Stress, faults, and folds - Tectonic Geomorphology - page 73

the yield strength of the rock. Therefore,
Δ

Clearly, faulting occurs in response to imposed
stresses. But why should we care about the
orientation and magnitude of local stresses?
Perhaps the most important reason is that large
gaps exist in our understanding of faulting
within the truly heterogeneous rocks of the
crust. Much of our current knowledge of the
mechanics of faulting derives from laboratory
studies, which commonly involve homogeneous
rocks of hand-specimen size. In the real world,
we need to know where and how slip occurs
along a fault. How do real rocks actually deform
when their yield strength is exceeded, and how
are the resulting structures oriented with respect
to prevailing stresses? Do stresses accumulate
on a fault such that earthquakes tend to initiate
in the same region and propagate in the same
direction over multiple earthquake cycles? How
does the stress across a fault surface change as
a result of a faulting event? What is the role
played by fluids? Until these questions are
answered, our ability to quantify and predict
deformation in earthquakes will be impeded.

s xx < 0, the horizontal stress is less than the ver-
tical stress, s xx = r gz + Δ

s xx , and s xx < s zz . If we
assume that no strain (deformation) exists in the
y direction, then the deviatoric stress in the y
direction either is zero or is also tensile, but is
some proportion ( p ) of the deviatoric stress in
the x direction. Therefore, Δ s xx , where

p < 1. The total stress in the y direction, s yy =
r gz + p Δ

s yy = p Δ

s xx , is less than s zz (or equal to it, if p = 0),
but greater than s xx . Thus, for normal faulting,
s zz ≥ s yy > s xx . In theory, a fault plane should make
an angle with the principal compressive stress of
45 ° − q /2, where q is equal to the angle of inter-
nal friction for the faulted material. Thus, given a
typical q value of 30 ° , a normal fault formed in a
relatively strong rock like granite should be
inclined at about 30 ° to s zz , and the fault trend
should be oriented perpendicular to s xx
(Fig. 4.1A). Two different fault planes, each
dipping in opposite directions at 60 ° from the
horizontal, satisfy these conditions and thus rep-
resent conjugate fault planes. Given these
stresses and this fault orientation, the hanging
wall (the fault block that is located above the
fault plane) moves down across the footwall ,
which is beneath the fault plane.
For thrust faults, a compressional deviatoric
stress exists in the x direction, typically resulting
from tectonic forces. Thus, Δ

The earthquake cycle

The classical model

Since at least the turn of the 20th century,
geologists have attempted to understand the
deformation that precedes, coincides with, and
follows an earthquake. The time and deforma-
tion that encompasses an earthquake and all
of the interval between successive earthquakes
is termed the earthquake cycle . As originally
described, the earthquake cycle had two parts:
an interseismic interval and a coseismic one
(Reid, 1910). Imagine two nearby pieces of the
crust that are moving in opposite directions with
respect to a fault that separates them. At some
depth below the surface, the fault slips continu-
ously and aseismically in a zone of ductile
deformation, but in the brittle crust during the
interseismic interval, the fault is “locked” such
that no slip occurs along it (Fig. 4.2). At some
distance from the fault, the rocks in the brittle
zone are moving at the same rate as the crustal
blocks. The amount of displacement decreases
to zero at the fault, such that an originally

s xx > 0, and s xx > s zz .
Once again, the deviatoric stress in the y
direction can be considered intermediate, so
that s xx > s yy ≥ s zz . For a horizontally oriented

maximum compressive stress, conjugate fault
planes should be inclined at 45 ° − q /2 from the
horizontal and also at 45 ° − q /2 from s xx (Fig. 4.1B).
For thrusts, the hanging wall moves upward
with respect to the underlying footwall.
Strike-slip faults are characterized by devia-
toric stresses of opposite sign in the x and y
directions. For example, if s yy is tensile, then
Δ s yy < 0. Consequently, s xx must be compressive,

such that Δ

s xx > 0. Therefore, for strike-slip faults,
either s yy > s zz > s xx , or s xx > s zz > s yy . For any stress
regime in which the lithostatic stress is the inter-
mediate stress, two conjugate vertically dipping
fault planes oriented at 45 ° − q /2 to the maximum
compressive stress will accommodate strike-slip
motion (Fig. 4.1C).