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

1. Stress and Deformation: Part II(D&R, 304-319; 126-149) 1. Anderson's Theory of Faulting2. Rheology (mechanical behavior of rocks) - Elastic: Hooke's Law - Plastic - Viscous3. Brittle-Ductile transition

2. Rocks in the crust are generally in a state of compressive stressBased on Coulomb's Law of Failure, at what angle would you expect faults to form with respect to s1?

3. Recall Coulomb's Law of Failure In compression, what is the observed angle between the fracture surface and s1 (q)? ~30 degrees! sc = critical shear stress required for failures0 = cohesive strengthtanf = coefficient of internal frictionsN = normal stress

4. 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:

6. conjugate normal faults

7. conjugate thrust faults

9. A closer look at rock rheology (mechanical behavior of rocks) Elastic strain: deformation is recoverable instantaneously on removal of stress – like a spring

10. An isotropic, homogeneous elastic material follows Hooke's Law Hooke's Law: s = EeE (Young's Modulus): measure of material "stiffness"; determined by experiment

11. Elastic limit: no longer a linear relationship between stress and strain- rock behaves in a different mannerYield strength: The differential stress at which the rock is no longer behaving in an elastic fashion

12. Mechanics of faulting

13. 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 deformationE.g., Soda can rings!

14. Ideal plastic behavior

15. Strength increases with confining pressure

16. Strength decreases with increasing fluid pressure

17. Strength increases with increasing strain rate

18. Role of lithology ( rock type) in strength and ductility (in brittle regime; upper crust)

19. STRONGultramafic and mafic rocksgranitesschistdolomitelimestonequartziteWEAK Role of lithology in strength and ductility (in ductile regime; deeper crust)

20. Temperature decreases strength

21. Viscous (fluid) behavior Rocks can flow like fluids!

22. For an ideal Newtonian fluid:differential stress = viscosity X strain rateviscosity: measure of resistance to flow

23. The brittle-ductile transition

24. The implications • Earthquakes no deeper than transition • Lower crust can flow!!! • Lower crust decoupled from upper crust

25. 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