CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION€¦ · CHAPTER Va : CONTINUOUS HETEROGENEOUS...
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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
Cylindrical folds have straight hinge lines (straight B axis).
BA
C
Hinge
Limb
Fold axes
B // HingeA hingeand // axial surfaceC axial surface
T
Tπ diagram
In cylindrical fold π poles areoriented at 90º of the B axis
π 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 π poles gives information about the geometry of folds.
β diagram
B axis
β facet
It is not possible to determine the attitude of the axial surface from π or β 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 (λ1λ2 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
Extrado fracturesIntrado stylolites
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
κ = kink angle
Axial surface
γ
γKink 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 (λ1λ2 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
Asymmetric boudinage, asymmetric pressure shadows
Va-2-2 BOUDIN AND BOUDINAGE
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-2 STRUCTURES
θ
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
γ = tg ψψ
γSIMPLE SHEAR
λ0
S1 trajecto
ries
θ
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.
α = λ1/λο
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, λ1
Z, λ3
Y, λ2
Y
c, N Z
YX
protolith
Va-2-3 DUCTILE SHEAR ZONES: The kinematic reference frame
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-2 STRUCTURES
λ3
λ1
A B
C
D
A'B'
C'
D'
A' B' C' D' λ1 λ1 λ1 λ1
λ3λ3
Surfaces of non-deformation
λ1
λ3 2D 3D
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOIDVa-3-1 FOLDS AND BOUNDINS
λ1
λ2
λ2 λ2
λ1
λ3
FlatteningConstriction
FlatteningConstriction
λ1
λ3
λ2
λ3
λ3
λ1
λ2Plane strain
Plane strain
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOIDVa-3-1 FOLDS AND BOUDINS
λ3
λ3
λ1
λ2
λ1
λ2
λ1
λ3λ3
λ1
λ2
λ1
λ2
λ1 λ3
λ3
λ3
λ2
λ1
λ3
λ1
λ2
λ3
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
λ1
λ1
λ2
λ2
λ3
λ3
S1//λ1λ2
Axial plane cleavage is parallel to the flattening plane (λ1λ2) 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 λ1 = Gliding line
Characteristic structure of reactivated basement
Contriction: L // λ1 N close to λ3 M close to λ2
Flattening : N close to λ3 ML close to λ1λ2
Plane strain: M // λ2 N close to λ3 L close to λ1
λ1
λ3λ2
λ1
λ3λ2
λ1
λ2λ3
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 (λ2/λ3)
Ln (
λ 1/λ
2)
0 1 2
K = 8
K = 0
λ2
λ1
λ3
λ2
λ1
λ3
λ2
λ1
λ3
λ3
λ2
λ1
λ1
λ3
λ3
λ3
λ1
λ2
λ1
λ3λ2
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)
Va-4-2 PRESSURE SHADOWS
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 (λ2/λ3)
Ln (λ1/λ2)
0 1 2
K = 8
K = 0
Uniaxial oblate
Uniaxial prolate
λ1
λ2
λ3
λ1
λ2
λ3
λ1
λ2
λ3
λ1
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-4 CHARACTERISATION OF THE FINITE STRAIN ELLIPSOID (K)
Va-4-3 DUCTILE SHEAR ZONES
λ3
λ1
λ3
λ1
λ3
λ1
λ3
λ1
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
λ3 λ1
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
λ3 λ1
λ3 λ1
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
λ1
λ3λ2
λ1
λ3λ2
M N L
M N L
λ3 λ3 λ3
λ3 λ3 λ3
λ1 λ1 λ1
λ1 λ1 λ1
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
θ
M N L
λ3 λ3 λ3
λ1 λ1 λ1
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-5 STRAIN REGIME
Va-5-3 C/S, C/S/C' fabrics
λ1 average trajectory
1mm
phg
grt
czo
omp
ENEWSW
b/
C plane
S plane1mm
phg
grt
czo
kyomp
ENEWSW
a/
Pressure shadows and crystallization tails during simple shear
Tiling structure
σ pressure shadows
δ pressure shadows
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-5 STRAIN REGIME
Va-5-4 PRESSURE SHADOWS
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-5 STRAIN REGIME
Va-5-4 PRESSURE SHADOWS
Pressure shadows and crystallization tails during pure shear
Face-controlled, deformable fibres formed and deformed in progresssive simple shear
Pyrite grain
Quartz fibres
ψ pressure shadows
Crystal slip
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-5 STRAIN REGIME
Va-5-5 MICRO-SHEARS
Mica fish
λ1
c 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
λ1
c axisλ1
λ3
C axis fabrics
λ1
c axis
λ1
c axis
λ3
C axis fabrics
Symmetric
Asymmetric
CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION
Va-5 STRAIN REGIME
Va-5-6 CRYSTALLOGRAPHIC FABRICS