Announcements Midterm next Monday! Midterm review during lab this week Extra credit opportunities: (1) This Thurs. 4 pm, Rm. Haury Bldg. Rm 216, "The role of orogen-parallel extension during the India-Asia collision", write 1 paragraph summary (+1%) (2) Volunteer at Earth Science Week (+1%/Hr, +2% max.) (3) Next Thurs. 4 Pm, Rm. Haury Bldg. Rm 216, "Tertiary structural and stratigraphic evolution of Tucson area", write 1 paragraph summary (+1%)
Transcript
Announcements
Midterm next Monday!
Midterm review during lab this week
Extra credit opportunities:(1) This Thurs. 4 pm, Rm. Haury Bldg. Rm 216, "The role
of orogen-parallel extension during the India-Asia collision", write 1 paragraph summary (+1%)
(2) Volunteer at Earth Science Week (+1%/Hr, +2% max.)
(3) Next Thurs. 4 Pm, Rm. Haury Bldg. Rm 216, "Tertiary structural and stratigraphic evolution of Tucson area",
write 1 paragraph summary (+1%)
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 1?CC
c = critical shear stress required for failure0 = cohesive strengthtan = coefficient of internal frictionN = normal stress
Recall Coulomb's Law of Failure
In compression, what is the
observed angle between the
fracture surface and 1 ()?
~30 degrees!
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 1, this gives:
conjugate normal faults
conjugate thrust faults
Anderson’s theory of faulting works in many cases- but certainly not all!
We observe low-angle normal faults and high-angle thrust faults- WHY??
-Pre-existing faults that are reactivated
-High fluid pressure
- Variable stress distribution in deeper crust due to topographic loads, intrusions, basal shear
stresses
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: = Ee
E (Young's Modulus): measure of material "stiffness"; determined by experiment
Some other useful quantities that describe behavior of elastic materials:
Poisson's ratio (): degree to which a material bulges as it shortens = elat/elong. A typical value for rocks is 0.25. For a marshmallow, it would be much higher.
Shear modulus (G): resistance to shearing
Bulk modulus (K): resistance to volume change
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
Plastic behavior
strain rate = stressn, where n=3 for many rocks
modeled by "power law creep"
Strain hardening and strain softening
More insight from soda can rings
Strength increases with confining pressure
Strength decreases with increasing fluid pressure
Strength increases with increasing strain
rate
Taffy experiment
Silly Putty experiment
Role of lithology ( rock type) in strength and ductility (in brittle regime; upper crust)
Role of lithology in strength and ductility
(in ductile regime; deeper crust)
STRONG
ultramafic and mafic rocks
granites
schist
dolomite
limestone
quartzite
WEAK
Temperature decreases strength
Viscous (fluid) behavior
Rocks can flow like fluids!
For an ideal Newtonian fluid:differential stress = viscosity X strain rateviscosity: 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/conceptsAnderson's theory of faulting
