Lecture 1, 08-02-2023
Deformation in the Earth’s crust and mantle:
- Geometry: description of structure
- Kinematics: motions that resulted in
development of structures
- Dynamics: forces, responses of rock
(mechanical properties)
Strain à change in shape, with or without
volume change.
Deformation is also possible without strain. The
deformation can then be found with an internal
and external reference frame. Internal à
changing in shape, external à with respect to.
Strain can be homogeneous or heterogeneous.
Homogeneous:
- Straight lines remain straight (2D)
- Parallel lines remain straight (2D)
- Planes remain straight (3D)
- Rigid rotation and translation
Heterogeneous: the state of strain (strain ellipse or ellipsoid)
varies within the area or volume in question. Strain and
volume/area change.
Scale is important, a deformation that is homogeneous on one
scale can be heterogeneous on a different scale.
Different measures of strain:
- Linear strain DL
o Difference between final and initial
o (L-L0)/L0 = elongation
o L/L0 = stretch
o (L/L0)2 = quadratic elongation
o Ln(S) = natural strain = related to strain
rate
- Volumetric strain DV
o (V-V0)/V0
o V/V0
- Shear (angular) strain Dy
o g = tany
o Angular shear describes the change in angle between two originally
perpendicular lines in a deformed medium.
Strain ellipse:
- Axes S1, S2 (or x, y)
- Ratio S1/S2
- 2 lines of no finite longitudinal strain
,Lecture 2, 10-02-2023
FLINN diagram and logarithmic FLINN diagram. Logarithmic describes volume change, to the
right is decrease to the left is increase. When you’re looking at 1 line, to the left is the
constriction field and to the right the flattening field.
Rf-f’ method:
The effect of deformation on a series of elliptical
objects. The original objects are ellipses Ri. The ellipses
deform into ellipses of a new axial ratio Rf. The final
ratio Rf depends on Ri, strain ratio Rs and orientation f’.
A. Pebbles in different orientations, different
shapes. The initial ratio is 2 so both plot on the Ri
2 line.
B. Shortened in vertical direction, ratio goes down,
angle decreases of the green one.
C. Strain ratio is more à more shortening.
When Rs<Ri à 𝑅𝑠 = $𝑅𝑓𝑚𝑎𝑥/𝑅𝑓𝑚𝑖𝑛 and
𝑅𝑖 = $𝑅𝑓𝑚𝑎𝑥 ∗ 𝑅𝑓𝑚𝑖𝑛
When Rs>Ri à 𝑅𝑠 = $𝑅𝑓𝑚𝑎𝑥 ∗ 𝑅𝑓𝑚𝑖𝑛 and
𝑅𝑖 = $𝑅𝑓𝑚𝑎𝑥/𝑅𝑓𝑚𝑖𝑛
Angular method:
- In 2D
- Uses distortion/shearing of objects that were originally symmetrical.
- Strain ratio only
- Formula’s: g= f(f’, f, R)
f’ = final orientation
f = initial orientation
R = ratio s1 / s2
- With the Breddin curve
, Bulk method (Fry):
- In 2D
- Uses relative positions of centres of grains, ooids etc.
- Assumes spheres/circles before straining.
- Best fit ellipse through ‘band’ of highest data density: strain ratio
- Improves through ‘normalization’ for size.
- With the dots moving
- Zooms in on grain aggregates à elliptic shape forms à strain ellipse.
Lecture 3, 15-02-2023
Different fold mechanisms:
- Buckling: shortening parallel to the layering
- Bending: equal but opposite torques (intrusion)
- Passive/shear folding: flow
Passive shear folding:
- Contrast is material properties are small
- Markers indicate bulk strain
Reduction spots à reduction of ferric oxide (Fe2O3) to ferrous oxide.
Bending Buckling
Initiation Pairs of forces: equal but Instability needs (parallel to
Compression opposite torques layer)
Net shearing (perpendicular to layer)
Orthogonal flexure: lines originally perpendicular and remain so
Flexural shear: internal shearing of layers
Solution flexure: volume loss (notably in inner arc)
Different position of the neutral surface
No neutral surface, different orientation long axis in hinge
No strain in outer arc in case of bending
Deformation in the Earth’s crust and mantle:
- Geometry: description of structure
- Kinematics: motions that resulted in
development of structures
- Dynamics: forces, responses of rock
(mechanical properties)
Strain à change in shape, with or without
volume change.
Deformation is also possible without strain. The
deformation can then be found with an internal
and external reference frame. Internal à
changing in shape, external à with respect to.
Strain can be homogeneous or heterogeneous.
Homogeneous:
- Straight lines remain straight (2D)
- Parallel lines remain straight (2D)
- Planes remain straight (3D)
- Rigid rotation and translation
Heterogeneous: the state of strain (strain ellipse or ellipsoid)
varies within the area or volume in question. Strain and
volume/area change.
Scale is important, a deformation that is homogeneous on one
scale can be heterogeneous on a different scale.
Different measures of strain:
- Linear strain DL
o Difference between final and initial
o (L-L0)/L0 = elongation
o L/L0 = stretch
o (L/L0)2 = quadratic elongation
o Ln(S) = natural strain = related to strain
rate
- Volumetric strain DV
o (V-V0)/V0
o V/V0
- Shear (angular) strain Dy
o g = tany
o Angular shear describes the change in angle between two originally
perpendicular lines in a deformed medium.
Strain ellipse:
- Axes S1, S2 (or x, y)
- Ratio S1/S2
- 2 lines of no finite longitudinal strain
,Lecture 2, 10-02-2023
FLINN diagram and logarithmic FLINN diagram. Logarithmic describes volume change, to the
right is decrease to the left is increase. When you’re looking at 1 line, to the left is the
constriction field and to the right the flattening field.
Rf-f’ method:
The effect of deformation on a series of elliptical
objects. The original objects are ellipses Ri. The ellipses
deform into ellipses of a new axial ratio Rf. The final
ratio Rf depends on Ri, strain ratio Rs and orientation f’.
A. Pebbles in different orientations, different
shapes. The initial ratio is 2 so both plot on the Ri
2 line.
B. Shortened in vertical direction, ratio goes down,
angle decreases of the green one.
C. Strain ratio is more à more shortening.
When Rs<Ri à 𝑅𝑠 = $𝑅𝑓𝑚𝑎𝑥/𝑅𝑓𝑚𝑖𝑛 and
𝑅𝑖 = $𝑅𝑓𝑚𝑎𝑥 ∗ 𝑅𝑓𝑚𝑖𝑛
When Rs>Ri à 𝑅𝑠 = $𝑅𝑓𝑚𝑎𝑥 ∗ 𝑅𝑓𝑚𝑖𝑛 and
𝑅𝑖 = $𝑅𝑓𝑚𝑎𝑥/𝑅𝑓𝑚𝑖𝑛
Angular method:
- In 2D
- Uses distortion/shearing of objects that were originally symmetrical.
- Strain ratio only
- Formula’s: g= f(f’, f, R)
f’ = final orientation
f = initial orientation
R = ratio s1 / s2
- With the Breddin curve
, Bulk method (Fry):
- In 2D
- Uses relative positions of centres of grains, ooids etc.
- Assumes spheres/circles before straining.
- Best fit ellipse through ‘band’ of highest data density: strain ratio
- Improves through ‘normalization’ for size.
- With the dots moving
- Zooms in on grain aggregates à elliptic shape forms à strain ellipse.
Lecture 3, 15-02-2023
Different fold mechanisms:
- Buckling: shortening parallel to the layering
- Bending: equal but opposite torques (intrusion)
- Passive/shear folding: flow
Passive shear folding:
- Contrast is material properties are small
- Markers indicate bulk strain
Reduction spots à reduction of ferric oxide (Fe2O3) to ferrous oxide.
Bending Buckling
Initiation Pairs of forces: equal but Instability needs (parallel to
Compression opposite torques layer)
Net shearing (perpendicular to layer)
Orthogonal flexure: lines originally perpendicular and remain so
Flexural shear: internal shearing of layers
Solution flexure: volume loss (notably in inner arc)
Different position of the neutral surface
No neutral surface, different orientation long axis in hinge
No strain in outer arc in case of bending
