1. Brittle deformation II
Inference of stress orientation from conjugate faults and earthquakes
Consequences of pre-fractured rocks
Does Anderson theory holds for all faults?
Coulomb failure envelop in terms of principal stresses
The mechanics of low angle faults

2. Izu peninsula (Japan):
Brittle deformation: Inference of stress orientation from conjugate faults and earthquakes
Izu peninsula (Japan):
Figure from Scholz [1990]

3. Brittle deformation: Inference of stress orientation from conjugate faults and earthquakes
Imperial Valley (CA):
Figure from Scholz [1990]

4. Brittle deformation: Consequences of pre-fractured rocks
If the rock is already fractured, faults with certain orientation may be reactivated.
Fractures oriented outside the red area may not be reactivated.
The range of angles beyond which fault reactivation is impossible is referred to as the lock-up angles

5. Brittle deformation: Consequences of pre-fractured rocks
Under constant stress (strain) field, faults rotate.
Once faults orientation reaches the lock-up angle, they become inactive and a new set forms.
Figure from Ron et al. [2000]
(the idea that strain accommodation in the brittle crust results in
fault rotation is attributed to Freund [1974].)

6. Brittle deformation: Consequences of pre-fractured rocks
Note that exactly the same fault configuration may result from rotation of the stress field.
Figure from Ron et al. [2000]
Question: suggest ways to distinguish fault rotation from stress rotation?

7. Brittle deformation: Does Anderson theory hold for all faults?
Geological map of Tinos Island (Cyclades, Greece)
Question: What the nature of the contact?
Greenschist
Eclogite-Blueschist
Figure from Vepnik and Avigad [2004]

8. Brittle deformation: Does Anderson theory hold for all faults?

9. Brittle deformation: Does Anderson theory hold for all faults?
These low angle normal faults are widespread all over the Cycladic massif (Greece).
Such tectonic contacts are commonly referred to as detachments.
Figure from Zeffren et al. [2004]

10. Brittle deformation: Does Anderson theory hold for all faults?
Very low angle reverse faults are referred to as thrust sheets.
Allochthon: A package of rocks which has been moved a long way from their original place of deposition.
Autochthon: Rocks that have moved little from their place of formation.
Klippe: An isolated remnant of allochthon resting on a lower plate.
Tectonic window: A ''hole'' through the thrust sheet that exposes isolated area of rocks that lie beneath the thrust.

11. Brittle deformation: Does Anderson theory hold for all faults?
Chief Mountain (Montana) is an example of a klippe. It consists of a Precambrian block which rests directly above younger Cretaceous gray shales. The surrounding portion of the thrust sheet has be removed by erosion leaving behind this isolated block of Proterozoic rock.

12. Brittle deformation: Does Anderson theory hold for all faults?
Find the tectonic window

13. Brittle deformation: Mechanics of low angle faults
Low angle normal faults are inconsistent with Anderson model. Possible explanations for the formation of these faults include:
Reactivation of thrust faults.
Rotation of Andersonian normal faults.
But sometimes neither of the above explanations is plausible, and this poses a major problem.
The problem is: how to force a very thin sheet to slide as a (almost) rigid body without causing internal faulting.

14. Brittle deformation: Coulomb failure criterion in terms of principal stresses
The Coulomb failure criterion in terms of normal and shear stress is simply:
where:
 is the coefficient of friction (equals tan)
c is cohesion
The Coulomb failure criterion in terms of the principal stresses is:

15. Brittle deformation: Mechanics of low angle faults
The problem: is how to force a very thin sheet to slide as a (almost) rigid body without causing internal faulting.
Force balance along the x direction requires that:

16. Brittle deformation: Mechanics of low angle faults
Let’s first evaluate the right-hand side of the force balance equation. Since zx is the frictional resistance to sliding, we write:
where  is the coefficient of friction. The normal stress is just the lithospheric stress:
with  being the rock density and g being the acceleration of gravity. So:

17. Brittle deformation: Mechanics of low angle faults
Next we evaluate the left-hand side of the force balance equation. We are seeking an expression for the largest xx that the block can support without breaking. So we'll use the expression for Coulomb criterion. We identify:
We thus get:
Equation the right and left hand sides gives:

18. Brittle deformation: Mechanics of low angle faults
Thus, given a thrust sheet of thickness z, the largest x is given by:
We plug in realistic numbers:  = 300 (i.e.,  = 0.6), S0 = 20 MPa, and  = 2300 Kg/m3.
With these values we get: x = 5.4 km z (not sure about that...).

19. Brittle deformation: Mechanics of low angle faults
There are several ways out of this paradox:
Rheology is incorrect.
Elevated pore pressure.
My favorite solution for this ''paradox'' is that thrust sheets do not move as rigid bodies, instead they slide like a wrinkle of a rug!

20. Brittle deformation: Mechanics of low angle faults
The wrinkle model:

21. Brittle deformation: Mechanics of low angle faults
Insight from seismology, the 1992 Landers example and the carpet wrinkle analogy:
Wald and Heaton, 1994