Formation of sheath folds around a crack: An analytical and experimental study

The term 'sheath fold' describes a cone-shaped fold with a rounded apex. Such folds can occur in metamorphic rocks, sediments, ignimbrites, evaporites, and ice, ranging in size from sub-millimeters to kilometers. They are in many cases associated with simple shear and high strain. How sheath folds form and how they evolve with increasing strain is still a matter of debate, however, the geometry of sheath folds has been used to deduce kinematic information such as strain, shear sense, and bulk strain type. Several mechanisms for sheath fold development have been proposed such as the passive amplification of a perturbed layer interface, the flow perturbation above a rigid, corrugated basement, or the flow perturbation around a rigid inclusion. We propose that the flow perturbation around weak, planar objects, such as veins, weak sedimentary strata, or fractures is another triggering mechanism. To test this hypothesis, we developed a quantitative and integrating study of analytical and experimental modeling of sheath fold development around a crack. In the analytical model setup we place an elliptical, weak inclusion, which represents a crack, in a stiff matrix and apply simple shear up to γ=10. The analytical model is truly three-dimensional where the flow around the crack is obtained with an adapted external Eshelby solution for incompressible viscous materials in the limit of an elliptical and inviscid inclusion. The evolving structures are visualized by tracking passive marker layers in the matrix. We have tested the influence of the initial crack orientation (0°, 90°, or 135° with respect to the shear direction) on the development of sheath folds. The analytical model shows that the sheath folds develop irrespectively of the initial crack orientation. However, the shapes of the folds depend on the initial crack orientation as well as on the applied shear strain. As the analytical model does not consider a heterogeneous matrix, we designed experimental models to test the effect of mechanical layering (viscosity contrast, layer thickness) on the development of sheath folds around a crack. The layered rock was simulated using silicons of different viscosities, in which a lubricated cut represented the crack. The model underwent deformation in a simple shear apparatus to a shear strain of γ=6. To analyze the results we cut the models perpendicular to the stretching direction. The experimental results show that sheath folds also develop in a layered matrix with a viscosity contrast between the layers from up to 20. The thickness of the layers has a strong impact on the visibility of the sheath fold. Results from the analytical and experimental study show that a crack in simple shear can lead to the formation of sheath folds at a relatively low shear strain (γ<5). Both models capture the first order observations and variety of shapes found in nature.