Stress and Deformation: Part II D

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Stress and Deformation Part II(DR, 304-319
126-149)
1. Important Role of Fluid Pressure 2.
Anderson's Theory of Faulting3. Rheology
(mechanical behavior of rocks) - Elastic
Hooke's Law - Plastic - Viscous4. Strength
vs. Depth Diagram
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Preexisting fractures of suitable orientation may
fail before a new fracture is formed
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fluid pressure serves to decrease confining
pressure
effective stress confining pressure fluid
pressure
Analogies 1. Air hockey table air pressure
reduces effective weight of puck2. Ice Skating
Ice melts under pressure fluid pressure beneath
skate decreases effective weight3. Extreme Free
Diving fluid (blood) pressure in lungs
counteracts confining pressure
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What about fluid pressure?
Increasing fluid pressure favors failure!-Also
may lead to tensile failure if low differential
stressEffective stress s1,2,3 fluid pressure
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What is it?
Tensile fracture filled with vein during dilation
What is it?What is the orientation of s1? What
does this suggest about the magnitude of
effective stress?What mechanism may help produce
this structure within the deeper crust?
Theta 0
very low
high fluid pressure to counteract lithostatic
stress
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What happens at higher confining pressures?
Von Mises failure envelope- Failure occurs at
45 degrees from s1
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Concept of strength vs. depth diagram
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Rocks in the crust are generally in a state of
compressive stressBased on Coulomb's
Law of Failure, at what angle would you expect
faults to form with respect to s1?
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Recall Coulomb's Law of Failure
In compression, what is the observed angle
between the fracture surface and s1 (q)?
30 degrees!
sc critical shear stress required for
failures0 cohesive strengthtanf coefficient
of internal frictionsN normal stress
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Anderson's Theory of Faulting
The Earth's surface is a free surface (contact
between rock and atmosphere) with no 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
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conjugate normal faults
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conjugate thrust faults
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young conglomerate
old granite
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A closer look at rock rheology (mechanical
behavior of rocks)
Elastic strain deformation is recoverable
instantaneously on removal of stress like a
spring
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An isotropic, homogeneous elastic material
follows Hooke's Law
Hooke's Law s EeE (Young's Modulus) measure
of material stiffness determined by experiment
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Yield strength The differential stress at which
the rock is no longer behaving in an elastic
fashion
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Mechanics of faulting
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What happens at higher differential stress and
confining pressure?
Plastic behavior produces an irreversible change
in shape as a result of rearranging chemical
bonds in the crystal lattice- without
failure!Ductile rocks are rocks that have
undergone a lot of plastic deformation
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Ideal plastic behavior
like pulling gum out of your mouth
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"Real" plastic behavior
modeled by "power law creep"
strain rate is proportional to stressm and
increases exponentially with Temperature
Show on Strength vs. Depth Diagram
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Viscous (fluid) behavior
Rocks can flow like fluids!
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For an ideal Newtonian fluiddifferential stress
viscosity X strain rateviscosity measure of
resistance to flow
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Starting to put things together- A generalized
Strength vs. Depth diagram for the CRUST
The elastic-plastic or brittle-ductile transition
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The implications

• Earthquake ruptures nucleate near transition and
  propagate upward toward surface
• Eathquakes are rare deeper than transition
• Lower crust can flow in hot orogens (regions of
  mountain building)
• Lower crustal deformation can be decoupled from
  upper crustal deformation