Folding of a single layer in an anisotropic viscous matrix under layer-parallel shortening

Folds are common structures that provide valuable insights into the direction and amount of shortening and the rheological properties of deformed rocks. Most thin plate folding theory started from M.A. Biot has historically been applied to isotropic materials, but rocks are often anisotropic due to the presence of tectonic foliations, bedding, veins, dykes, etc. Mechanical anisotropy can enhance partitioning of deformation, resulting in low-strain domains and localised high-strain shear domains. Using the Viscoplastic full-field code coupled with the modelling platform Elle (VPFFT-Elle), we investigate the evolving fold geometries, stress field and strain-rate field differences and redistributions resulting from layer-parallel shortening deformation of an isotropic, competent layer embedded in an anisotropic, weaker power-law viscous matrix. We focus on the effect of the orientation of the mechanical anisotropy relative to the competent layer. The simulation results illustrate that the deformation localisation behaviour, and hence fold geometry, depend on (i) the initial orientation of the anisotropy, (ii) the intensity of anisotropy, and (iii) strength of the competent layer, relative to that of the matrix. Variation in the localisation behaviour resulting from different strain-rate distributions lead to two end-member fold geometries: (1) classical Biot-type buckle folding and thickening of the competent layer coupled to the formation of a new axial-planar crenulation cleavage in the matrix, and (2) what we call ‘shear-band folding’ in which sections of the competent layer are offset due to the formation of shear bands in the matrix with opposite sense of shear. This leads to rapid fold amplification. Classical Biot-type buckle folds dominate when the initial anisotropy is parallel or subparallel to the shortening direction, while shear-band folds dominate when the initial anisotropy is normal or at high angle to the shortening direction. Results presented here contribute to our understanding on how mechanical anisotropy controls folding and the rearrangement of the matrix components. Furthermore, the modelled scenarios can serve as a “virtual glossary” to compare real folds in different tectonic settings, providing insights into the possible pre-fold configuration of the folded layer and its anisotropic matrix.