Page 172 - Applied Petroleum Geomechanics

166 Applied Petroleum Geomechanics

in the principal effective stress domain for a fault is shown in the following
equation, if there is no shear failure/sliding:
2c f cos4 1
0 f 0
s þ s (5.5)
1 3
1 sin 4 f k f
0
0
where s 1 is the maximum effective stress; s 3 is the minimum effective
stress; 4 f is the angle of internal friction of the fault; c f is the cohesion of
the fault; and
1 sin 4 f ffiffiffiffiffiffiffiffiffiffiffiffiffi 2
q
2
k f ¼ ¼ m þ 1 þ m f (5.6)
f
1 þ sin4 f
where m f is the coefficient of friction of the fault, and m ¼ tan 4 .
f
f
For deep formations, the cohesion of the fault is often neglected and
Eq. (5.5) can be simplified. Therefore, to avoid a fault from frictional
sliding, the in situ stresses should satisfy the following equationda similar
equation used by Sibson (1974) and Zoback et al. (2003):
1
0 0
s s (5.7)
1 3
k f
Substituting the total principal stresses into Eq. (5.7), the in situ stresses
can be expressed in the following equations for different faulting stress
regimes (as shown in Fig. 5.1):
Normal faulting regime:
s 0 s V ap p 1
1
¼ (5.8)
s 0 s h ap p k f
3
where a is Biot’s coefficient; p p is the pore pressure.
Strike-slip faulting regime:
s 0 s H ap p 1
1
¼ (5.9)
s 0 s h ap p k f
3
Reverse faulting regime:

s 0 s H ap p 1
1
¼ (5.10)
s 0 3 s V ap p k f
LB
Hence, from Eq. (5.8) the lower bound minimum horizontal stress (s )
h
can be obtained:
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiq
2
s LB ¼ m þ 1 þ m f ðs V ap p Þþ ap p (5.11)
f
h