Explanation for fracture spacing in layered materials

Abstract

The spacing of opening-mode fractures in layered materials—such as certain sedimentary rocks and laminated engineering materials—is often proportional to the thickness of the fractured layer^1,2,3,4. Experimental studies of this phenomenon^1,5 show that the spacing initially decreases as extensional strain increases in the direction perpendicular to the fractures. But at a certain ratio of spacing to layer thickness, no new fractures form and the additional strain is accommodated by further opening of existing fractures: the spacing then simply scales with layer thickness, which is called fracture saturation^5,6. This is in marked contrast to existing theories of fracture, such as the stress-transfer theory^7,8, which predict that spacing should decrease with increasing strain ad infinitum. Recently^9,10, two of us (T.B. and D.D.P.) have used a combination of numerical simulations and laboratory experiments to show that, with increasing applied stress, the normal stress acting between such fractures undergoes a transition from tensile to compressive, suggesting a cause for fracture saturation. Here we investigate the full stress distribution between such fractures, from which we derive an intuitive physical model of the process of fracture saturation. Such a model should find wide applicability, from geosciences^11,12,13,14 to engineering^1,2,6,15,16.