Anderson’s theory of faulting

1. Anderson’s theory of faulting Goals: 1) To understand Anderson’s theory of faulting and its implications. 2) To outline some obvious exceptions to Anderson’s theory and some possible explanations for how these exceptions work.

2. Primary assumptions • Surface of the earth is not confined, and not acted on by shear stresses. • Also, tectonic plates move parallel with Earth’s surface (unknown in 1951) • Homogenous rocks • Coulomb behavior

3. Three possible stress combinations Hypothetically requires 2 of the 3 principal stresses to be parallel with the surface of the earth What are they? What kind of faults would you expect at each?

4. σ1 horizontal, σ3 vertical — reverse faults • σ1 vertical, σ3 horizontal — normal faults • σ1 horizontal, σ3 horizontal — strike-slip faults

5. Most rocks have an angle of internal friction ≈ 30° What dip angles does Anderson’s theory predict for • σ1 horizontal, σ3 vertical — reverse faults? • σ1 vertical, σ3 horizontal — normal faults? • σ1 horizontal, σ3 horizontal — strike-slip faults?

6. Hypothetically Reverse faults: should form at ~30° dip Normal faults: should form at ~60° dip Strike-slip faults: should form at ~90° dip Can you think of any exceptions??

7. Common exceptions • Thrust faults— mechanically unfavorable • Low-angle normal faults— mechanically very unfavorable

9. Possible explanations • Elevated pore fluid pressure • Pre-existing weaknesses • Rolling-hinge model for low-angle normal faults

10. 1. Elevated pore fluid pressure (Pf)

11. σs High Pf can lower effective stress σ1eff σ1 σn σ3eff σ3

12. σs This can activate slip on a low-angle fault σn σ3eff σ1eff

13. σs However, if cohesive strength is sufficiently low... σn σ3eff σ1eff

14. Pore-fluid-pressure mechanism requires low σeff on fault, but high σeff in surrounding rocks

15. σs It also doesn’t work well for low-angle normal faults σn σ3eff σ1eff

16. 2. Pre-existing anisotropy • Bedding • Weak layer (salt, shale) • Foliation

17. Donath (1961) produced shear fractures at very low angles to σ1 in anisotropic rock

18. 3. Rolling-hinge model for low-angle normal faults

19. Cartoon cross section illustrating the rolling-hinge model

21. East Humboldt Range Ruby Mountains

22. Geologic map of the Ruby Mountains and East Humboldt Range

24. Cross section of a low-angle normal-fault system

25. Cartoon cross section illustrating the rolling-hinge model