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?

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

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

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)

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

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