Stress and Deformation: Part II D

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Stress and Deformation Part II(DR, 304-319
126-149)
1. Anderson's Theory of Faulting2. Rheology
(mechanical behavior of rocks) - Elastic
Hooke's Law - Plastic - Viscous3.
Brittle-Ductile transition (an intro)
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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), 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
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conjugate normal faults
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conjugate thrust faults
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A closer look at rock rheology (mechanical
behavior of rocks)
Three basic models of rheologyElastic Think
of a springPlastic will not deform until
yield stress is exceededViscous like a
fluid--- the smallest stress will deformThese
help us picture the ways rocks have been found to
respond to stress
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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 Ee or E s/e (stress/strain)E
(Young's Modulus) measure of material
stiffness" determined by experiment
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Some other useful quantities that describe
behavior of elastic materialsPoisson's ratio
(n) degree to which a material bulges as it
shortens elat/elong. A typical value for rocks
is 0.25. For a marshmallow, it would be much
higher.Shear modulus (G) resistance to
shearingBulk modulus (K) resistance to volume
change
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Elastic limit no longer a linear relationship
between stress and strain- rock behaves in a
different mannerYield 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 confining pressure and
higher differential stress?
Plastic behavior produces an irreversible change
in shape as a result of rearranging chemical
bonds in the crystal lattice- without failure!
No deformation until yield strength exceeded.
Ductile rocks undergo a lot of plastic
deformation
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Ideal plastic behavior
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Plastic behavior
modeled by "power law creep"
strain rate stressn, where n3 for many rocks
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Strain hardening and strain softening
More stress needed to deform
Less stress needed to deform
More insight from beer or soda can rings
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Strength increases with confining pressure
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Strength decreases with increasing fluid pressure
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Strength increases with increasing strain rate
Taffy experiment
Silly Putty experiment
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Role of lithology ( rock type) in strength and
ductility (in brittle regime upper crust)
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STRONGultramafic and mafic rocksgranitesschi
stdolomitelimestonequartziteWEAK
Role of lithology in strength and ductility (in
ductile regime deeper crust)
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Temperature decreases strength
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Viscous (fluid) behavior
Rocks can flow like fluids!Boudins or boudinage
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For an ideal Newtonian fluiddifferential stress
viscosity X strain rateviscosity measure of
resistance to flow
sd differential stress
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The brittle-ductile transition
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The implications

• Earthquakes no deeper than transition
• Lower crust can flow!!!
• Lower crust decoupled from upper crust

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• Important terminology/concepts
• Anderson's theory of faulting
• significance of conjugate faults
• rheology
• elastic behavior
• Hooke's Law
• Young's modulus
• Poisson's ratio
• brittle behavior
• elastic limit
• yield strength
• plastic behavior (ideal)
• power law creep
• strain hardening and softening
• factors controlling strength of rocks
• brittle-ductile transition
• viscous behavior
• ideal Newtonian fluid