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
σ1eff
σ3eff
σ1
σ3
σn
σs
This can activate slip on a low-angle
fault
σ3eff
σ1eff
σn
σs
However, if cohesive strength is
sufficiently low...
σ3eff
σ1eff
σn
Pore-fluid-pressure mechanism requires low
σeff on fault, but high σeff in surrounding
rocks
σs
It also doesn’t work well for low-angle
normal faults
σ3eff
σ1eff
σn
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
East Humboldt
Range
Ruby
Mountains
Geologic map of
the Ruby
Mountains and
East Humboldt
Range
Cross section of a
low-angle normalfault system
Cartoon cross
section illustrating
the rolling-hinge
model