Calculation of Lo

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Calculation of Lo
Assumption Volume constant strain
4/3Pr3 4/3P((X/2)(Y/2)(Z/2))
r3 4/3P((X/2)(Y/2)(Z/2)) 4/3P
r (X/2)(Y/2)(Z/2)(1/3)
d (X)(Y)(Z)(1/3) Lo
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Stress and Deformation Part I(DR, 122-126
226-252)
The goal for today is to explore the stress
conditions under which rocks fail (e.g.,
fracture), and the orientation of failure with
respect to the principal stress directions.1.
Coulomb law of failure2. Byerlee's law
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Experimental studies are fundamental in the study
of rock failure
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Common types of deformation experiments
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Compressive strength tests The Goal
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Compressive strength tests The Approach
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2
1
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Compressive strength tests The resultsLinear
envelope of failure. The fractures form at
angles of 25 to 35 degrees from s1- very
consistent!
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Coulomb's Law of Failure
sc s0 tanf(sn)
sc critical shear stress required for
failures0 cohesive strengthtanf coefficient
of internal friction (f 90 - 2q) sN normal
stress
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Tensile strength tests with no confining
pressureApproach Similar to compressive
strength testsResults (1) Rocks are much weaker
in tension than in compression (2) Fracture
oriented parallel to s1 (q 0)
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Tensile Compressive strength testsResult
Failure envelope is parabolic0 lt q lt 30
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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
failures0 cohesive strengthtanf
coefficient of internal frictionsN normal
stress
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What See You!?
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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 cohesionFrictional sliding envelope
sc tanf(sN), where tanf is the coefficient of
sliding friction
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Preexisting fractures of suitable orientation may
fail before a new fracture is formed
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What about pore fluid pressure?
Increasing pore fluid pressure favors
failure!-Also may lead to tensile failure deep
in crustEffective stress sn fluid pressure
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What is it?
Tensile fracture filled with vein during dilation
What is it?s1 is parallel to the structure.
What does this suggest about the magnitude of
effective stress?What mechanism may help produce
this structure within the deeper crust?
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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Next Lecture Stress and Deformation II...A
closer look at fault mechanics and rock behavior
during deformation( DR pp. 304-319
126-149)
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• Important terminology/concepts
• Uniaxial vs. axial states of stress
• Coulomb law of failure known how it is
  determined and equation
• q values for compression
• q values for tension
• Cohesive strength
• Coefficient of internal friction
• Byerlee's Law / frictional sliding envelope- know
  equation
• Important role of pore fluid pressure