Deformation – Progressive or multiphase?

We study high-amplitude folding in layered rocks with two-dimensional numerical simulations. We employ the finite-element method to model shortening of an incompressible multi-layer with power-law viscous rheology. The Lagrangian numerical mesh is deformed and re-meshed to accurately follow the layer interfaces. Three settings are considered: (i) pure shearing of a confined multi-layer, (ii) simple shearing of a multilayer above a detachment, and (iii) slump folding owing to gravity sliding. In our pure shear simulations, finite-amplitude folds always develop despite confinement and thin weak interlayers. The fold shapes can be significantly irregular, resulting from initial geometrical heterogeneities that are perturbations of the layer interfaces and differences in layer thickness. The bulk normal viscosity of the multi-layer decreases significantly with progressive folding. This structural softening decreases the bulk normal viscosities by a factor of 2–20. For simple shear, the multi-layer does not develop asymmetric fold shapes significantly. Fold axial planes in the multi-layer are mostly curved and not parallel. For slump folding, fold shapes can be significantly asymmetric exhibiting strongly curved fold axial planes and overturned fold limbs. The rheology of the competent layers has a major impact on the fold shapes for gravity-driven multi-layer folding.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2011.0421

Folding in power-law viscous multi-layers

[1] Field relationships combined with new U-Pb zircon geochronology suggest that the shallow-level Krkonose-Jizera plutonic complex, northern Bohemian Massif, was assembled successively from bottom to top, starting with emplacement of the separately evolved S-type Tanvald granite (317.3 ± 2.1 Ma), followed by at least two voluminous batches of the I-type porphyritic Liberec (319.5 ± 2.3 Ma) and Jizera (320.1 ± 3.0 Ma and 319.3 ± 3.7 Ma) granites. The intrusive sequence was completed by uppermost, minor intrusions of the equigranular Harrachov (315.0 ± 2.7 Ma) and Krkonose granites. The I-type granites exhibit an unusually complex pattern of superposed feldspar phenocryst and magnetic fabrics as revealed from the anisotropy of magnetic susceptibility (AMS). The outer Liberec granite preserves margin-parallel foliations and lineations, interpreted to record emplacement-related strain captured by cooling from the pluton floor and walls. In contrast, the inner Jizera, Harrachov, and Krkonose granites were overprinted by synmagmatic strain resulting from dextral movements along regional strike-slip faults cutting the opposite ends of the plutonic complex. Late-stage felsic dikes in the Liberec and Jizera granites reorient from horizontal to vertical (lineation-perpendicular) attitude in response to changing the least principal stress direction, whereas mafic schlieren do not do so, representing only randomly oriented small-scale thermal-mechanical instabilities in the phenocryst framework. In general, this case example challenges the common approach of inferring pluton-wide magma flow from interpolated foliation, lineation, and schlieren patterns. More likely, magmatic fabrics in large plutons record complex temporal succession of superposed strains resulting from diverse processes at multiple scales.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/tect.20088

Multistage magma emplacement and progressive strain accumulation in the shallow‐level Krkonoše‐Jizera plutonic complex, Bohemian Massif

. The shortening and extension of mechanically layered ductile rock generates folds and pinch-and-swell structures (also referred to as necks or continuous boudins), which result from mechanical instabilities termed folding and necking, respectively. Folding and necking are the preferred deformation modes in layered rock because the corresponding mechanical work involved is less than that associated with a homogeneous deformation. The effective viscosity of a layered rock decreases during folding and necking, even when all material parameters remain constant. This mechanical softening due to viscosity decrease is solely the result of fold and pinch-and-swell structure development and is hence termed structural softening (or geometric weakening). Folding and necking occur over the whole range of geological scales, from microscopic up to the size of lithospheric plates. Lithospheric folding and necking are evidence for significant deformation of continental plates, which contradicts the rigid-plate paradigm of plate tectonics. We review here some theoretical and experimental results on folding and necking, including the lithospheric scale, together with a short historical overview of research on folding and necking. We focus on theoretical studies and analytical solutions that provide the best insight into the fundamental parameters controlling folding and necking, although they invariably involve simplifications. To first order, the two essential parameters to quantify folding and necking are the dominant wavelength and the corresponding maximal amplification rate. This review also includes a short overview of experimental studies, a discussion of recent developments involving mainly numerical models, a presentation of some practical applications of theoretical results, and a summary of similarities and differences between folding and necking.

/pdf/folding-and-necking-across-the-scales-a-review-of-3e8qjrlmuw.pdf

Folding and necking across the scales: a review of theoretical andexperimental results and their applications

A hand brush having an elongated bristle block body, with substantially planar top and bottom surfaces. The brush bristles extend downwardly from the bottom of the body. The forward end of the body is provided with a forwardly extending nose. A handle has a first portion extending upwardly from the nose and the adjacent forward portion of the top of the body and a second grip portion directed rearwardly above the top of the body. The nose is narrower than the forward end of the body forming a recessed alcove to either side of the nose. A pair of mirror image fingernail cleaners extend forwardly from the forward end of the brush body along and spaced from each side of the nose. The forward ends of the fingernail cleaners are sharp enough to remove grime from beneath the user's nails, but do not represent a hazard to the user since they are set back in their respective alcoves and do not extend beyond the brush nose.

Rheology of fine-grained siliciclastic rocks in the middle crust

Fold geometry toolbox – Automated determination of fold shape, shortening, and material properties ☆

Theoretical analysis of large amplitude folding of a single viscous layer

Folder: A numerical tool to simulate the development of structures in layered media

We present Folder, a numerical toolbox for modelling deformation in layered media subject to layer parallel shortening or extension in two dimensions. The toolbox includes a range of features that ensure maximum flexibility to configure model geometry, define material parameters, specify numerical parameters, and choose the plotting options. Folder builds on an efficient finite element method model and implements state of the art iterative and time integration schemes. We describe the basic Folder features and present several case studies of single and multilayer stacks subject to layer parallel shortening and extension. Folder additionally comprises an application that illustrates various analytical solutions of growth rates calculated for the cases of layer parallel shortening and extension of a single layer with interfaces perturbed with a single sinusoidal waveform. We further derive two novel analytical expressions for the growth rate in the cases of layer parallel shortening and extension of a linear viscous layer embedded in a linear viscous medium of a finite thickness. These solutions help understand mechanical instabilities in layered rocks and provide a unique opportunity for benchmarking of numerical codes. We demonstrate how Folder can be used for benchmarking of numerical codes. We test the accuracy of single-layer folding simulations using various 1) spatial and temporal resolutions, 2) iterative algorithms for non-linear materials, and 3) time integration schemes. The accuracy of the numerical results is quantified by: 1) comparing them to analytical solutions, if available, or 2) running convergence tests. As a result, we provide a map of the most optimal choice of grid size, time step, and number of iterations to keep the results of the numerical simulations below a given error for a given time integration scheme. Folder is an open source MATLAB application and comes with a user-friendly graphical interface. Folder is suitable for both educational and research purposes.

FOLDER: A numerical tool to simulate the development of structures in layered media

. At laboratory timescales, rock salt samples with different composition and
microstructure show variance in steady-state creep rates, but it is not
known if and how this variance is manifested at low strain rates and
corresponding deviatoric stresses. Here, we aim to quantify this from the
analysis of multilayer folds that developed in rock salt over geological timescale in the Ocnele Mari salt mine in Romania. The formation is composed of
over 90 % of halite, while distinct multiscale layering is caused by
variation in the fraction of impurities. Regional tectonics and mine-scale
fold structure are consistent with deformation in a shear zone after strong
shearing in a regional detachment, forming over 10 m scale chevron
folds of a tectonically sheared sedimentary layering, with smaller folds
developing on different scales in the hinges. Fold patterns at various
scales clearly indicate that during folding, the sequence was mechanically
stratified. The dark layers contain more impurities and are characterised
by a more regular layer thickness compared to the bright layers and
are thus inferred to have higher viscosities. Optical microscopy of gamma-decorated samples shows a strong shape-preferred
orientation of halite grains parallel to the foliation, which is reoriented
parallel to the axial plane of the folds studied. Microstructures indicate
dislocation creep, together with extensive fluid-assisted recrystallisation
and strong evidence for solution–precipitation creep. This provides support
for linear (Newtonian) viscous rheology as a dominating deformation
mechanism during the folding. Deviatoric stress during folding was lower
than during shearing in the detachment at around 1 MPa. We investigate fold development on various scales in a representative
multilayer package using finite-element numerical models, constrain the
relative layer thicknesses in a selected outcrop, and design a numerical
model. We explore the effect of different Newtonian viscosity ratios between
the layers on the evolving folds on different scales. By comparing the field
data and numerical results, we estimate that the effective viscosity ratio
between the layers was larger than 10 and up to 20. Additionally, we
demonstrate that the considerable variation of the layer thicknesses is not
a crucial factor to develop folds on different scales. Instead, unequal
distribution of the thin layers, which organise themselves into effectively
single layers with variable thickness, can control deformation on various
scales. Our results show that impurities can significantly change the
viscosity of rock salt deforming at low deviatoric stress and introduce
anisotropic viscosity, even in relatively pure layered rock.

/pdf/rheological-stratification-in-impure-rock-salt-during-long-317pkkarpr.pdf

Rheological stratification in impure rock salt during long-term creep: morphology, microstructure, and numerical models of multilayer folds in the Ocnele Mari salt mine, Romania

Marta Adamuszek

Papers

Fold geometry toolbox – Automated determination of fold shape, shortening, and material properties ☆

Theoretical analysis of large amplitude folding of a single viscous layer

Folder: A numerical tool to simulate the development of structures in layered media

FOLDER: A numerical tool to simulate the development of structures in layered media

Rheological stratification in impure rock salt during long-term creep: morphology, microstructure, and numerical models of multilayer folds in the Ocnele Mari salt mine, Romania