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. Experimental studies of this phenomenon 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. This is in marked contrast to existing theories of fracture, such as the stress-transfer theory, which predict that spacing should decrease with increasing strain ad infinitum. Recently, 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 to engineering.