Predicting patterns of strain from three-dimensional fold geometries: neutral surface folds and forced folds

Abstract The geometries and densities of fractures associated with fold structures can be predicted by assuming that the strains accommodated by fractures mimic the bulk strains induced in the strata during folding. This paper examines, from a theoretical standpoint, the distributions of bedding-plane strains expected in folds formed by various folding mechanisms. The relationship between the state of bedding-plane strain and fold-surface geometry is found to vary according to different fold types, distinguished on the basis of their curvature properties. The first type are developable fold surfaces, which have Gaussian curvature equal to zero. Folding mechanisms which are dominated by the mechanical strength of the layering, such as buckling, produce surfaces of this type. Folds of this type allow the possibility of estimating the bedding-plane strains from the geometrical features of the folded layer. Neutral surface folds and flexural-slip folds are discussed as examples. The other main class of folds have non-developable surfaces, which have non-zero Gaussian curvature. Folded surfaces with this form arise predominantly from mechanisms that involve the passive deflection of the layering in response to displacement gradients originating outside of the layer, e.g. drape folding. Although the geometry of these surfaces implies the presence of bedding plane strains, the quantification of these strains cannot be made from the fold geometry but requires additional information on these displacement patterns.