Opening-mode fractures in siliciclastic and carbonate host rocks from different geologic settings consistently show power-law aperture-size distributions when measured along one-dimensional scanlines. Exponents (slopes) and pre-exponential coefficients (intensities) of the power laws, were compared in order to constrain the range of fracture intensities of various aperture sizes over the observation scales. The coefficients range over two orders of magnitude, from 0.1 to 62.4, and the exponents range from -0.45 to -1.36. On a compilation plot of power laws a broad wedge-shaped envelope defines the natural range of frequencies of fractures for aperture sizes from approximately 1000 to 0.01 mm. There is an inverse correlation between the coefficient and exponent for most of the data sets. Power laws having steep slopes tend to have low intensities, whereas power laws having shallow slopes tend to have higher intensities. There are, however, a few exceptions to this correlation. The reasons for the correlation and the departures from it are considered in the light of geologic and mechanical properties at the time of fracture formation for each case. The subcritical crack index, mechanical layer thickness, total strain and strain rate are all likely controls over the relative proportion of narrow to wide fractures in a population.
1. INTRODUCTION
Empirical studies have shown that the aperture sizes of opening-mode fractures within a single set are self-organized into power-law distributions [1-3]. Power-law aperture-size distributions ranging over five orders of magnitude have been reported in sandstone and limestone [1] and over three orders of magnitude in dolomites [4]. The range over which power-law distributions apply is typically that observed at the field outcrop scale down to microfractures; on the order of 1 m to 1 µm. Small and large opening-mode fractures that have the same orientation may be different size fractions of the same fracture set.
Power-law descriptions of fracture aperture populations take the form: F = ab-c, where F is cumulative fracture frequency, a is the coefficient, b is the fracture aperture, and c is the exponent of the power-law relationship. At any given aperture size, the intensity of fractures is defined by the pre-exponential coefficient, which governs the position of the curves on the ordinate, and the exponent, which is the slope of the curves and is negative. The exponent reflects the relative proportions of wide and narrow fractures in the population. A small exponent (shallow slope) indicates a fracture population with few narrow fractures relative to wide fractures, whereas a large exponent (steep slope) indicates a population with a large number of narrow fractures relative to wide fractures. The values of the exponent and coefficient are different for different fracture sets but the range and reasons for the variation have not been addressed previously.
The aim of this contribution is to present a compilation of opening-mode fracture aperture-size data sets so that the aperture-size distributions from different rocks may be compared and the range of intensities of naturally occurring fractures of different aperture sizes may be constrained.
