| The concept of the neutral line in a buckle fold is fundamental in structural geology. The
neutral line divides the outer arc of a fold where layer-parallel extension occurs
from the inner arc where layer-parallel compression occurs. Indeed, in nature
outer-arc-extension-structures, such as mode 1 fractures normal to the layer, and
inner-arc-compression-structures, such as enhanced cleavage development or pressure
solution, can be observed.
In the past, the neutral line has often been used for the kinematic construction of folds.
The technique that has been used is called neutral line folding or tangential longitudinal strain
folding and the fold is constructed from a given neutral line geometry. One of the necessary
and fundamental assumptions for these fold construction techniques is that the neutral line is
continuous along the folded layer.
In this study, the neutral line is calculated for the first time in a mechanically calculated
fold, rather than in a kinematically constructed one. The finite element method is used to
numerically buckle an individual layer and a multi-layer sequence with Newtonian viscous
rheology. The strain distribution resulting from the numerical simulations is used to calculate
the neutral line. The findings of this study are:
Two neutral lines have to be distinguished, the finite neutral line and the
incremental neutral line. The former is the zero-contour line of the finite
layer-parallel strain, the latter is the zero-contour line of the strain rate.
Both neutral lines are not continous along the folded layer, but terminate at the
bottom or top interface of the layer.
The neutral lines start to develop at the hinge point at the outer arc and first
encircle a small area at the outer arc. They move through the layer and, in a late
stage of the folding process, encircle a small area at the inner arc.
The incremental neutral line develops first and then moves through the layer
ahead of the finite neutral line.
The finite neutral line does not always develop, depending on the viscosity
contrast between the folded layer and the surrounding matrix and on the initial
perturbation of the layer. The incremental neutral line always develops when
folding is strong enough.
In a multi-layer folding scenario, the neutral lines in the individual layers develop
differently and in a complex way.
The development of some fold-related structures (e.g., fractures) depends on the
momentary state of the fold, others (e.g., cleavage) depend on the folding history. Therefore,
the new findings of this study are of great relevance when interpreting fold-related structures,
such as outer-arc-extension-structures and inner-arc-compression-structures. Also, this study
shows that fundamental assumptions of kinematic fold constructions, such as tangential
longitudinal strain folding or neutral line folding, are wrong. |