CHAPTER Va : CONTINUOUS HETEROGENEOUS DEFORMATION

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1 Va-1 INTRODUCTION 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 µ0 µ1 µ2 µ3 µ4 µ0=µ1<µ2<µ3<µ4 Viscosity Competence Folding Boudinage

2 Va-2 STRUCTURES Va-2-1 FOLDS-Morphology Fold axes A B Hinge 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 C Limb B // Hinge A hinge and // axial surface C axial surface T T Cylindrical folds have straight hinge lines (straight B axis). π circle B axis In cylindrical fold π poles are oriented at 90º of the B axis π diagram On a stereonet, the distribution of π poles gives information about the geometry of folds.

3 Va-2 STRUCTURES Va-2-1 FOLDS-Morphology β facet B axis β diagram Construction of the axial surface 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. Axial trace Ground surface Axial surface B axis B axis Axial trace This construction assumes that the B axis and the axial trace are not parallel to each other.

4 Va-2 STRUCTURES Va-2-1 FOLDS-Classification hinge t t e e Concentric t Isopach t t t t Similar e e younging Open Tight Axial surface Crest horizontal Isoclinal Inclined fold Overturned fold hinge Recumbent fold Trough Plunging fold Vertical fold Reclined fold Kink fold Ptygmatic fold Rootless

5 Va-2 STRUCTURES Va-2-1 FOLDS-Associated linear and planar microstructures Parasitic fold S1 Crenulation cleavage: The development of fine scale microfolding can produce systematic realignment of pre-existing layering. So Cleavage refraction So S1 1 cm Cleavage fan 1 m Fracture cleavage S1: A xial plane cleavage (λ 1 λ 2 plane) 10 cm Intersection lineation So S1 Quartzite Fold rodding lineation or crenulation lineation Phyllite

6 Va-2 STRUCTURES Va-2-1 FOLDS-Kinematic models of folding 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. Orthogonal flexure Flexural shear folding Volume loss flexure Neutral surface Outer arc lengthens shear planes Extrado fractures Inner arc shortens Intrado stylolites Shear // to limbs hinge Dissolution Neutral surface Neutral 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. Shear planes Symmetric fold Asymmetric fold Axial surface Shear zone Shear zone

7 Va-2 STRUCTURES Va-2-1 FOLDS-Kinematic models of folding 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. Geometry of a kink band and terminology. Development of chevron folds by kinking. Kink band Axial surface γ Development of kink folds. Kink band γ κ = kink angle 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. Fault-bend fold Fault-propagation fold Fault ramp Anticlinal stacks Fault tip 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 Rollover anticline

8 Va-2 STRUCTURES Va-2-1 FOLDS-Kinematic models of folding Progressive flatenning

Such folds are called drag folds and are the result of velocity gradient in the shear zone. Drag folds are noncylindrical and asymmetric.

9 Va-2 STRUCTURES Va-2-1 FOLDS-Kinematic models of folding 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.

10 Va-2 STRUCTURES Va-2-1 FOLDS-Fold systems Scale independent microtectonic laws Fold asymmetry, bedding-cleavage relationships, stratigraphy up direction, and vergence. A xial plane cleavage (λ2 plane) Bedding Stratigraphy up 100 m Z fold M fold S fold Z fold S fold Vergence is a term used to indicate the direction of movement and rotation that occured during deformation.

11 Va-2 STRUCTURES Va-2-1 FOLDS-Fold systems Scale independent microtectonic laws m 3 bedding-cleavage 1 Stratigraphy up direction 2 fold asymmetry The determination of two of these criteria lead to the determination of the two others. 4 Vergence of displacement

12 Va-2 STRUCTURES Va-2-1 FOLDS-Fold systems Scale independent microtectonic laws So S1 Vergence of the fold?

13 Va-2 STRUCTURES Va-2-1 FOLDS-Fold systems Scale independent microtectonic laws Vergence of the fold?

14 Va-2 STRUCTURES Va-2-2 BOUDIN AND BOUDINAGE Pinch-and-swell structures Boudin Neck Boudin lines Neck fold Neck lines Symmetric boudinage Crystallization in pressure shadow Asymmetric boudinage, asymmetric pressure shadows

15 Va-2 STRUCTURES Va-2-3 DUCTILE SHEAR ZONES Inhomogeneous progressive simple shear θ S1 trajectories Shear zone Orientation and magnitude of finites strain ellipses and trajectories of S1 across a ductile shear zone resulting from inhomogeneous progressive simple shear. SIMPLE SHEAR γ λ0 ψ θ γ = tg ψ

16 Va-2 STRUCTURES Va-2-3 DUCTILE SHEAR ZONES Inhomogeneous progressive pure shear Shear zone Orientation and magnitude of finites strain ellipses and trajectories of S1 across a ductile shear zone resulting from inhomogeneous progressive pure shear. PURE SHEAR α = λ 1 /λ ο

17 Va-2 STRUCTURES Va-2-3 DUCTILE SHEAR ZONES: The kinematic reference frame (a, L), (b, M), (c, N) : kinematic axes Movement plane c, N Shear plane Shear direction a, L b, M Mylonitic zone b, M a, L c, N Z Y X Z, Y X, Y, λ2 protolith

18 Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOID Va-3-1 FOLDS AND BOUNDINS λ 3 λ 1 A B C A' B' C' Surfaces of non-deformation D D' λ 1 2D λ 3 3D λ 1 λ 1 λ 1 A' B' C' D' λ 3 λ 3

19 Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOID Va-3-1 FOLDS AND BOUDINS λ 3 λ 1 λ 2 λ 2 λ 3 λ 1 λ 1 λ 3 λ 2 λ 1 Constriction Flattening λ 3 λ 2 λ 1 λ 3 λ 2 λ 1 λ 2 Plane strain λ 2 λ 1 λ 3 λ 3 λ 2 λ 3 λ 1 Plane strain λ 1 λ 3 λ 2 λ 2 λ 1 λ 1 λ 3 λ 3 λ 2 Constriction Flattening λ 3 λ 1

20 Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOID Va-3-1 FOLDS AND BOUDINS Development of cleavage during progressive flatenning λ2 λ2 S1//λ2 Axial plane cleavage is parallel to the flattening plane (λ2) of the F.S.E.

21 Va-3 ORIENTATION OF THE AXES OF THE FINITE STRAIN ELLIPSOID Va-3-2 DUCTILE SHEAR ZONES 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. Characteristic structure of reactivated basement λ2 λ2 Plane strain: M // λ2 N close to L close to Flattening : N close to ML close to λ2 λ2 Contriction: L // N close to M close to λ2 Lineation = Gliding line

22 Va-4 CHARACTERISATION OF THE FINITE STRAIN ELLIPSOID (K) Va-4-1 FOLDS AND BOUDINS Two directions of stretching => pan-cacke shape ellipsoid Two directions of shortening => cigar shape ellipsoid One invariant direction (direction of non-deformation)=> plane strain ellipsoid 2 λ2 Ln (λ 1 /λ 2 ) λ2 K=1 λ2 1 λ2 K = 8 λ2 λ2 0 K = 0 Ln (λ 2 /λ 3 ) 0 1 2

23 Va-4 CHARACTERISATION OF THE FINITE STRAIN ELLIPSOID (K) Va-4-2 PRESSURE SHADOWS Constriction Plane strain Flattening

24 Va-4 CHARACTERISATION OF THE FINITE STRAIN ELLIPSOID (K) Va-4-3 DUCTILE SHEAR ZONES Two directions of stretching => pan-cacke like ellipsoid Two directions of shortening => cigar like ellipsoid One invariant direction (direction of non-deformation)=> plane strain ellipsoid 2 Uniaxial prolate λ2 K=1 Ln (X/Y) Ln (/λ2) 1 λ2 λ2 K = 8 0 K = Ln (Y/Z) Ln (λ2/) Uniaxial oblate

25 Va-5 STRAIN REGIME Va-5-1 DEFORMED VEINS Line of non-deformation during progressive pure shear Initial state Incremental extended domain Non-deformation line Incremental strain ellipse The shortened domain increases during progressive pure shear. Material lines rotate more rapidly than the non-deformation lines. Finite extended domain Finite strain ellipse

26 Va-5 STRAIN REGIME Va-5-1 DEFORMED VEINS Line of non-deformation during progressive simple shear Incremental shortened domain Incremental extended domain Initial state Non-deformation line Incremental strain ellipse During simple shear the shearing plane is a plane of non-deformation, therefore there is only one area in which lines will be shortened then stretched. On the field, one looks for directions along which veins have been shortened then stretched. If those veins are within one quadrant then we conclude for the non-coxiality of the deformation. Finite extended domain Finite strain ellipse

27 Va-5 STRAIN REGIME Va-5-2 Anastomosed ductile shear zones Coaxial deformation λ2 M N L Non-coaxial deformation λ2 M N L

28 Va-5 STRAIN REGIME Va-5-3 C/S, C/S/C' fabrics average trajectory S planes: Schistosity C planes: shear planes The number of C planes increase toward the mylonite. C planes θ S planes C/S fabrics C' planes C' shear planes are extensional shear bands which tend to reduce the thickness of the ductile shear zone. C/S/C' fabrics C/S planes M N L Asymetric boudinage of a mylonitic zone C' planes

29 Va-5 STRAIN REGIME Va-5-4 PRESSURE SHADOWS Pressure shadows and crystallization tails during simple shear σ pressure shadows δ pressure shadows C plane WSW ENE czo omp grt ky S plane a/ phg 1mm Tiling structure WSW czo ENE omp phg grt b/ 1mm

30 Va-5 STRAIN REGIME Va-5-4 PRESSURE SHADOWS Face-controlled, deformable fibres formed and deformed in progresssive simple shear Quartz fibres Pyrite grain Pressure shadows and crystallization tails during pure shear ψ pressure shadows

31 Va-5 STRAIN REGIME Va-5-5 MICRO-SHEARS Crystal slip Mica fish

32 Va-5 STRAIN REGIME Va-5-6 CRYSTALLOGRAPHIC FABRICS Ductile deformation by dislocation creep produces characteristic preferred orientations of mineral crystallographic axes. The pattern of CPO depends on: Preferred crystallographic orientation by dislocation glide Macroscopic pure shear ->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 c axis Slip plane c axis C axis fabrics Symmetric Macroscopic simple shear c axis c axis Slip plane c axis C axis fabrics Asymmetric

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Provided by Tasa Graphic Arts, Inc. for An Introduction to Structural Methods DVD-ROM http://www.tasagraphicarts.com/progstruct.html AN INTRODUCTION TO STRUCTURAL METHODS - DETAILED CONTENTS: (Navigate