Term 1 - Finite strain, tectonite fabrics & volume change Flashcards
Types of deformation
- Translation
- Rotation
- Distortion (=strain)
- Volume change (=dilation)
Finite strain
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
Homogeneous vs. Heterogeneous strain
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
Finite strain ellipsoid
- 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
Types of strain:
• 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
Tectonite fabrics
• 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
What does each type of fabric tells you type of strain?
• 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!
The Flinn plot
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
Finn Plot equation
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
Finn Plot knowledge
(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
Finn Plot construction process
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
Assumptions made when using a Finn Plot for whole rock unit
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
What assumption have we made concerning the original shape of the pebbles? Is this reasonable? (Finn Plot deformation)
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
Volumetric strain derivation
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