock fracture process zone is being introduced. It is explained how the exponent of this power function λi is related to the crossover length of correlation function ξ, and how this critical length scale can be objectively identified.