Percolation of the interacting elastic stress fields of aligned cracks as an alternative explanation of critical crack densities

Abstract

AbstractThe concept that the lithosphere is in a general critical, or near-critical, mechanical state has previously assumed spatial intersection of fractures at the critical point. This paper provides an initial basis for an alternative mechanism in which elastic interactions between aligned, open, spatially separated (micro-)cracks in rock can, by themselves, lead to a continuous phase change at a critical threshold of crack density lower than that required for crack coalescence. The existence of a critical density of aligned cracks is first demonstrated on a regular 2D hexagonal grid when subjected to a central stress perturbation; at this critical density the elastic tensile stress interactions have a long-range effect. From the results of those calculations an approximation of the tensile stress field around a crack in 3D is provided. The percolation behaviour of such 3D bodies is discussed and a critical crack density in 3D for elastic interaction of 0.035 is deduced. This falls within the range of crack densities (0.015–0.045) interpreted from observations of shear-wave splitting in many different rocks. The possibility that critical crack interactions can be mostly elastic provides one explanation of the long-range nature of correlations in flowrate fluctuations in oilfields without large-scale seismicity.