Tectonic Stress Fields and Karst - Dynamic Tectonics and Karst - page 8

Table 2.1

Causes of fracture-density variation (after Hunt et al. 2011 )

Type Parameter Direction of correlation

Material property Rock brittleness Positive

Grain size Negative

Porosity Negative

Bed thickness Negative

In situ Depth Variable effect

Pore pressure May hold fractures open

Strain Structural position Positive with strain

The orientation of the shear plane is defined by the
equation:

tg2h ¼ 1

l :

ð 2 : 1 : 4 Þ

It follows, that the shear angle h is depending
exclusively from the type of the material. The theory
is considered to describe with sufficient accuracy, the
destruction of rocks at low and moderate pressures
(Brace 1960 ; Lundborg 1968 ).
From physical point of view, the Theory of Griffith
published in 1921, was accepted as more justified,
because it is based on the internal characteristics of
the brittle material. This theory accepts that the real
material contains a number of randomly oriented
micro-joints. Under stress conditions in the material,
at the ends of these joints, a stress concentration is
present. The maximum stress concentration is along
the direction u. If a critical value of the stress is
reached, the micro-joints with orientation u will grow
by secondary micro-fracturing, and finally a macro-
fracturing shall be produced. Following this theory
McClintock and Walsh ( 1962 ) proposed the so-called
Modified Griffith's Theory. They have accepted that
under a minimum pressure the micro-joints are
closed. When differential stresses exist, on the walls
of the joints reactive frictional stress appears, being
proportional to the compression stress. The equation
of destruction is:

Fig. 2.3 Relationship between the terms fracture, fault, joint,

and fissure (according to Norsk Geologisk Tidsskrift 69,

Supplement 1989 )

A fissure, commonly used term in karst studies, is
an open joint or crack. Some fissures appear clearly to
be open, but they could be subsequently filled with
mineral growth, as well as eroded and enlarged by the
water in karstified rocks.
Here a brief overview of the most popular theories
of the shear joints formation will be presented,
because the shear joint systems are widely used in our
studies for reconstruction of the tectonic stress fields'
main axes.
One of the most valid theories of failure of rock-
like materials is this of Coulomb-Navier, widely
accepted in the geotectonic practice. According to this
theory, the shear strength consists of two compo-
nents—cohesion shear strength s c and the frictional
resistance on the corresponding plane s f ¼ lr h (fol-
lowing Stoyanov 1970 ). The destruction appears
when the tangential stress on the plane reaches the
value of the strength:

s u ¼ 2 K þ l e r u : ð 2 : 1 : 5 Þ

s h ¼ s c þ lr h : ð 2 : 1 : 3 Þ

Here s u is the tangential stress acting on the plane
oriented at the angle u toward the maximum stress r 1 ,
K is the uniaxial tensile strength, l e is the frictional
coefficient along the walls of the initial joints (i.e., it

Here h is the shear angle (the orientation of the shear
plane toward the maximum normal stress r 1 ) and l is
the coefficient of internal friction.