The problem of area change in tangential longitudinal strain folding

Abstract

This paper deals with some problems with the concept and properties of the folding mechanism named tangential longitudinal strain. A general two-dimensional mathematical description of this mechanism in terms of displacements and finite strains is presented. In the analysis of this mechanism of folding, two geologically reasonable variants are considered. The first of these, referred to as parallel tangential longitudinal strain folding, involves no finite elongation of lines perpendicular to the layer and produces class 1B (parallel) folds. The second variant is characterized by the conservation of area across the fold profile and is therefore termed equiareal tangential longitudinal strain folding; it produces folds ranging from class 1B to more complex shapes with the development of a bulge in the hinge zone inner arc when amplitude and curvature are high. Using the computer program “FoldModeler” which incorporates the derived equations for displacements and finite strains, the geometrical features of idealized folds produced by these two variants have been studied, together with those arising from their successive or simultaneous combination. The implications of the operation of these two deformation mechanisms in natural folds are then considered and a discussion is presented about the features that can be diagnostic of their operation in nature. It is suggested that the two mechanisms operate together in the formation of natural folds, in a way that deformation probably begins with equiareal tangential longitudinal strain, but subsequently gives way to parallel tangential longitudinal strain when strain concentration in some parts of the folded layer makes area change probable.