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

frehner@erdw.ethz.ch

2EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

3EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

4EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

5EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Methods: Standard visualization

Resolution 11’250

elements

100’576 nodes

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

Layer-parallel strainrate

40% shortening

6EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Strain ellipse: A reminder

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

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

7EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Two-layer folds: Strain distribution

Color:Accumulated strain Color: Rotation angle

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

40% shortenig

8EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Two-layer folds: Three phases of deformation

Fold limb S Transition zone JFold hinge I

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

9EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

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

10EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

11EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

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

12EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

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

13EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

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

14EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Acc

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ted

stra

in

Acc

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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

15EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Work in progress: More complex geometry

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

Different thicknesses

Random initial perturbation on all layers

16EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz

Thank you

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