12.1.2 Tectonic Stress in the Earth’s
Lithosphere
As we have seen already, in addition to stresses
generated at tectonic plate contacts, several other processes contribute to the generation of stresses. We
may, for example, have residual stress, which is
inherited from previous deformation, where a rock
body may have become bent with the elastic stress
component remaining unreleased, and thermal stress
which is related to expansion of rocks during heating
or contraction during cooling and stress related to local
gravitational gradients. Accordingly, the total stress
consists of several components:
Total stress ¼ reference stress þ residual stress
þ thermal stress þ tectonic stress
where the reference stress refers to the stress inside the
plate, devoid of plate tectonic stresses, and thus the
Tectonic stress ¼ contemporary stress þ local stress:
We will not go further into the analysis of residual
and thermal stress here, but concentrate on stress
generated by primary interactions at plate margins or
forces derived thereof.
Taking into consideration the reference stress
conditions, one can describe the stress situations for
the three principal conditions of deformation, namely
extension, contraction and strike-slip. This was done
by Anderson in two influential works in 1934 and
1951, in which the framework for all modern tectonic
and structural geological analysis is defined. Anderson
used the vertical lithostatic stress (σ v ) as a reference:
σ v ¼ ρgz
(12.1)
(where ρ is the specific weight, g is the constant of
gravity and z is the height of the rock column). This
applies for the three principal stress conditions
because σ v can be considered similar for one rock
type for a constant h, assuming that the burial history
has been similar. Thereby the three principal stress
systems can be defined, each corresponding to a
regime of deformation (Fig. 12.2a, b):
σ v > σ H > σ h ; extension;
(12.2)
σ H > σ v > σ h ; strike-slip;
(12.3)
σ H > σ h > σ v ; contraction;
(12.4)
where σ H and σ h are the maximum and minimum
horizontal stresses, respectively. By using σ v as a
reference, further calculations become dependent on
the reference system applied. In the contractional
regime there will be a tectonic component σ
Ã
t
À Á
in
addition to the reference stress, so that the greatest
(horizontal) stress is:
σ H ¼ ρgz þ σ
Ã
t
(12.5)
Assuming uniaxial stress, which implies that the
reference stress is a function of the elastic properties
of the rock, and ignoring the thermal expansion, we
can describe the stress as:
σ H ¼
υ
1 À υ
h
i
ρgz þ σ t
(12.6)
where υ is Young’s modulus (Chap. 11). Because
υ=1 À υ
ð
Þ< 1, σ t > σ
Ã
t . Accordingly, the reference
stress condition selected also influences the calculated
total tectonic stress as long as the buried rock is
compressive. For a non-compressive rock υ ¼ 0:5
ð
Þ ,
lithostatic and uniaxial reference systems are equal.
12.1.3 Deformation Mechanisms and
Analogue Models
Our daily contact with the physical world tells us that
materials deform in many ways, depending on the
applied stress and type of material and its physical
state. Thus, a liquid reacts to outer stress very differently from a piece of rock, and one type of rock like
chalk has very different physical properties as
compared to another like granite. Furthermore, one
material may change its mechanical properties dramatically by change of temperature and pressure.
These contrasts are founded on processes occurring
on the scale of the grains (of the rock) and on the
molecular and atomic scales. We have given these
processes and their associated meso- and macroscopic
physical expressions names like brittle, elastic, plastic,
12 The Structure and Hydrocarbon Traps of Sedimentary Basins
323
Lithosphere
As we have seen already, in addition to stresses
generated at tectonic plate contacts, several other processes contribute to the generation of stresses. We
may, for example, have residual stress, which is
inherited from previous deformation, where a rock
body may have become bent with the elastic stress
component remaining unreleased, and thermal stress
which is related to expansion of rocks during heating
or contraction during cooling and stress related to local
gravitational gradients. Accordingly, the total stress
consists of several components:
Total stress ¼ reference stress þ residual stress
þ thermal stress þ tectonic stress
where the reference stress refers to the stress inside the
plate, devoid of plate tectonic stresses, and thus the
Tectonic stress ¼ contemporary stress þ local stress:
We will not go further into the analysis of residual
and thermal stress here, but concentrate on stress
generated by primary interactions at plate margins or
forces derived thereof.
Taking into consideration the reference stress
conditions, one can describe the stress situations for
the three principal conditions of deformation, namely
extension, contraction and strike-slip. This was done
by Anderson in two influential works in 1934 and
1951, in which the framework for all modern tectonic
and structural geological analysis is defined. Anderson
used the vertical lithostatic stress (σ v ) as a reference:
σ v ¼ ρgz
(12.1)
(where ρ is the specific weight, g is the constant of
gravity and z is the height of the rock column). This
applies for the three principal stress conditions
because σ v can be considered similar for one rock
type for a constant h, assuming that the burial history
has been similar. Thereby the three principal stress
systems can be defined, each corresponding to a
regime of deformation (Fig. 12.2a, b):
σ v > σ H > σ h ; extension;
(12.2)
σ H > σ v > σ h ; strike-slip;
(12.3)
σ H > σ h > σ v ; contraction;
(12.4)
where σ H and σ h are the maximum and minimum
horizontal stresses, respectively. By using σ v as a
reference, further calculations become dependent on
the reference system applied. In the contractional
regime there will be a tectonic component σ
Ã
t
À Á
in
addition to the reference stress, so that the greatest
(horizontal) stress is:
σ H ¼ ρgz þ σ
Ã
t
(12.5)
Assuming uniaxial stress, which implies that the
reference stress is a function of the elastic properties
of the rock, and ignoring the thermal expansion, we
can describe the stress as:
σ H ¼
υ
1 À υ
h
i
ρgz þ σ t
(12.6)
where υ is Young’s modulus (Chap. 11). Because
υ=1 À υ
ð
Þ< 1, σ t > σ
Ã
t . Accordingly, the reference
stress condition selected also influences the calculated
total tectonic stress as long as the buried rock is
compressive. For a non-compressive rock υ ¼ 0:5
ð
Þ ,
lithostatic and uniaxial reference systems are equal.
12.1.3 Deformation Mechanisms and
Analogue Models
Our daily contact with the physical world tells us that
materials deform in many ways, depending on the
applied stress and type of material and its physical
state. Thus, a liquid reacts to outer stress very differently from a piece of rock, and one type of rock like
chalk has very different physical properties as
compared to another like granite. Furthermore, one
material may change its mechanical properties dramatically by change of temperature and pressure.
These contrasts are founded on processes occurring
on the scale of the grains (of the rock) and on the
molecular and atomic scales. We have given these
processes and their associated meso- and macroscopic
physical expressions names like brittle, elastic, plastic,
12 The Structure and Hydrocarbon Traps of Sedimentary Basins
323