Using joint interactions to estimate paleostress ratios

Abstract

Because they grow perpendicular to a minimum principal stress ( σ 3), joints are paleostress markers. Younger joints may show a systematic change in orientation as they approach older, throughgoing, joints. This change in orientation reflects a change in the stress field in which the younger joint set is growing. Analytical solutions for the stress field around a single joint subject to a combination of opening (Mode I) and anti-plane shear (Mode III) loadings are given. The sense of rotation and change in magnitude of principal stresses near an existing joint are functions of the orientation and ratio of magnitudes of the far-field stresses and the coefficient of friction across the joint. Assuming that a later, non-parallel joint nucleates distant from, and grows toward, the throughgoing joint, the stress field in which it is growing will be systematically rotated and changed by the presence of the throughgoing joint. The effect of interaction between the older and younger joints is ignored in the analysis. The systematic change in orientation of the later joint reflects the change in principal stresses near the throughgoing joint, and can be used to place approximate limits on the ratio of the far-field horizontal stresses. Zoned joints are individual, subparallel en échelon joints which are confined to a narrow zone, separated from adjacent zones by a characteristic distance, and confined to a single lithologic interval. A joint zone can be modeled as a single, infinitely long joint with a characteristic height. Comparison of analytic stress field solutions with field examples of interacting zoned joints in Arches National Park, Utah, suggest that a curving-parallel geometry of younger joints is indicative of a stress field in which −3 < σ 2 ∞/σ 3 ∞ < − 1 3 . A curving-perpendicular geometry of younger zones is compatible with principal stress ratios of − 1 3 < σ 2 ∞/σ 3 ∞ < 1 .