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In situ stress regimes with lithology-dependent and depletion effects 173

stress polygons: one in a sandstone with Poisson’s ratio of 0.3 and the other
in a shale with Poisson’s ratio of 0.4. It indicates that the stress polygon is
markedly related to Poisson’s ratio of the rock. Fig. 5.7 shows that Poisson’s
ratioebased stress polygon can narrow the area of the conventional stress
polygon, particularly in shales. Using this Poisson’s ratioedependent stress
polygon and combining with other methods (borehole breakouts and
drilling-induced tensile fractures; refer to Chapters 6 and 10), in situ stresses
can be estimated.

5.3.3 Relationship of the coefficient of friction of the fault
and Poisson’s ratio

As indicated before, two methods can be used to calculate the lower bound
minimum horizontal stress: one from the uniaxial strain model (Eq. 5.15),
the other from the faulting stress regime constraint (Eq. 5.11). Assuming
that the two lower bounds are equal, the coefficient of friction can be
estimated, as shown in the following:

2
q ffiffiffiffiffiffiffiffiffiffiffiffiffi n
2
m þ 1 þ m f ¼ (5.17)
f
1 n
Therefore, one obtains:
1 2n
f
m ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (5.18)
2 nð1 nÞ
This equation is applicable in the following range of Poisson’s ratio:
0.16 < n < 0.5.
Fig. 5.7 shows that the stress polygon depends highly on Poisson’s ratio.
Because Poisson’s ratio is dependent on lithology and depth, the coefficient
of friction of the fault also depends on lithology and depth. For example, a
sandstone normally has a lower Poisson’s ratio than a shale; hence, the
sandstone in the fault has a larger coefficient of friction (e.g., when
n ¼ 0.23, m f ¼ 0.64 from Eq. 5.18) than that in the shale. This explains why
the sandstone normally has a smaller horizontal stress. A shale normally has a
higher Poisson’s ratio, thus a smaller coefficient of friction (e.g., if n ¼ 0.4,
then m f ¼ 0.2 from Eq. 5.18). This is verified by the following experimental
results: the measurements by Ikari et al. (2011) show that fault gouges
containing clay minerals are frictionally weak (m f < 0.5), whereas gouges
rich in silicate minerals (e.g., quartz, feldspar) are stronger (m f > 0.6). From
the well data in claystone sequences containing polygonal fault systems in