Theoretical analysis of cross-joint geometries and their classification

One commonly observed bedrock joint pattern consists of cross joints that terminate against an older set of longer systematic joints. Dyer [1988] showed that unique cross-joint geometries may develop in response to a combination of remote stresses and local perturbations of the stress field in the vicinity of preexisting joints. We expand upon Dyer's analysis by providing the general solutions for cross-joint geometry as a function of remote principal stress orientations and ratios. Specific cross-joint geometries are determined by solving for the local cross-joint angle as a function of distance from the preexisting joint. On the basis of theoretical derivations, cross-joint geometries are grouped into five main categories: curving parallel, curving perpendicular, quasi-curving parallel, quasi-curving perpendicular and noncurving geometries. Furthermore, by discussing the stress state in the vicinity of the preexisting joint, a general expression for the dimension of compressive zone is derived, and a more detailed classification of cross-joint geometry is provided. Results from this study provide a method to estimate the relative magnitudes of remote principal stresses simply based on the observed cross-joint geometry, which may help constrain the tectonic history of a region. In addition, knowledge of precise cross-joint curvature and intersection geometries may provide important insights into their connectivity and fluid flow characteristics.