Investigating the effect of mechanical discontinuities on joint spacing

In rocks without systematic mechanical discontinuities (e.g., granite), joint spacing follows an approximately log-normal frequency distribution (i.e., the distribution has a kurtosis near zero). Joint spacing in rocks with systematic mechanical boundaries differs from the spacing in Isotropie rocks, exhibiting consistently positive values of kurtosis (i.e., the distribution is more clustered around the mode than a perfectly log-normal distribution). We attribute this difference in joint-spacing distribution to mechanical boundaries such as bed partings in sedimentary rocks that constrain joint height and control joint spacing. Existing systematic joints can also act as mechanical boundaries during the development of later 'cross' joints. Two parallel mechanical boundaries determine the mechanical-layer thickness that influences joint spacing. In this paper, we investigate the effect of sampling geometry and mechanical discontinuities on joint-spacing statistics. In many situations, neither pavement surfaces nor properly oriented boreholes are available for measuring the spacing of cross joints that develop between existing systematic joints. When joint-spacing data come from scanlines that are oblique to a systematic joint set (e.g., crossing many systematic joints on a sub-vertical outcrop face), we consider whether the median spacing of the systematic joint set is statistically equivalent to the mechanical-layer thickness thought to control cross-joint spacing between individual pairs of systematic joints. The basis of our analysis is the fracture spacing index (FSI), which is the slope of a line fitted to a plot of mechanical-layer thicknesses vs. median joint spacing. We collected joint-spacing data along oblique scanlines from a large outcrop of the Devonian Brallier Formation, a distal turbidite sequence, near Huntingdon, PA. Our analysis indicates that the spacing of cross joints correlates better with a mechanical-layer thickness defined by the median systematic ('strike') joint spacing (r² = 0.78, FSI = 1.02) than with a mechanical-layer thickness defined by the stratigraphie bed thickness (r² = 0.69, FSI = 0.97). This is consistent with the conclusions of previous workers. We also note that the spacing data from the cross joints exhibit a higher (i.e., more positive) value of kurtosis than the data from the earlier strike joints (1.66 vs. 0.98). This is consistent with the idea that mechanical discontinuities alter joint spacing in a systematic manner. In this case, the cross joints may have been influenced by two sets of mechanical boundaries (bedding and existing joints), whereas the earlier strike joints were constrained by only one set (bedding).