Orthogonal cross joints: do they imply a regional stress rotation?

Orthogonal cross joints extend across intervals between systematic joints in brittle sedimentary strata and abut the systematic joints at about 90° angles. These joints typically form a ‘ladder-like’ pattern if viewed on a bedding surface. A common interpretation is that orthogonal cross joints define the orientation of the regional stress field during their formation: least compressive stress perpendicular to the joints. It follows that they indicate a rotation of regional principal stresses by 90° after the formation of the systematic joints. Using a three-dimensional boundary element code (Poly3D), we considered a simple geologic case of vertical systematic fractures developing in horizontal strata under a triaxial remote load with: the maximum principal tensile stress being horizontal and perpendicular to the strike of the fractures, the intermediate principal stress being horizontal and parallel to the strike of the fractures, and the least principal tensile stress (i.e. maximum compressive stress) being vertical. The results show that the local maximum principal stress is first perpendicular, and then parallel to, the strike of the systematic fractures as the ratio of fracture spacing to height changes from greater than to less than a critical value when the horizontal remote principal stress ratio, the ratio of the intermediate remote principal stress to the maximum remote principal stress under the sign convention of positive for tensile stresses, is greater than a threshold value (∼0.2). Thus, the fracturing process changes from infilling of systematic fractures to the formation of orthogonal cross fractures. This provides an alternative mechanism for the formation of orthogonal cross joints that does not require a systematic rotation of the regional stress field by 90°. The critical spacing to height ratio for the local principal stress switch is independent of the least remote principal stress (i.e. overburden). It increases nonlinearly with increasing ratio of the horizontal remote principal stresses, and decreases nonlinearly with increasing Poissonʹs ratio of the material.