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:
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
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!
Role of lithology in strength and ductility
(in ductile regime; deeper crust)
STRONG
ultramafic and mafic rocks
granites
schist
dolomite
limestone
quartzite
WEAK
For an ideal Newtonian fluid:differential stress = viscosity X strain rateviscosity: measure of resistance to flow
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