5 fracture and faulting
DESCRIPTION
fracture and faultingTRANSCRIPT
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Brittle Fracture and Faulting
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How do faults form?
• they are macroscopic shear cracks• coalescence of mode I fractures
Healy et al., 2006, Nature
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'Wing' cracks
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Griffith theory (1920, 1924)
• Real material contain imperfections– Imperfections concentrate stress– Failure at lower stress than theoretical
strength• Griffith applied a thermodynamic approach
– strength of real materials can be explained by the presence of microcracks ~1 µm long
– these ‘Griffith cracks’ were entirely hypothetical until the advent of electron microscopy
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Displacement mode of fractures
Mode I Opening mode fractureMode II In plane shear fractureMode III Antiplane shear fracture
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Formation of axial cracks(Mode I fractures)
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‘Quasistatic’ fault growth from acoustic emissionsLockner et al., 1991
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Using fracture mechanics to interpret fault displacementsand
structure• Non-linear elastic approach needed
– fault damage zones– displacement/length relationships
see Scholz (2002)
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• Fault damage zones have been suggested to be the damage ‘wake’ of a migrating process zone. (e.g. Vermilye + Scholz, JGR, 1998)
• Damage also occurs from– Earthquake rupture (Rice et al., BSSA, 2005)– Geometric irregularities (Chester and Chester, JGR, 2000)
a) b) c)
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Microfracture damage
=
91.7
α1
=
68.5
α1
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Brittle failure of a cylinder in axial compression
• Axial cracks are Mode I fractures– volume increase
• Brittle deformation is always accompanied by volume increase (as fracture density increases)
• Brittle deformation is highly pressure sensitive– increase in pressure suppresses the formation of new
fractures
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Unconfined uniaxial compression test
stress
strain
elastic
Yield
Failure
compressionextension
axial straincircumferential strainvolumetric strain
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Effect of confining pressure
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Mohr-Coulomb failure envelope
σn
τ
confining pressuresfor the 3 tests ( )σ3
failure stressfor the 3 tests ( )σ1
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σn
τ
σ3 σ1
stable
where:tan = coefficient of internal frictionC = cohesive strength
φ
unstable
Mohr-Coulomb failure envelopeslope = tanφ
φ C
φστ tannC +=Mohr-Coulomb failure criterion:
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Alternate expression of the Mohr-Coulomb criterion
31 σσ ba +=
gradient = b
a
σ3
σ1
where
φφ
sin1sin1
2
−+
=
=
b
bCa
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A note on the tensile field of the Mohr diagram
σn
τ
σ3 σ1
stable
where:tan = coefficient of internal frictionC = cohesive strength
φ
unstable
Mohr-Coulomb failure envelopeslope = tanφ
φ C
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Griffith failure criterion (tensile)
a C
)(4 002 TT n += στ parabolic in shape
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Summary
• Real materials contain imperfections (Griffith cracks)
• Brittle deformation involves opening of cracks – pressure sensitive
• Mohr-Coulomb failure criterion is empirical• Griffith failure criterion is mechanistic,
although it only describes tensile failure