Characterizing stress fields in the upper crust using joint orientation distributions

Linear elastic fracture mechanics predicts that joint orientation is controlled by the stress field in which the joints propagate. Thus joint sets are effective proxies for stress trajectories during joint growth. Complexity in joint orientation indicates stress trajectory variability, a phenomenon quantified using an eigenvalue method that measures dispersion of joint normal vectors (i.e. poles) around the mean vector. Ratios between the eigenvalues of a joint orientation tensor give the clustering strength (ζ) and the shape factors (γ) of the distribution. A joint set that forms in a relatively isotropic rock subject to a rectilinear stress field should exhibit strong clustering and small random orientation variation that can be described by the Fisher statistical model. However, most joint orientation distributions in bedded rocks have non-random variation, greater in strike than in dip. This relative stability of the vertical stress orientation is strongest When joints are bounded by bedding interfaces, reflecting the tendency for deflection in the local stress field arising from the growth of side cracks, joint segments and adjacent joints in joint zones. Even when joint growth across bedding interfaces indicates negligible strength anisotropy, joint orientation distributions reflect less joint-joint interaction during vertical growth than during horizontal growth. As strike variation grows due to the presence of a non-rectilinear stress field, the orientation data better fit a Kent statistical model. Joint sets formed during fold development or in rocks with irregular bedding boundaries are more weakly clustered with Fisher-like orientation distributions. Orientation distributions for joint sets formed throughout a stress rotation have Kent-like shapes that indicate the magnitude of stress trajectory variation and clustering strength that depends on the joint density at each increment of the stress rotation.