Reconciliation of contrasting theories for fracture spacing in layered rocks

Natural and man-made brittle layers embedded in a weaker matrix and subjected to layer-parallel extension typically develop an array of opening-mode fractures with a remarkably regular spacing. This spacing often scales with layer thickness, and it decreases as extension increases until fracture saturation is reached. Existing analytical one-dimensional (1-D) 'full-slip' models, which assume that interfacial slip occurs over the entire length of the fracture-bound blocks, predict that the ratio of fracture spacing to layer thickness at saturation is proportional to the ratio of layer tensile to interface shear strength (T/s). Using 2-D discontinuum mechanical models run for conditions appropriate to layered rocks, we show that fracture spacing at saturation decreases linearly with decreasing T/s ratio, as predicted by 1-D models. At low T/s ratios (ca.