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

Brittle deformation: Inference of stress orientation from conjugate faults and earthquakes

Izu peninsula (Japan):

Figure from Scholz [1990]

Brittle deformation: Inference of stress orientation from conjugate faults and earthquakes

Imperial Valley (CA):

Figure from Scholz [1990]

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

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.

(the idea that strain accommodation in the brittle crust results infault rotation is attributed to Freund [1974].)

Figure from Ron et al. [2000]

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?

Brittle deformation: Does Anderson theory hold for all faults?

Question: What the nature of the contact?

Figure from Vepnik and Avigad [2004]

Eclogite-Blueschist

Greenschist

Geological map of Tinos Island (Cyclades, Greece)

Brittle deformation: Does Anderson theory hold for all faults?

Brittle deformation: Does Anderson theory hold for all faults?

Figure from Zeffren et al. [2004]

• These low angle normal faults are widespread all over the Cycladic massif (Greece).

• Such tectonic contacts are commonly referred to as detachments.

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.

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.

Brittle deformation: Does Anderson theory hold for all faults?

Find the tectonic window

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.

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.

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 cohesionThe Coulomb failure criterion in terms of the principal stresses is:

where:

€

σ s = c + μσ n ,

€

σ1 =C0 +Kσ 3 ,

€

K =1+ sinφ

1− sinφ and C0 = 2c

cosφ

1- sinφ .

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.

€

σ xxdz0

z

∫ = σ zx0

x

∫ dx .

Force balance along the x direction requires that:

Brittle deformation: Mechanics of low angle faults

Let’s first evaluate the right-hand side of the force balance equation. Since σzx 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:

€

σ zx = μσ n = μσ zz ,

€

σ zz = ρgz ,

€

σ zx0

x

∫ dx = μρgz0

x

∫ dx = μρgzx .

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 σxx 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:€

σ xx =σ 1 and σ zz =σ 3 .

€

σ xxdz0

z

∫ = C0 +Kρgz( )0

z

∫ dz =C0z +Kρgz2

2 .

€

C0z +Kρgz2

2= μρgzx .

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 + 2.6 z (not sure about that...).

€

x =C0

μρg+

Kz

2μ .

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!

Brittle deformation: Mechanics of low angle faults

The wrinkle model:

Brittle deformation: Mechanics of low angle faults

Insight from seismology, the 1992 Landers example and the carpet wrinkle analogy:

Wald and Heaton, 1994