Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out
Get this document free

Stress and Deformation Part II rheology

VIEWS: 5 PAGES: 25

									    Stress and Deformation: Part II
       (D&R, 304-319; 126-149)


    1. Anderson's Theory of Faulting

2. Rheology (mechanical behavior of rocks)
            - Elastic: Hooke's Law
                    - Plastic
                   - Viscous

       3. Brittle-Ductile transition
Rocks in the crust are generally in a state of
            compressive stress




Based on Coulomb's Law of Failure, at what
angle would you expect faults to form with
             respect to s1?
Recall Coulomb's
 Law of Failure

In compression,
   what is the
 observed angle
  between the
fracture surface
   and s1 (q)?


  ~30
            sc = critical shear stress required for failure
degrees!
            s0 = cohesive strength
            tanf = coefficient of internal friction
            sN = normal stress
       Anderson's Theory of Faulting


The Earth's surface is a free surface (contact
between rock and atmosphere), and cannot be
subject to shear stress. As the principal stress
directions are directions of zero shear stress,
they must be parallel (2 of them) and
perpendicular (1 of them) to the Earth's
surface. Combined with an angle of failure of
30 degrees from s1, this gives:
  conjugate
normal faults
conjugate thrust faults
  A closer look at rock rheology (mechanical
  behavior of rocks)




Elastic strain: deformation is recoverable
instantaneously on removal of stress – like a spring
 An isotropic, homogeneous elastic material
 follows Hooke's Law
Hooke's Law: s = Ee

E (Young's Modulus): measure of material
"stiffness"; determined by experiment
Elastic limit: no longer a linear
relationship between stress and
strain- rock behaves in a
different manner




Yield strength: The differential
stress at which the rock is no
longer behaving in an elastic
fashion
Mechanics of faulting
   What happens at higher confining
pressure and higher differential stress?
                   Plastic behavior produces
                   an irreversible change in
                   shape as a result of
                   rearranging chemical
                   bonds in the crystal lattice-
                   without failure!

                   Ductile rocks are rocks
                   that undergo a lot of plastic
                   deformation

                   E.g., Soda can rings!
Ideal plastic behavior
Strength increases with confining
            pressure
Strength decreases with increasing fluid pressure
 Strength increases
with increasing strain
         rate
Role of lithology ( rock type) in strength and
  ductility (in brittle regime; upper crust)
        STRONG

ultramafic and mafic rocks

         granites
                              Role of lithology in
                             strength and ductility
          schist
                               (in ductile regime;
        dolomite                  deeper crust)

        limestone

        quartzite

         WEAK
   Temperature
decreases strength
                 Viscous (fluid)
                    behavior




Rocks can flow
  like fluids!
For an ideal Newtonian fluid:
differential stress = viscosity X strain rate
viscosity: measure of resistance to flow
The brittle-ductile
    transition
            The implications



• Earthquakes no deeper than transition

• Lower crust can flow!!!

• Lower crust decoupled from upper crust
Important terminology/concepts
      Anderson's theory of faulting
     significance of conjugate faults
                   rheology
               elastic behavior
                 Hooke's Law
             Young's modulus
               Poisson's ratio
               brittle behavior
                  elastic limit
                yield strength
          plastic behavior (ideal)
              power law creep
     strain hardening and softening
   factors controlling strength of rocks
          brittle-ductile transition
              viscous behavior
           ideal Newtonian fluid

								
To top