Geology Reference
In-Depth Information
P3
The angle D that the shear fracture
plane makes with the maximum com-
pressive stress decreases with increasing
normal stress; i.e. with increasing lithos-
tatic pressure.
The shape of the shear failure enve-
lope is specific to a particular material;
thus in laboratory experiments, for
example, it was found that the curve
for dolerite was steeper than that for
marble; that is, the shear strength of the
dolerite increased more rapidly with
increasing compressive stress.
normal
stress
P3
shear
stress
shear
fracture
o
o
45
45
α
α
P1
P1
P1
α
α
α
shear
fracture
shear
fracture
planes of
maximum
shear stress
B
A
unstable stress
states
shear failure envelope
shear
stress
Application to fault orientation
The above relationships can be used
to predict the geometry of shear faults
under idealised conditions in homo-
geneous rocks (Figure 5.11). Because
there are three possible orientations
of the three principal stress axes, and
we can assume that shear stress paral-
lel to the Earth's surface must be zero,
two of these principal stress axes must
be horizontal. This leads to three theo-
retical types of fault arrangement.
ß
stable stress
states
extension
compression
C
normal
stress
Figure 5.10
Stress conditions for shear fracture.
A.
as seen in 2D, shear fractures (red) intersect
on intermediate principal stress axis P2 and make an angle
D
with the maximum principal stress
axis P1; this angle is smaller than the angles of 45° which the planes of maximum shear stress
make with the P1 and P3 axes.
B.
This diagram illustrates the relationship in two dimensions
between shear stress, normal stress and the two principal stresses, P1 and P3 for a fracture
plane making an angle a with the direction of maximum compressive stress, P1. Note that the
shear stress will be proportional to the stress difference (P1 - P3) and that the normal stress will
be proportional to the mean stress (P1 + P3)/2.
C.
The shear failure envelope, represented by
the red line, shows the variation in normal stress and shear stress at failure for a given material.
Note that the shear strength is much smaller under extension than under compression, and that
the strength increases with increasing normal stress. The angle
E
(= 90° − 2
D
) which measures
the gradient of the failure envelope also decreases with increasing normal stress, signifying an
increase in the angle
D
towards its maximum value of 45°.
Where the maximum principal
stress is vertical (usually equiva-
lent to gravitational load), two sets
of normal faults can form, with
opposed dips (Figure 5.11A), espe-
cially where the minimum principal
stress is negative (i.e. extensional).
its maximum theoretical value of 45°.
Where the shear stress decreases to zero,
at the left end of the graph, failure is
by extensional fracture, at right angles
to the maximum principal stress.
The effect of pore-fluid pressure is to
reduce the effective normal stress com-
ponent. It is clear from this diagram,
based on a typical rock material, that:
1. failure occurs at a lower shear stress
under extension than under com-
pression - i.e. its tensile strength is
less than its compressive strength;
2. the shear stress required for failure
(its
shear strength
) increases with
increasing lithostatic pressure;
3. the strength under extension (its
tensile strength
) is limited to the
point at the left end of the failure
curve, but there is no theoretical
limit to the compressive strength if
the shear stress lies within the failure
envelope. This illustrates that mate-
rials in general are much stronger
under compression than under
tension.
Where the maximum principal
stress is horizontal and the minimum
principal stress vertical, two sets of
thrust faults are predicted, again with
opposed dips (Figure 5.11B); this situa-
tion is more likely to apply at relatively
high levels in the crust, where the effect
of gravitational load is less important.
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