Surface roughness of natural rock fractures : implications for prediction of fluid flow

Where open, connected fractures are present, they dominate both fluid flow and transport of solutes, but the prediction of hydraulic and transport properties a priori has proven exceedingly difficult. A major challenge in predicting solute transport in fractured media is describing the physical characteristics of a representative surface that is appropriate to modeling. Fracture aperture, roughness, and channeling characteristics are important to predict flow and transport in hard rock terrains. In areas with little soil cover, fracture mapping can indicate areas or directions of greater permeability but not the magnitudes. Both cover and complex geology can limit mapping. Hand samples are generally available and upscaling from their properties would be highly beneficial. Assessing the impact of roughness on field-scale fluid flow through fractured media from samples of natural fractures on the order of 100cm² assumes a relationship between fracture morphology and discharge is either scale invariant or smoothly transformable. It has been suggested that the length scale that surface roughness significantly contributes to the discharge falls within the size of a typical hand sample, but few data exist to support extension of small-scale relationships to larger scales. I analyze the results of flow tests on a single fracture through a 60 x 30cm block of rhyolitic tuff. The results are compared with relationships of smaller samples in a similar tuffs and granites. The data are processed to yield regularly gridded surface elevations. Describing roughness as a ratio of surface area to footprint, variances of the roughnesses of surface covering equivalently sized square samples are plotted against sample size to determine if a representative surface exists. For specimens of fractures measuring up to 25 x 29cm, a 3.2 x 3.2cm sample of granite with an iron oxide/clay fracture skin yields a reasonable expression of the roughness of the entire surface. The number of data points included in a sample of this size transcends skin type, composition and grain/crystal size. The results suggest that the unmodified cubic law is valid for the range of gradients expected in the field using the geometric mean of areal aperture data to estimate hydraulic aperture. The data also indicate that fracture aperture is not well predicted by single aperture measurements or even by averaging along a particular scan line; three-dimensional laboratory analysis and/or field testing are required. There may be a suitable scale of data for upscaling fracture roughness on the order of 10cm². However, due to mismatch between top and bottom surfaces inherent in natural fractures, aperture samples are not consistent across the specimen and cannot be scaled. Upscaling of other factors, such as flow channeling, remain to be tested.