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