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Brittle Fracture and Faulting
How do faults form?
• they are macroscopic shear cracks• coalescence of mode I fractures
Healy et al., 2006, Nature
'Wing' cracks
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
Displacement mode of fractures
Mode I Opening mode fractureMode II In plane shear fractureMode III Antiplane shear fracture
Formation of axial cracks(Mode I fractures)
‘Quasistatic’ fault growth from acoustic emissionsLockner et al., 1991
Using fracture mechanics to interpret fault displacementsand
structure• Non-linear elastic approach needed
– fault damage zones– displacement/length relationships
see Scholz (2002)
• 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)
Microfracture damage
=
91.7
α1
=
68.5
α1
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
Unconfined uniaxial compression test
stress
strain
elastic
Yield
Failure
compressionextension
axial straincircumferential strainvolumetric strain
Effect of confining pressure
Mohr-Coulomb failure envelope
σn
τ
confining pressuresfor the 3 tests ( )σ3
failure stressfor the 3 tests ( )σ1
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:
Alternate expression of the Mohr-Coulomb criterion
31 σσ ba +=
gradient = b
a
σ3
σ1
where
φφ
sin1sin1
2
−+
=
=
b
bCa
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
Griffith failure criterion (tensile)
a C
)(4 002 TT n += στ parabolic in shape
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