Stress and Deformation

1. Stress and Deformation 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?CC

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. 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 reactivatedHigh fluid pressure- Variable stress distribution in deeper crust due to topographic loads, intrusions, basal shear stresses

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

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

12. Some other useful quantities that describe behavior of elastic materials:Poisson's ratio (n): 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 shearingBulk modulus (K): resistance to volume change

13. 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

14. Mechanics of faulting

15. 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!

16. Ideal plastic behavior Plastic behavior modeled by "power law creep“ strain rate = stressn, where n = 3 for many rocks

17. Strain hardening and strain softening More insight from soda can rings

18. Strength increases with confining pressure

19. Strength decreases with increasing fluid pressure

20. Strength increases with increasing strain rate Taffy experiment Silly Putty experiment

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

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

23. Temperature decreases strength

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

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

27. The brittle-ductile transition

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

29. 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

30. End of Lecture