Geoscience Reference
In-Depth Information
2
Tectonic Stress Fields and Karst
No mater how complex could be the applied
stresses they can be decomposed at three perpendic-
ularly to each other normal stresses. If the values of
the applied strains are known, it is possible to eval-
uate the values and the directions of these three
principal stresses. The stress tensor defines com-
pletely the state of stress. Practically, it is sufficient to
know the principal stresses for evaluating the state of
stress of the studied material and to determine the
values of the normal and tangential stresses on every
other plane crossing it. For these purposes, the for-
mulas and the circles of Moore can be used. The
method is well described in every topic on Engi-
neering Geology and Rock Mechanics (we can sug-
gest the topics of Jaeger
1975
or Spenser
1981
).
Trollop (
1983
) introduced the differential defini-
tion of the stress for expressing the basic conditions of
the Theory of Elasticity as continuous mathematical
function (Trollop
1983
):
2.1
Generalities About the Tectonic
Stress Fields
The notion for the stress from mechanical point
of view was firstly introduced by Augustin Louis
Cauchy (1789-1857). He defined the stress as the
average intensity of the strain applied on surface unit.
According to the general sense of the mechanics ter-
minology the stress has to be understood as the
integrity of the internal strains that appear when the
material is submitted under loads or deformations.
Every resulting deformation, no mater of its spatial
dimensions, has to be analyzed in the context of the
initialing strains. For estimating the state of stress of a
given material, the vectors of the impacting stresses
on every one of the infinite number of elementary
surfaces dividing the material have to be evaluated.
Six are the components forming the stress tensor
inside the elementary volume of given material—
three principal and three tangential (Fig.
2.1
).
df
n
da
¼
df
r
¼
lim
d
a
!
0
ð
2
:
1
:
1
Þ
da
where f
n
is the normal strain applied on the surface a.
This definition is valuable for ideal continuous
medium. But for discrete and granulate materials (that
are normally all geological bodies) this differential
definition is not acceptable. As it was mentioned
above, the total stress state is completely defined by
the three principal stresses r
1
, r
2
, and r
3
, where:
r
1
[ r
2
[ r
3
:
ð
2
:
1
:
2
Þ
The characterization of the state of stress in Tec-
tonophysics is defined at least by three vectors of the
principal stresses. If they are equal the state of stress
Fig. 2.1
Stress components impacting the elementary volume
