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.
Figure from Ron et al. [2000]
(the idea that strain accommodation in the brittle crust results in
fault rotation is attributed to Freund [1974].)
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?
Geological map of Tinos Island (Cyclades, Greece)
Question: What the
nature of the contact?
Greenschist
Eclogite-Blueschist
Figure from Vepnik and
Avigad [2004]
Brittle deformation: Does Anderson theory hold for all faults?
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]
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
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.
Brittle deformation: Coulomb failure criterion in terms of principal
stresses
The Coulomb failure criterion in terms of normal and shear stress
is simply:
 s  c   n ,
where:
•  is the coefficient of friction (equals tan)
• c is cohesion
The Coulomb
 failure criterion in terms of the principal stresses is:
1  C0  K 3 ,
where:
1 sin 
cos 
K
and C0 = 2c
.
1 sin 
1- sin

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:
z

0
xx
dz 
x

0
zx
dx .
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:
 zx =  n =  zz ,
where  is the coefficient of friction. The normal stress is just the
lithospheric stress:
 zz = gz ,

with  being the rock density and g being the acceleration of
gravity. So:
x
 gzdx  gzx .
0
0
  zx dx 
x
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:
 xx  1 and  zz =  3 .
Kgz
  xxdz   C0  Kgzdz  C0z + 2
0
0

z
z
Equation the right and left hand sides gives:
Kgz
C0z +
= gzx .
2
2
2
.
Brittle deformation: Mechanics of low angle faults
Thus, given a thrust sheet of thickness z, the largest x is given by:
C0 Kz
x
+
.
g 2
• We plug in realistic numbers:  = 300 (i.e.,  = 0.6), S0 = 20 MPa,
and  = 2300 Kg/m3.
values we get: x = 5.4 km + 2.6 z (not sure about
• With these
that...).
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