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Competence μ1 μ0 μ2 μ3 μ4 μ0=μ1<μ2<μ3<μ4 Viscosity Heterogeneous deformation results from mechanical instabilities (folding and boudinage) within an heterogeneous material or from strain localization in an homogeneous material (shear bands). Folding and boudinage Boudinage Folding CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION Va-1 INTRODUCTION
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• Competence

1

0

2

3

4

0=1

• Cylindrical folds have straight hinge lines (straight B axis).

BA

C

Hinge

Limb

Fold axes

B // HingeA hingeand // axial surfaceC axial surface

T

T diagram

In cylindrical fold poles areoriented at 90 of the B axis

circle

B axis

Va-2-1 FOLDS-Morphology

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES The hinge line joins the points of maximum curvature on a folded surface.The axial surface contains the hinge lines of many folded surfaces. This surface is not necessarily planar

On a stereonet, the distribution of poles gives information about the geometry of folds.

• diagram

B axis

facet

It is not possible to determine the attitude of the axial surface from or diagram alone. For this, we need to plot the axial trace (trace of the axial surface on the ground surface).The B axis and the axial trace are two lines that belong the axial surface.

B axis

Axial trace

Ground surface

B axis

Axial trace

Axial surface

This construction assumes that the B axis and the axial trace are not parallel to each other.

Construction of the axial surface

Va-2-1 FOLDS-Morphology

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• Isopach

hinge

Inclined fold Recumbent fold

Vertical foldPlunging fold

SimilarConcentric

younging

Open Tight

Isoclinal

Reclined fold

Axial surface

Overturned fold

Crest

hinge

Trough

horizontal

t

tt

t

t t

t

e

ee

e

Kink foldRootlessPtygmatic fold

Va-2-1 FOLDS-Classification

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• So

S1

Cleavage fan

Crenulation cleavage: The development of fine scale microfolding can produce systematic realignment of pre-existing layering.

S1So 1 cm

1 m

S1: A xial plane cleavage (12 plane)

S1So

Fracture cleavage

10 cm

Intersection lineation

Fold rodding lineationor crenulation lineation

Parasitic fold

Cleavagerefraction

Quartzite

Phyllite

Va-2-1 FOLDS-Associated linear and planar microstructures

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• Outer arc lengthens

Inner arc shortens

Neutral surface

Flexural shear foldingOrthogonal flexure

hinge

shear planes

Volume loss flexure

Va-2-1 FOLDS-Kinematic models of folding

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

Neutral surface

The geometry of folds largely depends on the way they are formed. There are a limited number of kinematic models...

Flexural folding produces isopach folds. This mode of folding can be achieved through three mechanisms: Orthogonal Flexure, Shear Flexure or Volume-loss Flexure.

Dissolution

Shear // to limbs

Neutral surface

Shear planes

Axial surface

Passive shear folding produces similar folds. This mode of folding is achieved through heterogeneous simple shear. Folds develop with their axial surfaces parallel to the shearing planes.

Shearzone

Shearzone

Symmetric fold

Asymmetric fold

• Va-2-1 FOLDS-Kinematic models of folding

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

Fault-bend fold Fault-propagation fold

Fault tip

Fault ramp

Anticlinal stacks

Rollover anticline

Kink band

= kink angle

Axial surface

Kink band

Formation of kink and chevron folds.Folds with straight limbs and sharp hinge are chevron folds if they area symmetric and kink folds if they are asymmetric. They develop in strongly layered or laminated sequences that have a strong planar mechanical anisotropy.

Development of chevron folds by kinking.

Development of kink folds.

Geometry of a kink band and terminology.

Folds may develop in close association with and as the result of faulting. The first example (sketches on the left) illustrates the development of a faut-bend fold in association with a fault ramp. The second example (sketches on the right) illustrates the development of a fault-propagation fold above the tip of a propagating thrust.

Finally, folds also develop has a consequences of extensional tectonics. The sketch on the rigth illustrate a rollover anticline in association with an extensional detachment fault.

Detachment

• Va-2-1 FOLDS-Kinematic models of folding

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

Progressive flatenning

• Va-2-1 FOLDS-Kinematic models of folding

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

Drag Folds. When rocks are subjected to shear, layers in the rock commonly form asymmetric folds whose sense of asymmetry reflects the sense of shear. Such folds are called drag folds and are the result of velocity gradient in the shear zone. Drag folds are noncylindrical and asymmetric. Their axial planar surface tends to be parallel to the shearing plane.

Sheath folds are a particular class of drag fold. They are tube-shaped fold with an elliptic or even a circular section. They develop with their a axis parallel to the direction of shearing.

• Z fold S fold

Fold asymmetry, bedding-cleavage relationships, stratigraphy up direction,and vergence.

A xial plane cleavage (12 plane)

Bedding

Stratigraphy up

Z fold S fold

100 m

M fold

Scale independent microtectonic laws

Va-2-1 FOLDS-Fold systems

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

Vergence is a term used to indicate the direction of movement and rotation that occured during deformation.

• 200 m1

1

3

2

23

Stratigraphy up direction

fold asymmetry

bedding-cleavage

4

Vergence of displacement4

The determination of two of these criteria leadto the determination of the two others.

Scale independent microtectonic laws

Va-2-1 FOLDS-Fold systems

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• So

S1

Vergence of the fold ?

Scale independent microtectonic laws

Va-2-1 FOLDS-Fold systems

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• Vergence of the fold ?

Scale independent microtectonic laws

Va-2-1 FOLDS-Fold systems

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• Boudin lines

Boudin

Neck lines

Neck

Pinch-and-swell structures

Crystallization in pressure shadowNeck foldSymmetric boudinage

Va-2-2 BOUDIN AND BOUDINAGE

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• Shearzone

Orientation and magnitude of finites strain ellipses and trajectories of S1 across a ductile shear zone resulting from inhomogeneous progressive simple shear.

Inhomogeneous progressive simple shear

= tg

SIMPLE SHEAR

0

S1 tra

jecto

ries

Va-2-3 DUCTILE SHEAR ZONES

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• Shearzone

Inhomogeneous progressive pure shear

Orientation and magnitude of finites strain ellipses and trajectories of S1 across a ductile shear zone resulting from inhomogeneous progressive pure shear.

= 1/

PURE SHEAR

Va-2-3 DUCTILE SHEAR ZONES

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• Mylonitic zonea, L

c, N

b, M

Shearplane

Movementplane

Sheardirection

(a, L), (b, M), (c, N) : kinematic axes

a, L

b, M

X, 1

Z, 3

Y, 2

Y

c, N Z

YX

protolith

Va-2-3 DUCTILE SHEAR ZONES: The kinematic reference frame

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-2 STRUCTURES

• 3

1

A B

C

D

A'B'

C'

D'

A' B' C' D' 1 1 1 1

33

Surfaces of non-deformation

1

3 2D 3D

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOIDVa-3-1 FOLDS AND BOUNDINS

• 1

2

2 2

1

3

FlatteningConstriction

FlatteningConstriction

1

3

2

3

3

1

2Plane strain

Plane strain

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOIDVa-3-1 FOLDS AND BOUDINS

3

3

1

2

1

2

1

33

1

2

1

2

1 3

3

3

2

1

3

1

2

3

• CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOIDVa-3-1 FOLDS AND BOUDINS

Development of cleavage during progressive flatenning

1

1

2

2

3

3

S1//12

Axial plane cleavage is parallel to the flattening plane (12) of the F.S.E.

• Usually, shear zones wrap around less deformed domains. The geometry of the shear zones net changes with the characteristics of the regional finite strain ellipsoid.

Lineation 1 = Gliding line

Characteristic structure of reactivated basement

Contriction: L // 1 N close to 3 M close to 2

Flattening : N close to 3 ML close to 12

Plane strain: M // 2 N close to 3 L close to 1

1

32

1

32

1

23

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOIDVa-3-2 DUCTILE SHEAR ZONES

• Two directions of stretching => pan-cacke shape ellipsoid

Two directions of shortening => cigar shape ellipsoidOne invariant direction (direction of non-deformation)=> plane strain ellipsoid

2

0

1

K=1

Ln (2/3)

Ln (

1/

2)

0 1 2

K = 8

K = 0

2

1

3

2

1

3

2

1

3

3

2

1

1

3

3

3

1

2

1

32

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-4 CHARACTERISATION OF THE FINITE STRAIN ELLIPSOID (K)Va-4-1 FOLDS AND BOUDINS

• Constriction Plane strain Flattening

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-4 CHARACTERISATION OF THE FINITE STRAIN ELLIPSOID (K)

• Two directions of stretching => pan-cacke like ellipsoid

Two directions of shortening => cigar like ellipsoidOne invariant direction (direction of non-deformation)=> plane strain ellipsoid

2

0

1Ln (X/Y)

Ln (Y/Z)

K=1

Ln (2/3)

Ln (1/2)

0 1 2

K = 8

K = 0

Uniaxial oblate

Uniaxial prolate

1

2

3

1

2

3

1

2

3

1

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-4 CHARACTERISATION OF THE FINITE STRAIN ELLIPSOID (K)

Va-4-3 DUCTILE SHEAR ZONES

• 3

1

3

1

3

1

3

1

Incrementalstrain ellipse

Finite strain ellipse

Non-deformation line

Line of non-deformation during progressive pure shear

The shortened domain increasesduring progressive pure shear.

Material lines rotate more rapidlythan the non-deformation lines.

Initial state

Incrementalextended domain

Finite extended domain

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

Va-5-1 DEFORMED VEINS

• Line of non-deformation during progressive simple shear

3 1

Incrementalstrain ellipse

Non-deformation line

Finite strain ellipse

During simple shear the shearing planeis a plane of non-deformation, thereforethere is only one area in which lineswill be shortened then stretched.

On the field, one looks for directions alongwhich veins have been shortened thenstretched. If those veins are withinone quadrant then we concludefor the non-coxiality of the deformation.

Initial state

Finite extendeddomain

Incrementalextended domain

3 1

3 1

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

Va-5-1 DEFORMED VEINS

Incrementalshortened domain

• CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

1

32

1

32

M N L

M N L

3 3 3

3 3 3

1 1 1

1 1 1

Coaxial deformation

Non-coaxial deformation

Va-5-2 Anastomosed ductile shear zones

• S planes: Schistosity

C planes: shear planes

C planes

S planes C/S fabricsThe number of C planes increase towardthe mylonite.

C/S planes

C' planes

C/S/C' fabrics

C' shear planes are extensional shearbands which tend to reduce the thicknessof the ductile shear zone.

Asymetric boudinage of a mylonitic zone C' planes

M N L

3 3 3

1 1 1

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

Va-5-3 C/S, C/S/C' fabrics

1 average trajectory

• 1mm

phg

grt

czo

omp

ENEWSW

b/

C plane

S plane 1mm

phg

grt

czo

kyomp

ENEWSW

a/

Pressure shadows and crystallization tails during simple shear

Tiling structure

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

• CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

Pressure shadows and crystallization tails during pure shear

Face-controlled, deformable fibres formed and deformed in progresssive simple shear

Pyrite grain

Quartz fibres

• Crystal slip

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

Va-5-5 MICRO-SHEARS

Mica fish

• 1c axis

Slip plane

Macroscopic pure shear

Preferred crystallographic orientation by dislocation glide

Ductile deformation by dislocation creep produces characteristic preferred orientations of mineral crystallographic axes. The pattern of CPO depends on:

->the slip systems that are actived (depends on temperature and stress)

->the geometry and the magnitude of the deformation

Coaxial deformation -> fabrics symmetric to the principal axes of finite strain

Noncoaxial deformation -> asymmetric fabric

c axis

Slip plane

Macroscopic simple shear

c axis

1

c axis1

3

C axis fabrics

1

c axis

1

c axis

3

C axis fabrics

Symmetric

Asymmetric

CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

Va-5 STRAIN REGIME

Va-5-6 CRYSTALLOGRAPHIC FABRICS