Page 124 - Applied Petroleum Geomechanics

116 Applied Petroleum Geomechanics

that after reaching the peak stress the strength decreases to a residual value
determined by frictional sliding (Schöpfer et al., 2013). The difference
between the peak and residual strengths is the stress drop (Fig. 3.25). At a
high confining pressure, however, no stress drop occurs, and the rock is in
elastic perfectly plastic deformation. The transition of the confining pressure
at which no loss in strength occurs is a possible definition of the brittlee
ductile transition (Schöpfer et al., 2013).
Astudy by Singh et al. (2011), involving reanalysis of thousands of
reported triaxial tests, has revealed the astonishing simplicity of the
following equality: UCS z s crti (i.e., critical s 3 ) for the majority of rock
types. In other words, the two Mohr circles referred to in Fig. 3.24 are
touching at their circumference. The curvature of peak shear strength
envelopes is more correctly described, so that few triaxial tests are
required, only needed to be performed at low confining stress, to
delineate the whole strength envelope. This simplicity does not of course
apply to the case, where triaxial tests are required over a wide range of
confining stress, to correct the envelope, usually to adjust to greater local
curvature.
Singh et al. (2011) basically modified the MohreCoulomb criterion
by absorbing the critical state defined in Barton (1976) and then
quantifying the necessary deviation from the linear form, using a large
body of experimental test data. This modified MohreCoulomb
nonlinear failure criterion may be written in the effective stress form as
follows:
2 sin 4
0 0 0 0 2
s s ¼ UCS þ s As (3.47)
1 3 3 3
1 sin 4
where A is an empirical constant for the rock type under consideration. Eq.
(3.47) is the linear MohreCoulomb failure criterion (Eq. 3.41) except the
0 2
last team As . For 0 s s , Singh et al. (2011) found that param-
0
0
3 3 crti
eter A has the following form:
1 sin 4
A ¼ (3.48)
s 0 crti 1 sin 4
where s crti is the critical effective confining stress and s crti z UCS.
0
0
In the tensile stress area (i.e., s 3 < 0) in Fig. 3.24, the Griffith failure
criterion described by a parabolic Mohr envelope can be used (refer to
Section 3.4.9, Eq. (3.83) and Fig. 3.31 for details).