Geoscience Reference
In-Depth Information
is a coefficient of external friction), and r
u
is the
normal stress on the critical planes (it is positive).
Finally, the critical angle of the shear joints is:
Our interest in the formation of suitable conditions for
the karst evolution is directed to the formation of open
fractures. If conditionally, the horizontal stress com-
ponents c
y
[ c
x
, than r
y
[ r
x
. The formation of ten-
sile fractures, as well as normal faults in larger scales,
can be possible under the condition:
tg2u
¼
1
l
e
:
ð
2
:
1
:
6
Þ
The difference between l (from Eq.
2.1.4
) and l
e
is
that the physical meaning of l is not well defined
especially for real rock conditions, while l
e
is a real
physical parameter (Stoyanov
1970
).
The caves in karst terrains are a result of the water
erosion along the most open fractures under given
tectonic conditions. In this case, the normal faults and
the tensional fractures (fissures) are most favorable
for the karst network evolution. The study of the
mechanism of formation of fractures in the rocks by
Price (
1959
,
1966
) lead to the conclusion, that the
vertical tensional and shear fractures and faults are
formed as a result of residual elastic stresses during
the post-tectonic uplifting of compressed volumes.
One very important statement in these works is that
these types of structures can be formed only if hori-
zontal tectonic extension exists.
If the Earth's crust is three-dimensionally ana-
lyzed, only in the state of the own weight of the rocks,
and taking into account that the horizontal enlarge-
ment of given volume is not possible because of the
environment conditions, r
x
, r
y
and r
z
will be the
principal stress axes. It could be written that:
r
0
x
\r
0
y
\r
0
z
:
ð
2
:
1
:
9
Þ
Because
the
vertical
stress
is
determined
as
r
0
z
¼
r
z
¼
ch, where c is the bulk weight of the rock
and h is the depth from the surface, it can be finally
written for the formation of tensile fractures:
c
x
\c
y
\
1
2m
1
m
ch
c
x
:
ð
2
:
1
:
10
Þ
Most of the quantitative studies of the tectonic
stress field of the Earth reflect the ongoing contem-
porary processes, and for them direct or indirect data
can be obtained depending of the chosen method of
investigation. The presumption for heritability of the
tendencies from the past geological times can be
applied only for the Quaternary time, under some
conditions it could be accepted also the heritability of
the Neotectonic tendencies for specific regions. Every
reconstruction of the tectonic stress field in older
geological formations needs careful analysis of the
studied parameters, taking into account the multiform
responses of the inverse problem solutions.
When explaining the causes for existing of tectonic
stresses and their evaluated rates, it is necessary to
realize that the analyses cover only relatively narrow
time window and they reflect the contemporary, ''the
moment'' state (in geological sense) of the tectonic
stress field. Hence, it is of critical importance to
understand what is measured when applying instru-
mental in situ investigations for stress determination.
The terminology used for describing in situ stresses is
analyzed by Amadei (
1983
). More complete and
hierarchically structured terminology is presented by
Bielenstein and Barron (
1971
), and it described well
the real situation for the near surface geological for-
mations of the Earth's crust (Fig.
2.4
).
When analyzing the processes of karst formation
and evolution, it is clear that the tectonic factor is the
principal controller of the fracturing in the rocks with
specific brittleness at given structural position of the
rock formations (see Table
2.1
). Our experience gives
reason
m
1
m
r
z
:
r
x
¼
r
y
¼
ð
2
:
1
:
7
Þ
In this case, we accept that the horizontal deforma-
tions along the horizontal axes X and Y, i.e.,
e
x
= e
y
= 0, and the axis Z is vertical. The coefficient
of Poisson m is less than 0.5 and r
z
will be the max-
imum stress = gravitational stress.
Now it is necessary to add the stress from the tectonic
strain. Let us say that the tectonic strain has only hori-
zontal components and the stress effect in every point
can be presented by two perpendicular stresses c
x
and c
y
.
The equations of superposition of the horizontal and
gravitational stresses will be (after Stoyanov
1970
):
m
1
m
r
z
þ
c
x
þ
mc
y
r
0
x
¼
m
1
m
r
z
þ
c
y
þ
mc
x
r
0
ð
2
:
1
:
8
Þ
y
¼
r
0
z
¼
r
z
:
to
the
assumption
that
the
active
tectonic
