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Midterm next Monday, October 14
Midterm Review
What is structural geology?
- Study of rock deformation,
“the study of the architecture
of the Earth’s crust”
- “forensic science”
What are structures?
Two main types:
(1) Primary structures: Develop during formation
of a rock body; e.g.,
cross-bedding, ripple marks, mudcracks,
pillows (in basalt)
(2) Secondary structures: Form in rocks as a
result of deformation- the structures this class
are focused on!
Goals of Structural Analysis
• Geometry: mapping, measurements
• Kinematics: movements related to deformation
– Translation: change in position
– Rotation: change in orientation
– Distortion: change in shape
– Dilation: change in size
Dynamics/Mechanics: relating deformation to
stresses
Structural measurements
• Planar structures
• Strike: compass direction of trace of
horizontal line on a plane; bearing (quadrant,
E or W of north) or azimuth (degrees
clockwise from N)
• Dip: inclination of plane from horizontal,
perpendicular to strike
Linear structures
• Trend: direction of a vertical plane that
contains the linear feature in the direction of
plunge.
• Plunge: angle between line and horizontal
Oceanic Crust
- forms at mid-ocean
ridges by partial melting
of mantle
- basaltic (mafic) in
composition
- igneous extrusion and
intrusion
- 5 to 10 km-thick
- Oceanic crust is no
older than ~200 Ma.
Why??
Continental Crust
- 5 to 10 times thicker than
oceanic crust- 40 km avg.
- This is a simplified sketch!
Continental crust is very
heterogeneous
- Long and complex deformation
history. Majority of continental
crust formed during the
Precambrian (before ~570 Ma)
The oldest known rock is ~4 Ga!
Why so much older than
oceanic crust??
Rheology (behavior during deformation) of the Earth
Lithosphere: "lithos" = rock, implying strength. It exhibits a
component of elastic strength over geological time scales.
Includes crust + uppermost mantle! Varies in thickness. Moves
as a plate- exceptions are orogens.
Asthenosphere: Weak. It is solid, but behaves like a viscous
fluid (convective flow) over geological time scales.
How do we know that plates move?
- Earthquakes localized along plate
boundaries
Transform faults: more evidence for plate
motion
Not observed!
Observed!
Continents also break- to form new oceans
Ocean-Continent convergent margins
An example of
continent-continent
collision:
The Indo-Asian
Collision
Transform plate
boundaries
An example: San
Andreas
Pangea
supercontinent
and Tethys
Ocean
http://www.scotese.com/earth.htm
Joint: A natural fracture that forms by tensile loadingwalls of fracture move apart slightly as joint develops
Plumose structure: A
subtle roughness on
surface of some joints;
resembles imprint of a
feather. Due to
inhomogeneity of rock.
Joints/Fractures: Kinematics
ribs are arrest lines- opening is
not instantaneous, but rhythmic,
like splitting wood
Cooling joints: form by thermal contraction
Exfoliation joints: Form by unloading of bedrock through erosion.
They form parallel to topography
Tectonic joints: Form by tectonic stresses as opposed to
stresses induced by topography.
Strike-slip faults: Accommodate horizontal slip
between adjacent blocks
left lateral
(sinistral)
right lateral
(dextral)
left lateral vs. right lateral: sense-of-slip relative to a
chosen block
Hanging wall: The block toward which the fault dips.
Footwall: The block on the underside of the fault.
http://earth.leeds.ac.uk/learnstructure/index.htm
Slip vs. Separation
Slip: actual relative displacement
Separation: apparent relative displacement
The key to describing slip
along a fault lies in
measuring
(1) Direction of
displacement
(2) Sense of displacement
(3) Magnitude of
displacement
Main types of folds
Anticline: fold that is convex in
the direction of the youngest beds
Syncline: Fold that is convex in
the direction of the oldest beds
*requires that you know facing
direction (direction of youngest
beds); know stratigraphy!
anticline
synformal
anticline
syncline
Antiform: convex up
Synform: convex down
*simply describes geometry
antiformal
syncline
Geometric analysis
inflection point: point of
opposing convexity
median surface: imaginary
surface connecting inflection
points
fold width, fold height
symmetrical vs. asymmetrical
concept of vergence
Geometric analysis cont.
hinge zone – hinge line: zone of max. curvature
fold axis: imaginary line, which when moved parallel
to itself can define the form of a fold
Geometric analysis cont.
axial surface: surface that passes through
successive hinge lines
axial trace: line of intersection of axial
surface and ground surface
parallel/concentric folds: layer thickness does not
change (lower T)
similar folds: layer thickness changes; thickening in
hinge and thinning along limbs (higher T)
Fold mechanisms for "free folds", where fold shapes
depend on layer properties
(1) Flexural-slip folding- accommodates
buckling by layer-parallel slip
-direction of relative slip is perpendicular to
hinge
-individual displacement small, but sum is
enough to accommodate bending of rock
-marked by strong stiff layers with contacts of
low cohesive strength
-occurs in uppermost levels of crust
minor structures related to flexuralslip folding
minor structures related to flexural-flow
folding
occur at higher temperature
plunging folds and map patterns, cont.
Introduction to geologic maps
Geologic maps show traces of contacts between different
rock units, commonly superimposed on topography
First step: Every time you see a contact, ask yourself the
following questions:
(1) Is it a depositional contact?
(2) Is it an intrusive contact?
(3) Is it a fault contact?
So far, we have talked quite a bit about faults, but not the
other types of contacts. To fill you in...
Second step: Study how the trace of the contact interacts
with topography- It will tell you about orientation!
Permian
limestone
ophiolitic
melange
Which way does the fault dip?
Stereographic projection
plotting 3D structural data on a hemisphere (usually
the lower), which is projected onto a horizontal plane
Rake = The acute angle between the horizontal
(strike line) and a line in the plane,
MEASURED IN THE PLANE
Determining the true thickness of a bed
1. Draw a structural profile (Xsection) perpendicular to strike
2. Plot the true dip of the beds and
project them to depth
3. Use trigonometry to calculate
the true thickness
For a dipping bed, the map-view thickness is an
"apparent" as opposed to "true" thickness!
Determining strike and dip from geologic maps
(revisited)
75 m
What is strain?
Strain is dilation (change in size) and/or
distortion (change in shape).
The Goal of strain analysis is to explain how
every line in a body changes in length and angle
during deformation.
How is this attempted?
Some important quantities for describing strain
Extension (e): (Lf-Lo)/Lo, where Lf is the final length
of a line and Lo is the initial length of a line
Stretch (S): Lf/Lo, where 0 = severe shortening, 1 =
no shortening, and infinity = severe stretching
Quadratic elongation (l): = (1+e)2 = (Lf/Lo)2 = S2
So far- we have only talked about changes in
lengths of lines- what about angles?
Angular shear (y, psi): degree to which 2 initially
perpendicular lines are deflected from 90 degrees
Shear strain (g, gamma): = tan (y)
Finite vs. Instantaneous strain
What does 'finite' mean? It is total strain, the final
result of deformation that we see as geologists
Instantaneous or infinitesimal strain describes a
tiny increment of deformation
As will become apparent when studying how
fabrics form in rocks, the orientation of finite
strain may be very different than that of
instantaneous strain
Strain ellipse and ellipsoid for homogeneous
deformation:
Shows how circular reference object is deformed
3-D
2-D
Vs=4/3pr3
Ve=4/3pabc
2 end-member types of plane strain
Simple shear: Rock is
sheared like a deck of cards.
A square becomes a
parallelogram. **The finite
stretching axes rotate during
deformation. Distortion by
simple shear is the most
important process in shaping
shear-zone structures!
Pure shear: Rock is
shortened in one direction and
extended in the perpendicular
direction. A square becomes
a rectangle. **The finite
stretching axes do not rotate.
Strain Rate
strain rate = extension (e) divided by time (t) = e/t
The rate at which a rock is strained has important
implications for the manner in which it deforms.
"Lab" Strain Rates
During 1 hour experiment, an initially 2.297 cm-long
sample is shortened to 2.28 cm. What is the average
strain rate during this experiment?
Force vs. Stress
Force: That which changes, or tends to change,
body motion
Newton's first law of motion: F=ma
mass in kg; acceleration in m/s2
1 Newton (1N) = 1kg m/s2
Forces are vector quantities; they have magnitude
and direction.
Stress may be thought of as a description of
force concentration
Stress on a plane (traction), s = F/A
what about units of stress?
1N/m2 = 1 Pa
100 MPa = 1 kbar
lithostatic stress
vertical force = rVg =
rL3g
vertical stress =
rL3g/L2 = rgL
rgL = (2700 kg/m3)(10m/s2)(1500m) = 40500000 Pa
= 40.5 MPa = .405 kbar
A complete definition of Stress = a description of
tractions at a given point on all possible surfaces
going through the point
s1
s1: axis of greatest principal stress
s3: axis of least principal stress
s3
s3
s1 and s3 always perpendicular
and always perpendicular to
planes of no shear stress
s1
Geometric approach: Mohr Stress Diagram
a plot of ss vs. sn
first step: plot s1 and s3 recalling that they are in
directions of no shear stress; draw Mohr circle
second step: Draw a line representing the plane at
2q, measured from s3.
differential stress: (s1-s3)
causes distortion
mean stress: (s1+s3)/2
causes dilation
diameter of circle
center of circle
s3
s1
s3
s1
instantaneous
strain ellipse
Common types of deformation experiments
Compressive strength tests: The Approach
#1
#2
#3
Coulomb's Law of
Failure
sc = s0 + tanf(sn)
sc = critical shear stress required for failure
s0 = cohesive strength
tanf = coefficient of internal friction (f = 90 - 2q)
sN = normal stress
Tensile strength tests with no confining pressure
Approach: Similar to compressive strength tests
Results: (1) Rocks are much weaker in tension than in
compression (2) Fracture oriented parallel to s1 (q = 0)
Failure envelopes for different rocks: note that
slope of envelope is similar for most rocks
sc = s0 + tanf(sn)
sc = critical shear
stress required for
failure
s0 = cohesive
strength
tanf = coefficient of
internal friction
sN = normal stress
Byerlee's Law
Question: How much shear stress is needed to cause movement
along a preexisting fracture surface, subjected to a certain normal
stress?
Answer: Similar to Coulomb law without cohesion
Frictional sliding envelope: sc = tanf(sN), where tanf is the
coefficient of sliding friction
Preexisting fractures of suitable orientation may
fail before a new fracture is formed
What about fluid pressure?
Increasing pore fluid pressure favors failure by
counteracting confining pressure!
Effective stress = sn – fluid pressure
What happens at higher confining pressures?
Von Mises failure envelope
- Failure occurs at 45 degrees from s1
Anderson's Theory of Faulting
The Earth's surface is a free surface (contact
between rock and atmosphere), and cannot be
subject to shear stress. As the principal stress
directions are directions of zero shear stress,
they must be parallel (2 of them) and
perpendicular (1 of them) to the Earth's
surface. Combined with an angle of failure of
30 degrees from s1, this gives:
An isotropic, homogeneous elastic material
follows Hooke's Law
Hooke's Law: s = Ee
E (Young's Modulus): measure of material
"stiffness"; determined by experiment
Elastic limit: no longer a linear
relationship between stress and
strain- rock behaves in a
different manner
Yield strength: The differential
stress at which the rock is no
longer behaving in an elastic
fashion
What happens at higher confining
pressure and higher differential stress?
Plastic behavior produces
an irreversible change in
shape as a result of
rearranging chemical
bonds in the crystal latticewithout failure!
Ductile rocks are rocks
that undergo a lot of plastic
deformation
E.g., Soda can rings!
Viscous (fluid)
behavior
Rocks can flow
like fluids!
For an ideal Newtonian fluid:
differential stress = viscosity X strain rate
viscosity: measure of resistance to flow
The brittle-ductile
transition