FORMATION AND SPACING OF ORTHOGONAL CROSS JOINTS: IMPLICATIONS FOR SUBSURFACE FRACTURE NETWORKS Taixu Bai, Rock Fracture Project, Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305-2115. E-mail: [email protected] ABS TRACT the orthogonal cross fractures. This critical spacing depends on the spacing to height ratio of the Orthogonal cross joints extend across intervals systematic fractures: When the ratio is greater than between systematic joints in brittle sedimentary about 1.8, the critical spacing is proportional to the strata and abut the systematic joints at about 90° height of the systematic fractures; When the ratio is angles. These joints typically form a "ladder-like" less than about 0.6, the critical spacing is pattern if viewed on a bedding surface. A common proportional to the spacing of the systematic interpretation is that orthogonal cross joints define fractures; and when the spacing to height ratio of the orientation of the regional stress field during the systematic fractures is between 0.6 and 1.8, the their formation: least compressive stress critical spacing is neither proportional to the perpendicular to the joints. It follows that they spacing of the systematic fractures nor to their indicate a rotation of regional principal stresses by height. 90° after the formation of the systematic joints. Using a three-dimensional boundary element code (Poly3D), we considered a simple geologic case of INTRODUCTION vertical systematic fractures developing in horizontal strata under a triaxial remote load with: Joints are opening-mode fractures formed as a the maximum principal tensile stress being consequence of the deformation of brittle rock horizontal and perpendicular to the strike of the masses in the Earth's crust (Engelder, 1987; Pollard fractures, the intermediate principal stress being and Aydin, 1988). They are sensitive indicators of horizontal and parallel to the strike of the the paleo stress field and can be used to infer the fractures, and the least principal tensile stress orientation of the regional stress field along with its (i.e., maximum compressive stress) being vertical. temporal and spatial evolution (e.g., Engelder and The results show that the local maximum principal Geiser, 1980, Dyer, 1988; Olson and Pollard, 1989). stress first is perpendicular to, and then is parallel Joints also provide pathways for underground fluid to the strike of the systematic fractures as the ratio flow. Thus, understanding natural fracture networks of fracture spacing to height changes from greater in aquifers and hydrocarbon reservoirs as well as than to less than a critical value when the engineering sites (National Research Council, 1996) horizontal remote principal stress ratio (i.e., the is one of the key steps in modeling ground water ratio of the intermediate remote principal stress to flow and predicting hydrocarbon migration and the maximum remote principal stress) is greater accumulation (Barton and Hsieh, 1989; Gringarten, than a threshold value (~0.2) under the sign 1996; Taylor et al., 1999). convention of positive for tensile stresses. Thus, Cross joints extend across intervals between the fracturing process changes from infilling of systematic joints, without cutting across the systematic fractures to the formation of orthogonal systematic joints (e.g., Hodgson, 1961; Hancock, cross fractures. This provides an alternative 1985; Dyer, 1988; Gross, 1993; Bai and Gross, mechanism for the formation of orthogonal cross 1999). Orthogonal cross joints, as one of the joints that does not require a systematic rotation of commonly-observed categories of cross joints, the regional stress field by 90°. The critical typically resemble a "ladder-like" pattern in outcrop spacing to height ratio for the local principal stress (Rawnsley et al., 1992; Rives et al., 1994). They switch is independent of the least remote principal abut the systematic joints at angles near 90° and are stress (i.e., overburden). It increases nonlinearly limited in length by the intervening distance with increasing ratio of the horizontal remote between the systematic joints (Fig. 1). One of the principal stresses, and decreases nonlinearly with earliest recorded observations of cross joint increasing Poisson's ratio of the material. The geometries was made in the Comb Ridge-Navajo results also show that there is a critical spacing for Mountain area of Utah and Arizona by Hodgson Stanford Rock Fracture Project Vol. 11, 2000 F-1 (a) (b) (c) principal joint ladder normal joint ladder North 10 m Figure 1. Field photographs at different scales of orthogonal cross joints that developed between systematic joints. (a). Orthogonal cross joints in a steeply inclined carbonate bed of the Monterey Formation along the Santa Barbara coastline, California. Note geologist for scale. Photograph taken by Wendy Bartlett. (b). Orthogonal cross joints in a porcellanite bed (bedding surface) of the Monterey Formation along the Santa Maria coastline, California. (c). Joint patterns from Nash Point, Bristol Channel, U.K. (after Rawnsley et al., 1998). Stanford Rock Fracture Project Vol. 11, 2000 F-2 (1961). Typical orthogonal cross joint patterns have This will reveal the factors that control the spacing been reported from outcrops along the Bristol of orthogonal cross joints. Channel, United Kingdom (Rawnsley et al., 1992; Rives et al., 1994; Caputo, 1995; Rawnsley et al., 1998), from the Appalachian Plateau, western New PREVIOUS WORK ON THE York State (Engelder and Gross, 1993; Zhao and FORMATION AND SPACING OF Jacobi, 1997), from the Monterey Formation, Santa ORTHOGONAL CROSS JOINTS Barbara Coastline, California (Gross, 1993; Finn et al., 1999), and from Arches National Park, Utah Formation of orthogonal cross joints (Rives et al., 1994; Cruikshank and Aydin, 1995). Because opening-mode fractures in isotropic, Cross joint paths, which may be curved, are homogeneous materials propagate in the direction perpendicular to the local maximum tensile stress perpendicular to the local maximum tensile stress, and their main trend is inferred to be approximately or least compressive stress if fluid pressure drives perpendicular to the direction of regional maximum the fracturing (Pollard and Segall, 1987; Pollard and tensile stress (Dyer, 1988; Engelder and Gross, Aydin, 1988), a local principal stress rotation of 90° 1993; Bai and Gross, 1999). Given this is needed for orthogonal cross joints to form after interpretation, the presence of orthogonal cross the formation of the systematic joints. This stress joints implies a regional principal stress rotation rotation may be induced by either local or regional through 90° after the formation of the systematic mechanisms. Proposed local mechanisms in the joints and before the cross joints formed. geological literature include: rock band warping In studying the stress distribution between (Granier and Bles, 1988), stress release under biaxial adjacent equally-spaced fractures in layered rocks, Bai extension (Simon et al., 1988); regional and Pollard (2000) found that there is a stress mechanisms include: strain relaxation (Rives and transition for the component of local normal stress Petit, 1990; Rives et al., 1994), and regional in the direction perpendicular to the fractures. Their principal stress rotation (Eyal and Reches, 1983; numerical models suggest that under a remote Hancock et al., 1987; Bahat and Grossmann, 1988; extension in the direction perpendicular to the Dunne and North, 1990; Eyal, 1996). fractures, this normal stress changes from tensile to The rock band warping mechanism is based on compressive when the fracture spacing to layer the fact that the systematic joints cut the layer into thickness ratio changes from greater than to less long and narrow bands. Because of this shape, the than a critical value (approximately 1.0). This bands are very sensitive to bending or warping in the stress transition implies that, at a certain stage direction parallel to the systematic joints. Any during the formation of a systematic joint set by warping of the bands, for example, by sequential infilling (Gross, 1993), further infilling is inhomogenous settling of the overburden or large- inhibited. On the other hand, because the local scale folding or faulting, could result in local tensile stress in the direction perpendicular to the systematic stresses that would produce orthogonal cross joints joints becomes compressive, the stress in the (Granier and Bles, 1988; Rives et al., 1994). direction parallel to these joints may become the The stress release mechanism is based on the maximum tensile (least compressive) stress, and change of stress in the direction perpendicular to the orthogonal cross joints may form in response to this systematic joints after their formation. Because the local switch in principal stress orientation . In other surfaces of open (non fluid-filled) systematic joints words, orthogonal cross joints may form in the are traction free, their formation will release the absence of a regional stress rotation. In this paper, crack-normal tensile stress (Pollard and Segall, we use the three-dimensional boundary element 1987). In a rock layer subjected to biaxial method to explore the possibility for a local extension (e.g., Ghosh, 1988; Simon et al., 1988), principal stress switch between adjacent systematic it is possible that the stress parallel to the joints as a function of the ratio of spacing to layer systematic joints becomes the maximum tensile