egu vienna 04/17/2007 m. frehner & s.m. schmalholz 1 numerical simulations of parasitic folding...

1EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Numerical simulations of parasitic foldingand strain distribution in multilayers

EGU Vienna, April 17, 2007

Marcel FrehnerStefan M. Schmalholz

[email protected]


Motivation: Asymmetric parasitic folds on all scales

Mount RubinWestern Antarctica

Picture courtesyof Chris Wilson

~1200m

Foliated MetagabbroVal Malenco; Swiss Alps

Picture courtesy of Jean-Pierre Burg

| Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation


Motivation: The work by Hans Ramberg

Ramberg, 1963: Evolution of drag foldsGeological Magazine

| Methods | Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation

Ramberg‘s hypothesis for parasitic folding Thin layers buckle first

Asymmetry by shearing between the larger folds

Aim Test hypothesis with

numerical methods

Quantify and visualize strain field


Methods: Numerics

Self-developed 2D finite element (FEM) program

Incompressible Newtonianrheology

Mixed v-p-formulation

Half wavelengthof large folds

Viscosity contrast: 100

| Two-layer folds | Multilayer folds | Conclusions | Outlook || Motivation | Methods


Methods: Standard visualization

Resolution 11’250

elements

100’576 nodes


Layer-parallel strainrate

40% shortening


Strain ellipse: A reminder


1

1

x x

y y

t

u u

x yx x

u uy y

x y

G

Haupt, 2002:Continuum Mechanics and Theory of Materials

Ramsay and Huber, 1983:Strain Analysis

TC F F

Incremental deformationgradient tensor G

Finite deformationgradient tensor F

Right Cauchy-Green tensor C

Eigenvalues and eigenvectors are usedto calculate principal strain axes


Two-layer folds: Strain distribution

Color:Accumulated strain Color: Rotation angle

| Methods | Multilayer folds | Conclusions | Outlook || Motivation | Two-layer folds

40% shortenig


Two-layer folds: Three phases of deformation

Fold limb S Transition zone JFold hinge I



Two-layer folds: Results of strain analysis

Three regions of deformation Fold hinge, layer-parallel compression only

Fold limb

Transition zone, complicated deformation mechanism

Three deformation phases at fold limb Layer-parallel compression

Shearing without flattening

Flattening normal to the layers

SI J



Multilayer folds: Example of numerical simulation

Viscositycontrast: 100

Thickness ratioHthin:Hthick = 1:50

Random initial perturbation onthin layers

Truly multiscale model

Number of thin layers in this example: 20

Resolution: 24‘500 elements

220‘500 nodes

| Methods | Two-layer folds | Conclusions | Outlook || Motivation | Multilayer folds


Multilayer folds: Results

Layer-parallel compression No buckling of thick layers

Buckling of thin layersSymmetric fold stacks

Shearing without flattening Buckling of thick layers: shearing between them

Stacks of multilayer folds become asymmetric

Flattening normal to layers Increased amplification of thick layers:

flattening normal to layers

Amplitudes of thin layers decrease



Multilayer folds: Similarity to two-layer folding

Deformation of two-layersystem is nearly independentof presence of multilayerstack in between

50% shortening:

Black: Multilayer systemGreen: Two-layer system



Conclusions

Efficient strain analysis with computed strain ellipses

Ramberg‘s hypothesis verified

3 phases of deformation between a two-layer system Layer parallel compression: Thin layers build vertical

symmetric fold-stacks

Shearing without flattening: Asymmetry of thin layers

Flattening normal to layers: Decrease of amplitude of thin layers

Presence of thin multilayers hardly affectsdeformation of two-layer system

| Methods | Two-layer folds | Multilayer folds | Outlook || Motivation | Conclusions


Acc

um

ula

ted

stra

in

Acc

um

ula

ted

stra

in

Layer n=5, Matrix n=5

| Methods | Two-layer folds | Multilayer folds | Conclusions| Motivation || Outlook

Layer n=1, Matrix n=1

Work in progress: More complex rheology


Work in progress: More complex geometry

| Methods | Two-layer folds | Multilayer folds | Conclusions| Motivation || Outlook

Different thicknesses

Random initial perturbation on all layers


Thank you

Frehner, M. and Schmalholz S.M., 2006:Numerical simulations of parasitic folding in multilayersJournal of Structural Geology

egu vienna 04/17/2007 m. frehner & s.m. schmalholz 1 numerical simulations of parasitic folding...

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