A universal power-law scaling exponent for fracture apertures in sandstones

Abstract

A high-resolution data set of kinematic aperture (opening displacement) of opening-mode fractures, from large (up to 2 m long) quartz-cemented sandstone samples, shows that microfractures are ubiquitous and that most natural-fracture sets are better fit by power-law size distributions than by exponential, normal, or log-normal distributions. The data set includes 3822 fractures within 68 scanlines from eight formations on three continents. Kinematic apertures were measured along scanlines using scanning electron microscope–based cathodoluminescence (SEM-CL) and, for field data, using a hand lens. Microtextural evidence from SEM-CL shows that power law–distributed fractures typically have crack-seal texture and are composed of opening increments having a narrow (characteristic) aperture size range. In contrast, rare non-power-law–distributed fracture populations lack crack-seal texture. Power-law exponents, as measured in one dimension, have values of −0.8 ± 0.1. Most variation among fracture sets results from power-law coefficients, which constitute a scale-invariant measure of fracture intensity. We show how observed scaling patterns can be used to improve estimations of large-fracture spacing in cases where fracture sampling is limited, as by the width of cores. The low (