Page 171 - Applied Petroleum Geomechanics

In situ stress regimes with lithology-dependent and depletion effects 165

two horizontal stresses are the intermediate and minimum principal
stresses, i.e.,
(5.1)
s V s H s h
From the Mohr circle (see Fig. 3.21) the angle between the shear
failure plane (the fault plane) and the maximum stress (s V ) is:

a ¼ 45 4=2 (5.2)
where 4 is the angle of internal frication of the rock. It can be seen from
Eq. (5.2) that a < 45 degrees. Therefore, the angle of dip of the fault
plane in the normal fault is 90 degrees a ( > 45 degrees, see Fig. 5.1A).
2. Strike-slip faulting stress regime (Fig. 5.1B). In this case, the vertical
stress is the intermediate principal stress, i.e.,

(5.3)
s H s V s h
The maximum horizontal stress causes faulting (shear failure). The
angle between the shear plane of the fault and the maximum horizontal
stress is a ¼ 45 4=2.

3. Reverse (or thrust) faulting stress regime (Fig. 5.1C). In this case, the
vertical stress is the least principal stress, i.e.,

(5.4)
s H s h s V
The maximum horizontal stress causes thrust faulting (shear failure).
The angle between the fault plane and the maximum horizontal stress is

a ¼ 45 4=2, i.e., the angle of dip of the fault a < 45 degrees, a low
angle fault.
It should be noted that current stress state may be different from
observed fault types in the formations, particularly for the reverse fault-
ing stress regime. For example, the presence of reverse faults is not
necessary to represent a reverse faulting stress regime in the contempo-
rary stress field. The reason is that the paleostresses in this case might be
in the reverse faulting stress regime; however, it was an unstable stress
state and more likely to be changed to the strike-slip or normal faulting
stress regime because of stress relaxation or other reasons.

5.2 In situ stress bounds and stress polygons
Assuming that there are critically oriented faults constraining stress mag-
nitudes, the MohreCoulomb criterion ( Jaeger and Cook, 1979) expressed