Effect of mechanical interactions on the scaling of fracture length and aperture

Abstract

The aperture (or opening) of a fracture indicates the energy available for fracture growth and controls fracture permeability. The relationship between aperture and fracture length can therefore be used to infer the factors affecting fracture formation at different length scales and is of practical importance to hydrogeologists and petroleum engineers. A recent study1 of the scaling properties of tensile fractures in the Krafla fissure swarm, Iceland, revealed a distinct break in slope in the aperture–length scaling relationship, corresponding to fractures a few metres in length: this break in slope was interpreted qualitatively as indicative of non-universal, scale-dependent growth mechanisms1. Here we show, using quantitative fracture simulations, that the observed non-universal scaling of fracture apertures can be reproduced without recourse to multiple growth mechanisms. We argue that the break in slope is instead intrinsic to the fracturing process and represents the maximum length scale at which the apertures of smaller fractures are affected by stress perturbations induced by larger fractures.