Progressive deformation of single layers under constantly oriented boundary stresses

Competent single layers embedded in incompetent rock display a variety of structures if deformed by shortening or stretching: folds, boudins, or pinch-and-swells. Similarly, incompetent single layers hosted by more competent matrix rock may develop mullions, inverse folds, or both. The change in length of material planes with time is controlled by the type of bulk deformation and the initial layer orientation. The length and rotation history of material planes in a unit volume of rock is studied systematically by using, for the first time, deviatoric stresses of arbitrary-but constant-orientation making use of a fundamental deformation tensor. The traces of the eight planes in the unit volume of rock used in the analysis are in the plane of deformation and are treated as passive marker lines. The change in the length of these material lines is computed for arbitrary orientations of the principal deviatoric stresses. The history of the length change and rotation of the passive marker planes, carefully scaled against time, is subsequently used to predict the structures which would evolve in similarly oriented single layers of either competent or incompetent rock. The theoretical range of structural patterns evolving in the model is controlled by the orientations of the principal deviatoric stress. Conversely, the geometry of deformation patterns in nature can be used to constrain the possible orientations of the palaeostress axes.