Explanation far fracture spacing in layered materials

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(1-4). 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(11-13,14) to engineering(1,2,6,15,16).