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Anderson s-theory-of-faulting (1)

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Abhinav Porwal

Anderson's theory of faulting predicts that the orientation of faults depends on the principal stresses. It assumes reverse faults dip at 30 degrees, normal faults dip at 60 degrees, and strike-slip faults are vertical. However, exceptions like low-angle normal faults exist. Pore fluid pressure or pre-existing weaknesses in the rock can allow faults to form at shallower angles. The rolling-hinge model also explains how low-angle normal faults can develop.

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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.
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
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?
• σ1 horizontal, σ3 vertical — reverse faults • σ1 vertical, σ3 horizontal — normal faults • σ1 horizontal, σ3 horizontal — strike-slip faults
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?
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??
Common exceptions • Thrust faults — mechanically unfavorable • Low-angle normal faults — mechanically very unfavorable
Anderson s-theory-of-faulting (1)
Possible explanations 1. Elevated pore fluid pressure 2. Pre-existing weaknesses 3. Rolling-hinge model for low-angle normal faults
1. Elevated pore fluid pressure (Pf)
High Pf can lower effective stress σs σn σ1 σ3 σ1eff σ3eff
This can activate slip on a low-angle fault σs σn σ1eff σ3eff
However, if cohesive strength is sufficiently low... σs σn σ1eff σ3eff
Pore-fluid-pressure mechanism requires low σeff on fault, but high σeff in surrounding rocks
It also doesn’t work well for low-angle normal faults σs σn σ1eff σ3eff
2. Pre-existing anisotropy • Bedding • Weak layer (salt, shale) • Foliation
Donath (1961) produced shear fractures at very low angles to σ1 in anisotropic rock
3. Rolling-hinge model for low-angle normal faults
Cartoon cross section illustrating the rolling-hinge model
Anderson s-theory-of-faulting (1)
Ruby Mountains East Humboldt Range
Geologic map of the Ruby Mountains and East Humboldt Range
Anderson s-theory-of-faulting (1)
Cross section of a low-angle normal- fault system
Cartoon cross section illustrating the rolling-hinge model

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Anderson s-theory-of-faulting (1)