Term 1 - Finite strain, tectonite fabrics & volume change

Question 1

Types of deformation

Answer 1

• Translation
• Rotation
• Distortion (=strain)
• Volume change (=dilation)

Question 2

Finite strain

Answer 2

The analysis of finite strain relates the lengths, positions & orientations of objects (e.g. grains, beds, fossils etc.)

A one-dimensional measure of strain is extension, e

e = (change in length)/original length

Question 3

Homogeneous vs. Heterogeneous strain

Answer 3

Homogeneous strain
• = EQUAL strain throughout
• Straight lines remain strain;
• Parallel lines remain parallel

Heterogenous strain
• = strain VARIES throughout
• straight lines become curved;
• parallel lines become non-parallel

Question 4

Finite strain ellipsoid

Answer 4

• Describe the geometry of an ellipsoid completely in terms of 3 mutually perpendicular axes:
  X, Y, Z = principal axes of finite strain
  By definition X ≥ Y ≥ Z

Question 5

Types of strain:

Answer 5

• Can define three “end-member” types of strain
– i.e. three different types of ellipsoid
= according to the relative lengths of the X, Y & Z axes

Three-dimensional strain: All three axes change

Prolate strain: X > Y = Z: Elongate shape
Y & Z = same length
X = longer

Oblate strain: X = Y > Z: Minstrel
X & Y = same length
Z = shorter

Two-dimensional strain: 2 axes change

Plain strain: X > Y = 1 > Z : Rugby Ball
Y = 1 – i.e. Y doesn’t change
X = longer
Z = shorter

Question 6

Tectonite fabrics

Answer 6

• The preferential alignment of ellipsoids of different shape produces different types of fabric

S-tectonite: Cuboid
L-tectonite: more squished 3D rectangle
LS-tectonite: Angular rectangle

Question 7

What does each type of fabric tells you type of strain?

Answer 7

• Prolate strain
o Produces linear fabric (mineral stretching lineations)
o Only L-tectonites

• Oblate strain
o Produces planar fabric (cleavage/foliation) only
o Only S-tectonites

• Plane strain
o Produces rock with both planar and linear fabrics (mineral stretching lineation that lies in the foliation/cleavage plane)
Only LS-tectonites

• Mineral stretching lineation is parallel to the X axis of the finite strain ellipsoid
• Foliation/cleavage is parallel to the XY plane of the finite strain ellipsoid
•  We can determine the orientation of the finite strain ellipsoid by looking at the deformation fabrics!

Question 8

The Flinn plot

Answer 8

R_xy vs. R_yz

Flinn plot is good for showing variations in type and magnitude of finite strain

Does not illustrate how strain varies spatially
Does not show the rotational component of strain

• Prolate strain Y < 1
• Oblate strain Y > 1
• Plane strain Y = 1

Question 9

Finn Plot equation

Answer 9

Rxy vertical axis
Ryz horizontal axis
Origin at (1,1)

k=(Rxy-1)/(Ryz-1)

•	The k value defines the type of strain on the Flinn plot
o	Prolate (k = ∞)
o	Plane strain (k=1)
o	Oblate (k =0)
App. constriction (∞>k>1)
App. flattening (1>k>0)

• Greater magnitudes of strain plot further away from the origin

Question 10

Finn Plot knowledge

Answer 10

(A) If a deformed rock possesses a planar or linear fabric which reflects the finite strain geometry, then: (1) the planar fabric (e.g. foliation, cleavage etc) will lie in the XY plane of the finite strain ellipsoid; and (2) the linear fabric (e.g. mineral stretching lineation) will lie parallel to the X axis of the finite strain ellipsoid.
(B) The shape of the finite strain ellipsoid (i.e. the type of finite strain) is given by:

k = (Rxy-1)/(Ryz-1) (Equation 1)

Equation 1 is used for calculating “k” values on linear Flinn plots.

The cleavage is parallel to the XY principal plane so use that for

Question 11

Finn Plot construction process

Answer 11

Rxy = Cleavage long axis (x) / mean short axis (y) of cleavage
Ryz = Joint long axis (x) / joint short axis (y)
(optional) Rxz = Multiple Ryz by Rxy

Calculate K for each = (Rxy-1)/(Ryz-1)

Plot on graph, Rxy on Y, Rxz on X, draw a line through origin

Question 12

Assumptions made when using a Finn Plot for whole rock unit

Answer 12

We assume that the strain recorded by the deformed quartz pebbles reflects the bulk finite strain experienced by the surrounding quartzite, i.e. the strain was homogeneous.
it is a reasonable assumption if both pebbles and host rock have the same composition (i.e. both are composed of quartz), thus we expect them to deform in a similar manner

Question 13

What assumption have we made concerning the original shape of the pebbles? Is this reasonable? (Finn Plot deformation)

Answer 13

We assume that the pebbles were originally spherical. This may or may not be a reasonable assumption – we do not have enough information in the questions to decide. If we were in the field, you should have traced the pebble band outside the shear zone and measure the shapes of the undeformed pebbles before carrying out a strain analysis

Question 14

Volumetric strain derivation

Answer 14

𝑉_𝑑 is the volume of the deformed rock
𝑉_𝑜 is the original volume

Volume of a sphere =4/3 𝜋𝑟^3- and we assume r = 1
Volume of an ellipsoid =4/3 𝜋𝑋𝑌𝑍
So, the volumetric strain, ∆𝑉∆𝑉 =𝑋𝑌𝑍−1∆𝑉= (1+𝑒_𝑥 )(1+𝑒_𝑦 )(1+𝑒_𝑧 )−1