Geology Reference
In-Depth Information
=
=
=
Faults and Stresses
1 bar
10
5
Pa. Because
one pascal represents a rather small force acting
over a large area (one cubic meter of granite
exerts a pressure of
10
6
dyne/cm
2
10
5
N/m
2
A
N
o
rmal: sec
tion
str
ess
σ
yy
σ
xx
∼
27 500 Pa on its base!), pres-
sures are often expressed in megapascals
(1 MPa
ß
ß
intermediate,
orthogonal
stress direction
=
10
6
Pa), which is also equal to 10 bars.
A column of rock 1 km high would typically exert
a pressure at its base of 25-30 MPa. The shear
strength of many crustal rocks is in the range
10-100 MPa.
Each of the tractions acting on a rock surface
and resulting from tectonic, lithostatic, buoy-
ancy, or hydrostatic forces can be represented as
a vector which can be summed with all other
imposed tractions to define the total magnitude
and orientation of the imposed stress on any
specified plane. The total stress can be subdi-
vided into three orthogonal components, which
are typically labelled
s
1
,
s
2
, and
s
3
, for the
maximum, intermediate, and minimum principal
stresses, respectively. For simplicity in discuss-
ing types and orientations of faults and associ-
ated structures, we will refer to three
orthogonal
stress vectors, in which one (
s
zz
) is vertical and
the other two (
s
xx
,
s
yy
) are contained in a
horizontal plane (Fig. 4.1A). The vertical stress
results from the rock overburden at some depth
z
, such that
s
zz
σ
zz
B
Thru
st:section
ß
σ
yy
ß
σ
xx
σ
zz
C
Strike-slip: map view
σ
zz
σ
xx
σ
yy
y
y
Fig. 4.1
Fault orientations with respect to principal
stress orientations.
A. Normal faults:
b
=
45
°
+
q
/2, where
q
equals the
angle of internal friction. B. Thrust faults:
b
=
45
°
−
q
/2.
C. Strike-slip faults. Modified after Turcotte and
Schubert (1982).
rotation or the magnitude and orientation
of extension, shortening, or stretching, can be
defined through direct observations.
Not all strain in rocks is permanent. Below a
certain stress threshold, termed the
elastic limit
,
strain is recoverable. Thus, during the initial
build-up of differential stresses, a rock will
deform elastically, and, if the differential stress is
eliminated during this stage, the rock will return
to its original unstressed shape. Once a rock's
elastic limit or
yield strength
is exceeded, it will
either deform plastically or rupture; either case
causes a permanent change in shape. When a
rock deforms by rupture, discrete surfaces, or
faults
, are formed along which rocks are offset
by movements parallel to the fault surfaces.
Consider the stresses that are responsible for
normal faults. The vertical component of stress
is the lithostatic pressure,
s
zz
=
r
gz
, where
z
is
the thickness of overlying rock. For faulting
to occur, an applied deviatoric stress
Δ
r
gz
, where
r
is the mean
density of the overlying rock and
g
is the
gravitational acceleration. This is termed the
lithostatic stress
. When the orthogonal horizon-
tal stresses are equal to the vertical lithostatic
stress, such that
s
1
=
s
3
, this is termed a
lithostatic state of stress
. To the extent that
stresses differ from this lithostatic condition,
they are termed
deviatoric stresses
. In most of
the situations involving faulting, the deviatoric
stress (
=
s
2
=
Δ
s
) results from a tectonic contribution.
Strain and faults
The presence of deviatoric stresses can cause a
rock to undergo
strain
: any deformation that
involves a change in size (dilation), shape
(distortion), and/or orientation (rotation). Strain
in rocks can be observed and quantified,
whereas the deviatoric stresses that caused the
strain commonly can only be inferred. Various
components of strain, such as the amount of
s
xx
that
is tensile and, therefore, negative with
respect to its lithostatic value, must exceed
