Page 175 - Applied Petroleum Geomechanics

In situ stress regimes with lithology-dependent and depletion effects 169

friction of the fault is needed, which is not possible to be measured directly
in subsurface. Conventionally, it is assumed that the coefficient of friction of
the fault is a constant across the entire fault plane (m f ¼ 0.6e0.7) based on
Byerlee’s law (Byerlee, 1978). This assumption may lead to uncertainty in
in situ stress estimation because of the difficulty in m f estimate. In fact, some
faults are weaker with much lower m f . For example, Bird and Kong (1994)
and Carena and Moder (2009) concluded that all faults in the vicinity of the
transform plate boundary of the western United States are frictionally weak
to very weak (m f 0.2). Iaffaldano (2012) inferred that the coefficient of
friction of large-scale plate boundaries is in the range of 0.01e0.07. Byerlee
(1978) pointed out that if the sliding surfaces are separated by gouge
composed of some clay minerals, the friction is very low. Engelder and
Fischer (1994) concluded that the minimum horizontal stress calculated
from m f ¼ 0.6 underestimates the minimum stress in the central North Sea
Graben and does not match the measured data in the Scotian Shelf, Canada.
Not surprisingly, research work shows that the coefficient of friction of the
fault is highly related to the lithology or mineralogy of the fault gouge. For
example, extreme fault weakness (m f w 0.1) occurs within a 3-m wide
creeping fault core (Zoback et al., 2010) in the San Andreas of central
California because of the presence of weak clay minerals (Carpenter et al.,
2011; Collettini et al., 2011). Saffer and Marone (2003) observed a coef-
ficient of friction in the fault gouge of 0.42e0.68 for illitic shale; however,
under identical conditions, a low friction (m f ¼ 0.15 e 0.32) is inferred in a
smectitic shale. There are also questions concerning whether m f is the same
for all faults in a region, whether it is even constant along strike on the same
fault (Carena and Model, 2009), or whether it is depth-dependent.
Studies and experiments (e.g., Takahashi et al., 2007) in clayequartz
gouges show that the clay content has a significant effect on the frictional
strength of the fault, i.e., as clay content increases, the coefficient of friction
decreases (e.g., when clay content is 100%, m f < 0.1 for smectite).
Analyzing the data given by Takahashi et al. (2007), the following linear
relationship can be obtained for a smectite and quartz mixture:

m ¼ 0:68 0:6C S (5.13)
f
where C S is the weight fraction of smectite clay content and C S is between
0 and 1.
Analyzing experimental data presented by Tembe et al. (2010), the
following linear relationship can be obtained for illiteequartz mixture:

m ¼ 0:68 0:42C I (5.14)
f