Week 2 Flashcards
Forms of deformation
Translation
Rotation
Distortion
Dilation
(Latter two = strain, previous two can occur without strain)
Is ACW +ve or -ve?
+ve
Is compression +ve/-ve
+ve
What is the finite strain ellipsoid?
3 mutually perpendicular axes (3D) and 3 principle planes
X>=Y>=Z
XY, XZ, YZ
What is strain in 1 dimension?
Extension
= (ld-lo)/lo
e(x), e(y), e(z)
= principal longitudinal strain // to x/y/z
Magnitude of strain =
axial ratio (ellipticity, R) of cross section containing X and Z (longest and shortest) axes
R(xz) = X/Z = (1+e(x))/(1+e(z))
Equation of strain ellipsoid
(x/1+e(x))^2 + (y/1+e(y))^2 + (z/1+e(z))^2 = 1
How do you determine the orientation of the strain ellipsoid?
Plunge/azimuth of principle axes
(X = mineral stretching lineation)
Strike/dip/dip direction of principle planes
(XY = foliation/cleavage planes)
Types of strain (+how many dimensions?)
PROLATE (3D)
OBLATE (3D)
PLANE (2D)
PROLATE STRAIN
X > Y = Z
Lineation
L-tectonite
Linear fabric
‘rods’
// to x-axis of FSE
OBLATE STRAIN
X = Y > Z
Foliation/cleavage
S-tectonite
‘sheets’
Planar fabric
// to XY plane of FSE
PLANE STRAIN
X > Y > Z, Y = 1
Foliation and lineation (along foliation planes)
LS-tectonite
Planar and linear fabrics
‘Sheets with lineations on surface’
What is a Flinn plot as a graph?
y-axis = R(xy) = X/Y
x-axis = R(yz) = Y/Z
Goes through the point (1,1)
k = 1
GREATER MAGNITUDES OF STRAIN PLOT FURTHER AWAY FROM ORIGIN
k =
(R(xy)-1) / (R(yz)-1)
Importance of y values in the Flinn plot
Prolate Y < 1 ; k=infinity
Oblate Y > 1; k=0
Plane Y = 1; k=1
Where do different types of strain plot on the Flinn Plot?
Prolate to left of k=1 line
- apparent constriction
- L-tectonite
Plane on the k=1 line
- L-S tectonite
Oblate to the right of the k=1 line
- apparent flattening
- S-tectonite
Volumetric strain equation
/\V= (V(d)-V(o)) / V(o)
Since volume of ellipsoid = 4/3 x pi x (XYZ)
Volume of sphere = 4/3 x pi
/\V = XYZ - 1
= (1+e(x)) (1+e(y)) (1+e(z)) -1
/\V>0
Volume gain
e. g. veins/dykes/sills
- can identify X as EXTENDING
/\V<0
Volume loss
e. g. cleavage/stylolites
- can identify z as SHORTENING
/\V=0
Compensation
Strain;
how rock body has changed shape, vol, orientation and position during deformation
Kinematics;
how geometry of rock body and strain evolved during deformation
Dynamics;
orientation, magnitude and origin of forces/stresses that caused deformation
Why is structural geology important?
RECONSTRUCT EVENTS
- deformation processes
- plate motions, mountain building, basin formation
PETROLEUM
MINING
- minerals/metals in veins
- distribution of veins related to fractures and local/regional stresses
CONSTRUCTION + ENGINEERING
- e.g. landslide risk
- house foundations
Stress =
forces that cause the strain
Stress = force/area
Confining pressure;
force equal in all direction
Differential stress;
force not equal in all directions
Elastic deformation =
rocks return to original state when stress removed
Permanent deformation =
preserved after stress relaxation
Brittle vs ductile deformation
Brittle = cracks/fracture/cold-shallow
Ductile = flow/bend/hot-deep
Primary structures =
related to original deposition and formation of rock
Secondary structures =
formed by deformation (modify primary)
e.g. faults/folds/foliations
Kinematic predictions from geometric and evolutionary models
Approximates each limb of folds to stack of rigid layers (equivalent to “beds”)
Layers are free to slide past each other
(Follow evolutionary model as they do this)
GEOLOGICAL REALITY CHECK
Kinematic and stress predictions from mechanical models
Approximates each bed to a series of “elements” with stresses acting along their edges
Use computer simulation/mathematical solution = predict how shape/vol/position/orientation of each element and therefore over fold shape will change
GEOLOGICAL REALITY CHECK
Fundamental challenges in structural geology
Parts of structure missing = difficult to define geometry/quantify strain
We don’t see intermediate stages = difficult to test evolutionary model/kinematic predictions
Do not know state of stress at time of deformation = difficult to verify mechanical models
Do not know material properties at time of deformation = above
Which axis of the FSE is mineral stretching lineation parallel to?
X axis
Which plane of the FSE is foliation/cleavage // to?
XY plane
Rxz =
Rxy x Ryz
Assumptions when applying the Flinn plot to find the type of strain
Assume strain recorded by (e.g. deformed quartz pebbles) reflects the bulk finite strain experienced by the surrounding rock i.e. strain was homogeneous - reasonable if pebbles and host rock have same composition
Original shape of particle = sphere
Where would a veined rock plot on the Flinn plot? What is /\V?
/\V>0
Plot along k=infinity line
Where would a cleaved rock plot on the Flinn plot? What is /\V?
/\V<0
Plot along k=0 line
Where would a veined and cleaved rock plot on the Flinn plot? What is /\V?
/\V = 0
Plot along k=1 line
What does it mean if, across a shear zone, data plots will progressively lower values of K with greater strain?
RELATIVE lengths of X, Y and Z are not constant across the shear zone
