Fluid flow through rock joints is commonly described by the parallel plate model where the volume flow rate varies as the cube of the joint aperture. However, deviations from this model are expected because real joint surfaces are rough and contact each other at discrete points. To examine this problem further, a computer simulation of flow between rough surfaces was done. Realistic rough surfaces were generated numerically using a fractal model of surface topography. Pairs of these surfaces were placed together to form a “joint” with a random aperture distribution. Reynolds equation, which describes laminar flow between slightly nonplanar and nonparallel surfaces, was solved on the two‐dimensional aperture mesh by the finite‐difference method. The solution is the local volume flow rate through the joint. This solution was used directly in the cubic law to get the so‐called “hydraulic aperture.” For various surface roughnesses (fractal dimensions) the hydraulic aperture was compared to the mean separation of the surfaces. At large separations the surface topography has little effect. At small separations the flow is tortuous, tending to be channeled through high‐aperture regions. The parameter most affecting fluid flow through rough joints is the ratio of the mean separation between the surfaces to the root‐mean‐square surface height. This parameter describes the distance the surface asperities protrude into the fluid and accounts for most of the disagreement with the parallel plate model. Variations in the fractal dimension produce only a second‐order effect on the fluid flow. For the range of joint closures expected during elastic deformation these results show that the actual flow rate between rough surfaces is about 70–90% of that predicted by the parallel plate model.

The mechanical and hydraulic behavior of discontinuities in rock, such as joints and faults, depends strongly on the topography of the contacting surfaces and the degree of correlation between them. Understanding this behavior over the scales of interest in the earth requires knowledge of how topography or roughness varies with surface size. Using two surface profilers, each sensitive to a particular scale of topographic features, we have studied the topography of various natural rock surfaces from wavelengths less than 20 microns to nearly 1 meter. The surfaces studied included fresh natural joints (mode I cracks) in both crystalline and sedimentary rocks, a frictional wear surface formed by glaciation, and a bedding plane surface. There is remarkable similarity among these surfaces. Each surface has a “red noise” power spectrum over the entire frequency band studied, with the power falling off on average between 2 and 3 orders of magnitude per decade increase in spatial frequency. This implies a strong increase in rms height with surface size, which has little tendency to level off for wavelengths up to 1 meter. These observations can be interpreted using a fractal model of topography. In this model the scaling of the surface roughness is described by the fractal dimension D. The topography of these natural rock surfaces cannot be described by a single fractal dimension, for this parameter was found to vary significantly with the frequency band considered. This observed inhomogeneity in the scaling parameter implies that extrapolation of roughness to other bands of interest should be done with care. Study of the increase in rms height with profile length for two extreme cases from our data provides an idea of the expected variation in mechanical and hydraulic properties for natural discontinuities in rock. This indicates that in addition to the scaling of topography, the degree of correlation between the contacting surfaces is important to quantify.

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

The physical contact between two rough surfaces is referred to as a “joint,” and the deformation of such a joint under normal stress is called the “joint closure.” Toward better understanding of joint closure, we present a theory of contact between two random nominally flat elastic surfaces. This theory is a more general form of a theory presented previously by others for the elastic contact of a rough surface and a flat surface. In agreement with the previous theory we show that the joint closure property depends as much on the details of the surface topography as on the elastic properties of the material. To apply these results by using linear surface profiles requires mapping of profile information to three dimensions. The mapping techniques described here require the probability density function for the contacting surfaces to be approximated well by either a Gaussian distribution or an inverted chi‐square distribution. Laboratory experiments on ground surfaces of glass samples were done to test the theory. Both joint closure and surface topography were measured. In most cases, experimental results agreed quantitatively with predictions of the theory. However, in experiments on the smoothest surfaces, sample preparation problems often resulted in surfaces with a domed shape. These surfaces did not fit the assumptions of the theory, but the observed deviations from the theory were consistent with this domed shape. Surface topography measurements suggest that many surfaces are statistically similar. This implies that the success of the theory in predicting joint closure does not depend on a particular sample preparation technique. Therefore the theory should be valid for all nominally flat elastic surfaces. The form of the power spectrum implies that the surface topography and thus the joint closure depend on sample size.

The roughness of fault surfaces is important in the mechanics of fault slip and could play a role in determining whether sliding occurs via earthquakes or fault creep. We have made preliminary measurements of the power spectral density of several fault surfaces over the wavelength range from 10 -5 to 1 m. using field and laboratory scale profilimeters.