described a state of stress that provides a good reference state for investigations of problems in
structural geology:
It is possible to imagine a condition in which the
lateral pressure from all sides increases steadily with
depth, so as to be everywhere equal to the vertical.
This will not often happen in nature, but it forms a
convenient standard of reference, and may be defined
as the “standard state” (Anderson, 1951, pp. 13, 148).
From this description we understand that the
normal stress components (“pressure”) are equal
and the shear stress components are zero. In other
words this is an isotropic state of stress and the magnitude is determined by the weight of overlying
rocks. In this section we define a state of stress
that is consistent with Anderson’s concept and
then describe data from field measurements that
show typical variations from this state with
depth. Two techniques for measuring the state of
stress at shallow depths are described and the
data from such tests are summarized. Finally, we
provide examples at both the outcrop and the
crustal scale that illustrate how tectonic states of
stress act to supplement the standard state, and
cause different styles of deformation.
Can stress be measured in the Earth? The measurement is not direct in the sense that one measures a distance directly with a ruler. Instead,
calculations using measured values of other physical quantities and/or a model are required.
Several techniques for so-called in-situ stress measurement have been developed and used at exposures and in boreholes and mines (Engelder, 1993).
Amadei and Stephansson (1997) describe these
techniques and also document much of the available data. These data have been used by mining
engineers in the design of underground openings,
and by civil engineers in the design of foundations for dams and other large construction projects. As structural geologists, our interest in the
state of stress stems from the fact that the evolution of geologic structures depends upon the temporal and spatial variations of stress.
Because in-situ stress measurement techniques
require direct access to the rock mass, stress measurements have only been made at shallow depths
in the crust, typically less than a few kilometers.
Stress states at greater depths must be extrapolated from these data, inferred from studying
data recorded on seismographs during earthquakes, or calculated from models. Seismic data
indicate the orientations of the principal stresses
in the vicinity of a significant earthquake
(Engelder, 1993). Typically these events range
from a few kilometers depth to a few tens of kilometers, so this method extends our knowledge of
the stress state throughout much of the Earth’s
crust. The magnitudes of the stresses are not
determined by this method, and there can be considerable uncertainty about the orientations
(McKenzie, 1969). None-the-less, these so-called
fault-plane solutions have proved to be very valuable
in compiling maps of the principal stress orientations (Zoback, 1992).
In most in-situ stress measurement data sets
the vertical normal stress ranges from zero at the
surface to about 50 MPa at 2 km depth (Brown and
Hoek, 1978), more or less following a linear distribution (Fig. 6.26a). This is consistent with the vertical normal stress being related simply to the
weight of the overlying rock mass. On the other
hand, the horizontal components of normal stress
vary in a less systematic fashion with depth
(Fig. 6.26b), possibly reflecting differing tectonic
loading conditions. Here, the ratio of horizontal
to vertical stress is shown to be widely scattered
near the surface and converging toward values of
one or less at depths greater than 2 km.
The direction of principal stress and its variation in map view across continents, plate boundaries, and other tectonic features may be compiled
from the point measurements. Usually these data
are presented in terms of the direction of the most
compressive normal stress acting in the horizontal
plane, near the Earth’s surface (Fig. 6.27). In this
particular figure the authors have focused on
California and the orientation of this stress near
the San Andreas Fault system (Zoback et al., 1987).
They find that the direction of the greatest compression is remarkably consistent across this
region, being more or less from northeast to southwest. This direction varies from somewhat oblique
to nearly perpendicular to the trace of the San
Andreas Fault zone. Where the most compressive
stress is oblique to the fault, one can think of this
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FORCE, TRACTION, AND STRESS
structural geology:
It is possible to imagine a condition in which the
lateral pressure from all sides increases steadily with
depth, so as to be everywhere equal to the vertical.
This will not often happen in nature, but it forms a
convenient standard of reference, and may be defined
as the “standard state” (Anderson, 1951, pp. 13, 148).
From this description we understand that the
normal stress components (“pressure”) are equal
and the shear stress components are zero. In other
words this is an isotropic state of stress and the magnitude is determined by the weight of overlying
rocks. In this section we define a state of stress
that is consistent with Anderson’s concept and
then describe data from field measurements that
show typical variations from this state with
depth. Two techniques for measuring the state of
stress at shallow depths are described and the
data from such tests are summarized. Finally, we
provide examples at both the outcrop and the
crustal scale that illustrate how tectonic states of
stress act to supplement the standard state, and
cause different styles of deformation.
Can stress be measured in the Earth? The measurement is not direct in the sense that one measures a distance directly with a ruler. Instead,
calculations using measured values of other physical quantities and/or a model are required.
Several techniques for so-called in-situ stress measurement have been developed and used at exposures and in boreholes and mines (Engelder, 1993).
Amadei and Stephansson (1997) describe these
techniques and also document much of the available data. These data have been used by mining
engineers in the design of underground openings,
and by civil engineers in the design of foundations for dams and other large construction projects. As structural geologists, our interest in the
state of stress stems from the fact that the evolution of geologic structures depends upon the temporal and spatial variations of stress.
Because in-situ stress measurement techniques
require direct access to the rock mass, stress measurements have only been made at shallow depths
in the crust, typically less than a few kilometers.
Stress states at greater depths must be extrapolated from these data, inferred from studying
data recorded on seismographs during earthquakes, or calculated from models. Seismic data
indicate the orientations of the principal stresses
in the vicinity of a significant earthquake
(Engelder, 1993). Typically these events range
from a few kilometers depth to a few tens of kilometers, so this method extends our knowledge of
the stress state throughout much of the Earth’s
crust. The magnitudes of the stresses are not
determined by this method, and there can be considerable uncertainty about the orientations
(McKenzie, 1969). None-the-less, these so-called
fault-plane solutions have proved to be very valuable
in compiling maps of the principal stress orientations (Zoback, 1992).
In most in-situ stress measurement data sets
the vertical normal stress ranges from zero at the
surface to about 50 MPa at 2 km depth (Brown and
Hoek, 1978), more or less following a linear distribution (Fig. 6.26a). This is consistent with the vertical normal stress being related simply to the
weight of the overlying rock mass. On the other
hand, the horizontal components of normal stress
vary in a less systematic fashion with depth
(Fig. 6.26b), possibly reflecting differing tectonic
loading conditions. Here, the ratio of horizontal
to vertical stress is shown to be widely scattered
near the surface and converging toward values of
one or less at depths greater than 2 km.
The direction of principal stress and its variation in map view across continents, plate boundaries, and other tectonic features may be compiled
from the point measurements. Usually these data
are presented in terms of the direction of the most
compressive normal stress acting in the horizontal
plane, near the Earth’s surface (Fig. 6.27). In this
particular figure the authors have focused on
California and the orientation of this stress near
the San Andreas Fault system (Zoback et al., 1987).
They find that the direction of the greatest compression is remarkably consistent across this
region, being more or less from northeast to southwest. This direction varies from somewhat oblique
to nearly perpendicular to the trace of the San
Andreas Fault zone. Where the most compressive
stress is oblique to the fault, one can think of this
228
FORCE, TRACTION, AND STRESS