Lecture 02 Frictional brittle deformation by 7eraZxL

VIEWS: 8 PAGES: 16

									   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

								
To top