Implications of pericline geometries on 3D fold shape analysis, stress distribution and fracture analysis

The characterization of folds is often limited to two-dimensional cross-sectional views where folds are approximated as cylindrical. This enables simplification of fold shape analysis (using principles such as dip isogons, stereographs, tangent diagrams, and Bezier curve analysis), allows for a simplified analysis of the distribution of stress and strain, and enables and the analysis and visualization of folding associated fractures. However, in a heterogenous medium folds have to terminate somewhere, resulting in more complex three-dimensional geometries. In this study, a 3D finite element modeling approach using a Maxwell visco-elastic rheology is utilized to simulate 3D periclinal folds resulting from single layer buckle folding. With respect to fold shape analysis, we use the forward modeled pericline geometries to demonstrate that geometrical attitude data collected for various cross sections and plotted using traditional 2D methods such as stereographs and tangent diagrams may lead to the misinterpretation of the fold shape as conical. In contrast 3D geometric data such as Gaussian curvature can describe and quantify the 3D fold geometry in its entirety. With respect to folding associated fracture analysis, the 3D modeling results show that shear fractures of various orientations in the fold limb, which cannot be intuitively explained by the strain/stress regimes during 2D buckling and require unrealistic boundary conditions, are feasible to occur during a single deformation event during the development of a pericline. In summary, accounting for the true 3D geometry of buckle fold structures will lead to a better classification of folds, a better understanding of the processes and parameters affecting their development, and enable post-folding failure analysis.