Simple mathematical model of a rough fracture

Abstract

A simple mathematical model of rough-walled fractures in rock is described which requires the specification of only three main parameters: the fractal dimension, the rms roughness at a reference length scale, and a length scale describing the degree of mismatch between the two fracture surfaces. Fractured samples, collected from natural joints and laboratory specimens, have been profiled to determine the range of these three parameters in nature. It is shown how this surface roughness model can be implemented on a computer, allowing future detailed study of the mechanical and transport properties of single fractures and the scale dependence of these properties. 5941

Flow in rock fractures: The local cubic law assumption reexamined

“…The relation between the two surfaces is the one suggested by several recent studies [Brown et al, 1986;Plourabou• et al, 1994;Brown, 1995]' they are well mated on the larger scales and unmated on the smaller, local scales. The transition length between mated and unmated behavior is -1/X/-N of the lattice size, so that the complete surface contains a large number of No mechanical model of deformation is assumed; wherever the surfaces "interpenetrate," a contact (i.e., aperture zero) is shown [Brown, 1987].…”

Fluid flow in synthetic rough fractures and application to the Hachimantai geothermal hot dry rock test site

“…Up until now the synthetic fractures so used have been created from unmatched fractal surfaces [Arnadei and lllangsekare, 1994]. Recently, however, Brown [1995] has reported a simple code to create more realistic synthetic rock fractures. This code is based upon that of Saupe [1988] but includes simple single cutoff mismatching that allows the two surfaces that make up the fracture to be perfectly matched at long wavelengths (above a mismatch wavelength) and to behave independently at shorter wavelengths.…”

“…Fractal dimensions were calculated from the power spectra by linear fitting in log-log space and are given with their associated errors in Tables 1 and 2 Table 2). A probability analysis was carded out to provide the probability density and cumulative probability for each individual profile and aperture, as well as for stacked profiles and apertures [Brown, 1995;Russ, 1994]. These analyses were carded out with reference to an arbitrary datum plane defined by the profilometer and the profiling jig.…”

“…Perfect matching, which is never achieved in real fractures, is represented by a ratio value of zero. •Ilfis plot has been used to measure the two mismatch wavelengths defined by Brown [1995] (Table 2) rameter in such a way that any initial errors in its estimation from the profiled data do not affect the resulting synthetic fracture.…”

“…There are also flow measurements made in the field [e.g.. Hayashi and Abd, 1989]. The effect of the surface and aperture geometry on fluid flow has also been studied extensively by modeling [Brown, 1987[Brown, , 1989Brown et al, 1995;Pyrak-Nolte et al, 1988]. A conunon approach has been to measure the surface heights of a fracture by profilometry and then to use the resulting profiles as input to flow modeling programs that solve Reynolds equation [Brown, 1989;Lee et aL, 1996].…”