| Summary: | Sets of natural opening-mode fractures in sedimentary rocks may show a variety of types of aperture-size distributions. A frequently documented size distribution type, in the literature and in data presented here, is the power law. The emergence of power-law distributions of fracture aperture and length sizes has been simulated using various quasi-mechanical fracture-growth routines but models based on linear-elastic fracture mechanics rarely produce such patterns. I collected a fracture-size dataset of unprecedented size and resolution using core and field methods and scanning electron microscope-based cathodoluminescence (SEM-CL) images. This dataset confirms the prevalence of power laws with a narrow range of power-law exponents among fractures that contain synkinematic cement. Organized microfractures are ubiquitous in sandstones. A fracture-growth simulation I devised reproduces observed size-scaling patterns by distributing fracture-opening increments among actively growing fractures. The simulated opening increments have a uniform size, which can be specified; uniform opening size is consistent with observations of narrow ranges of micron-scale widths of opening increments within crack-seal texture in natural fractures. Thus power-law size scaling of natural fractures can be explained using non-power-law (uniform-sized) opening increments, arranged using rules designed to simulate the effects of cement precipitation during fracture opening. A fundamental shortcoming of previous models of fracture-set evolution is the absence of a test because only natural fracture end states, not growth histories, could be measured. Using a technique to constrain fracture timing based on fluid inclusion microthermometry and thermal history modeling, I tested growth models by reconstructing the opening history of a set of natural fractures in the Triassic El Alamar Formation in northeast Mexico. The natural-fracture data show that, consistent with simulations, new microscopic fractures are continually introduced during natural fracture pattern evolution. As well, larger fractures represent sites of concentrated reactivation, although smaller fractures may be reactivated after long periods of quiescence. The pattern likely arises through feedback between fracture growth and the mechanically adhesive effects of contemporaneous fracture cement deposition. The narrow range in power-law exponents documented among fractures can help improve estimates of meter-scale large-fracture spacing where limited fracture samples are available. === text
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