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

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

σnσ1effσ3eff

However, if cohesive strength is sufficiently low...

σs

σnσ1effσ3eff

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

σnσ1effσ3eff

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

RubyMountains

East HumboldtRange

Geologic map of the Ruby Mountains and East Humboldt Range

Cross section of a low-angle normal-fault system

Cartoon cross section illustrating the rolling-hinge model