sgm bern 11/25/2006 marcel frehner 1 numerical simulations of parasitic folding in multilayers sgm...

1SGM Bern 11/25/2006 Marcel Frehner

Numerical simulations ofparasitic folding in multilayers

SGM Bern, November 25, 2006

Marcel FrehnerStefan M. Schmalholz

[email protected]


Outline

Motivation

Method

Two-layer folds 3 regions of deformation 3 deformation phases

Multilayer folds 3 deformation phases reformulated Similarity to two-layer folds

Conclusions


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


Motivation: The work by Hans Ramberg

Ramberg, H.Geological Magazine1963:

Evolution of drag folds


Motivation

Asymmetric parasitic folds are used in field studies

Problem: Conditions for their development are not thoroughly studied

Why become parasitic folds asymetric?

Goal: Understanding of the strain history and the development of

multilayer folds

Quantify necesary conditions for the development of asymetric parasitic folds


Method

Self-developed finite element (FEM) program Incompressible Newtonian rheology

2D

Dimensionless formulation

Pure shear boundary conditions

Modelled area: Half wavelength of fold

Viscosity contrast: 100

Sinusoidal initial perturbation


Two-layer folds→ Example of numerical simulation

Resolution 11’250

elements

100’576 nodes


Two-layer folds→ After 40% shortening

Strain ellipses

coloured with:

Bulkstrain

Strain ellipses coloured with:

Rotation angle


Two-layer folds→ Three regions of deformation

Fold limb S Transition zone JFold hinge I


Two-layer folds→ Three deformation phases at fold limb

Increasing shortening

1 = Original distance

Co

mp

ress

ion

Sh

eari

ng

Fla

tten

ing

Ab

solu

te

flatte

nin

g


Two-layer folds→ Observations

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


Multilayer folds→ Influence of number of thin layers

5

10

1520


Multilayer folds→ Three deformation phases reformulated

Amplitude

of thin layers of thick layers


Multilayer folds→ Three deformation phases reformulated

Layer-parallel compression No buckling of thick layers

Thin layers start to buckle anddevelop symmetric fold stacks

Shearing without flattening Buckling of thick layers causes shearing between them

Folds of multilayer stack become asymmetric

Flattening normal to layers Increased amplification of thick layers

leads to flattening normal to layers

Amplitudes of thin layers are decreased


Multilayer folds→ Similarity to two-layer folding


Multilayer folds→ Similarity to two-layer folding

Deformation of double layersystem is nearly independentof presence of multilayerstack in between

50% shortening:

Black: Multilayer systemGreen: Two-layer system


Conclusions

Deformation history between a two-layer system at the fold limb can be divided into three phases Layer parallel compression Shearing without flattening Flattening normal to layers

Thin layers develop vertical symmetric fold-stacks during first phase;They deform passively afterwards (like in the double layer case)

Whether fold-stacks survive the flattening phase is due to their amplitude at the point of buckling initiation of the thick layers A bigger number of thin layers amplifies faster

Deformation of a two-layer system is nearly independent of the presence or absence of a multilayer stack in between


Test for more complex geometry


Thank you

sgm bern 11/25/2006 marcel frehner 1 numerical simulations of parasitic folding in multilayers sgm...

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