# Lecture 02 Frictional brittle deformation by 7eraZxL

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```									   Brittle rupture and
frictional sliding review
Goal: To revisit the mechanics of frictional
brittle faults and understand how this might
affect the behavior of the lithosphere.
The stress is resolved into 2 components:
1. Shear stress (σs), acting parallel with the
plane
2. Normal stress (σn), acting perpendicular
to the plane
σ1                          σ   n
θ
σs      σs
σ3             σ3

σn
σ1
X- and y-coordinates of intersection of line
and circle define σs and σn for the plane

σs        (σs, σn) of plane

σn
σ3                       σ1
Coulomb’s failure criterion
• Every homogeneous material has a
characteristic failure envelope for brittle
shear fracturing
• Combinations of σs and σn outside of the
envelope result in fracture
The Coulomb envelope
σs
φ

Stable
Fracture
Tensile

2θ
σn
σ3                      σ1

Stable
Shear
Fracture
Failure
envelopes
for different
rocks
• For most rocks, angle of internal friction ≈
30°
• Therefore, θ at failure is also ≈ 30°
• σs is greatest when θ = 45°
Envelope of sliding friction
σs

φf = angle of sliding friction

σn
Byerlee’s law for different rock types
Sliding vs. brittle rupture and crustal
strength
σs

σn
Strength (σd)
Coulomb’s failure criterion
Depth (σn)

Plot of crustal                  Byerlee’s Law
strength vs. depth

How does rock type
affect this plot?
Nonlinear rheologies — ė = (σd)n/η

n = stress exponent — typically between 2.4 and 4
Small increases in σd produce large changes in ė
Most models of the crust assume dislocation creep
is dominant deformation mechanism below the
brittle-to-plastic transition
Dislocation creep
ė = (σd)n x [A / e^(Ea/RT)]

1/viscosity (1/η)
So, ė = (σd)n /η
Therefore, viscosity is
proportional to temperature
Strength (σd)                          Plot of crustal
strength vs.
Frictional-brittle         depth and
behavior, Linear           temp.

How does
rock type

Temperature
Depth (σn)

affect this
plot?

Dislocation creep,
Power Law
Upper crust = granitic
Models of
lithospheric   Lower crust = basaltic
strength
Mantle = peridotite

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