Fracture spacing in layered rocks: a new explanation based on the stress transition

Opening-mode fractures (joints and veins) in layered sedimentary rocks often are periodically distributed with spacings linearly related to the thickness of the fractured layer. To better understand this linear relation, we have investigated the stress distribution between two adjacent opening-mode fractures as a function of the fracture spacing to layer thickness ratio using a three-layer elastic model with a fractured central layer. The results show that when the fracture spacing to layer thickness ratio changes from greater than to less than a critical value (approximately 1.0) the normal stress acting perpendicular to the fractures changes from tensile to compressive. This stress state transition precludes further infilling of fractures unless there are existing flaws and/or the fractures are driven by an internal fluid pressure or other mechanisms. Hence, for fractures driven by tectonic extension, the critical fracture spacing to layer thickness ratio defines a lower limit, which also defines the condition of fracture saturation. The critical value of the fracture spacing to layer thickness ratio is independent of the average strain of the fractured layer, and it increases with increasing ratio of Youngʹs modulus of the fractured layer to that of the neighboring layers. The critical value increases with increasing Poissonʹs ratio of the fractured layer, and with increasing overburden stress (depth), but it decreases with increasing Poissonʹs ratio of the neighboring layers. For representative variation of the elastic constants of the fractured layer and the neighboring layers, and overburden stress, the critical fracture spacing to layer thickness ratio varies between 0.8 and 1.2. This range encompasses the often cited spacing to layer thickness ratios in the literature for well-developed fractures sets.