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, ; ) 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 failure  0 = cohesive strength tan  = coefficient of internal friction  N = 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 = e lat /e long. A typical value for rocks is 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 = stress n, 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 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