Mechanics of Natural
Fractures and Faults
An
introduction
to
elastic
deformation and the techniques for
measuring stress within the Earth.
The possible origins of these stresses
are also discussed, and that
knowledge is applied to understand
the formation of extension fractures
and faults.
Elastic Deformation
-Elastic Deformation: removal of the
stress causes the strain to completely
disappear and the strain is therefore said
to be recoverable.
-Extensional Strain is given by:
en = L/L, where L is the change in
length and L is the initial length.
-In a uniaxial state of stress, the
magnitude of elastic extension (en)
parallel to the applied stress is directly
proportional to the magnitude of the stress
(n). In formula notation, n=Een
-Young’s Modulus (E): constant of
proportionality needed to characterize
elastic behavior of isotropic material. For
rocks, E characteristically has values in
the range of -0.5x105 to -1.5x105MPa.
-Poisson Ratio (): the absolute value
of the ratio given by the extension normal
to an applied compressive stress, divided
by the extension parallel to the applied
compression:
=
Techniques For Determining Stress in
the Earth
-Measurements of the change in strain
that accompanies unloading (stress relief)
allow us to infer the original stresses if we
know the elastic constants of the rock.
-Hydraulic Fracturing (hydrofrac):
uses fluid pressure to induce fracturing of
rock. By monitoring the fluid pressure as
it is increased to the failure point of the
rock, it is possible to determine the
magnitudes and orientations of the
principal stresses.
-First Motion Studies: the radiation
pattern of first motions of seismic P
waves (from an earthquake) defines the
orientation of two perpendicular nodal
planes at depth, one of which is the fault
plane.
Mechanisms of Stressing The Earth’s
Crust
-Overburden: stress at any depth from
the weight of the overlying column of
material.
-Driving Processes of Tectonics:
stresses associated with plate motion are
one of the major sources of regional stress
in the lithosphere (e.g.: slab-pull, trench
suction, ridge-push, mantle-drag).
-Horizontal and Vertical Motions:
bending of the lithosphere causes stress in
the earth’s crust.
-Thermal and Pressure Effects:
thermal expansion or contraction of rocks
in response to changes in temperature
induces stresses in the rocks if they are
not free to expand or contract. Changes in
pressure associated with the addition or
removal of overburden also induces strain
in the rocks.
-Pore Fluid Pressure: can cause
extension fracturing in rocks even under
conditions of purely compressive applied
stresses.
-Aquathermal Pressuring: pore fluid
pressure increases with temperature if
water is trapped in impermeable layers,
since water has a higher coefficient of
thermal expansion than sediment.
Stress in the Earth
-Vertical normal stress: should be
equal to the overburden, which is
determined by the density of the rocks.
-Nontectonic
Horizontal
Normal
stress: H = [/(1-)] V,
where H is the horizontal normal stress,
V is the vertical normal stress and  is
the Poisson ratio of the rock.
-Tectonic Horizontal Normal Stress:
the only constraint on horizontal stresses
of tectonic origin is that the differential
stress (the diameter of the Mohr circle)
must not exceed the strength of the rock.
Fractures associated with Faults
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-En echelon pinnate fractures along a
shear fracture. When formed, they are
oriented approximately perpendicular to
the minimum compressive stress.
-Gash factures may form as
extensional fractures perpendicular to the
minimum compressive stress. However,
they may be rotated by ductile
deformation during or after formation.
Fractures Associated with Folds
-Orientations of the principle stresses
change through time during the folding
process and the magnitudes changes as
well.
Stress Distributions and Faulting
- Anderson’s Theory of Faulting:
This theory depends on the fact that the
surface of the earth is a free surface which
can support no shear stress. Thus, the
Earth’s surface must be a principle plane
of stress, and the principle stresses must
be normal and parallel to it.
Fig 9.18 (p. 255 of Twiss & Moores)
The figure above shows 3 different
types of faults (normal, thrust, strike-slip)
and the directions of the principal stresses
acting on each fault plane.
-Vertical normal stress(from overburden):
zz=rgz,
where zz is the vertical normal stress, r is
the average density of the rock, g is the
acceleration due to gravity and z is the
depth.
-The corresponding horizontal stress, xx
is equal to a fraction,  of the vertical
stress.
xx=rgz
- Standard State: State of stress arising
only from the overburden.
Mechanics of Large Overthrusts
John Pierce, 2011
Edited by Sanjeevi Nagalingam 2013
-The driving force required to move a
block must be greater than or equal to the
frictional resistance.
-High pore fluid pressure along a
decollement would reduce the frictional
resistance. The greater the friction, the
smaller the block is allowed to be.
-Commonly follow layers of weak
rock in the stratagraphic section.
- Gravity as a driving force would act
on every individual point on the block.
- A slope of at least 31 is required
for a block to be moved gravitationally.
Critical Coulomb Wedge model:
-Describes the mechanisms of a
brittle,
deformable
thrust
sheet
undergoing frictional sliding on a basal
decollement.
- We assume that the rocks in the
thrust sheet are everywhere just at the
critical stress for failure as defined by the
coulomb fracture criterion.
- Dip of the decollement affects the
resistance to motion of the thrust sheet in
three ways
1) Steeper dip means move driving
force needed.
2) Higher slope increases the normal
stress on the decollement.
3) Increase in the slope increases the
area of the vertical face at any given
distance from the toe.
References & Resources
1. Robert J. Twiss, Eldridge M.
Moores, Structural Geology 2nd
edition, (W. H. Freeman), p. 231268, 2006.
2. Anderson's Theory of Faulting.
Web URL:
http://www.geology.cwu.edu/facs
taff/charlier/courses/g360/anderso
n.html
3. Faults and Stresses. Web URL:
http://homepage.usask.ca/~mjr34
7/prog/geoe118/geoe118.051.html
John Pierce, 2011
Edited by Sanjeevi Nagalingam 2013
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