Crack aperture statistics and pore space fractal geometry of westerly granite and rutland quartzite: Implications for an elastic contact model of rock compressibility

Micromechanical models based on the elastic contact of nominally flat pore surfaces covered with asperities have been formulated by other workers to analyze the effect of microcracks on the elastic and transport properties of rock. In this study we employ quantitative stereology techniques to measure the crack surface area per unit volume as a function of microcrack aperture and then test quantitatively the Hertzian contact model developed by Walsh and Grosenbaugh (1979). Although Westerly granite and Rutland quartzite have similar pressure-volumetric strain curves and crack porosity, the pore microstructures differ significantly and have features characteristic of igneous and metamorphic rocks, respectively. Our data show that the crack surface area decreases as a function of crack aperture and therefore imply that the exponential distribution used previously by Walsh and Grosenbaugh is not appropriate. However, the Hertzian contact model describes adequately the pressure dependence of compressibility when the appropriate crack aperture statistics are used. The crack aperture statistics data are also used to infer the fractal dimension of pore space roughness. The aperture statistics for both rocks can be fitted well with a power law, and fractal dimensions of 2.843 and 2.804 can be assigned to 85% and 65% of the crack surface of Westerly granite and Rutland quartzite, respectively.

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