Predicting the orientation of joints from fold shape: Results of pseudo–three-dimensional modeling and curvature analysis

Abstract

We treat layers of sedimentary rock as elastic plates and predict the orientations of joints by assuming that they open parallel to the maximum instantaneous stretch of a layer. Because the direction of maximum instantaneous stretch is parallel to the maximum curvature of a surface, we hypothesize that joints will trend parallel to the minimum curvature of an elastically deformed layer. After constructing pseudo–three-dimensional trishear models of Laramide-style uplifts that grow self-similarly, we calculated the direction of minimum-curvature axes during the evolution of the fold. Our analysis of minimum-curvature axes in evolving folds suggests several important characteristics for fold-related joint sets: (1) joints that are neither parallel nor perpendicular to the fold axis may be induced by local fold-related strains; (2) at any time during folding, joint orientations may vary according to the structural position on a fold; (3) at any location on a fold, joint orientation may depend on when a joint forms during the evolution of the fold; and (4) joint patterns in trishear folds may vary with stratigraphic position. Natural folds that evolve along simple geometric pathways may develop fold-related joint sets, the orientation, dominance, abutting relationships, spacing, and continuity of which will vary systematically throughout the structure. This variation in joint-system architecture may reflect the history of fold growth.