Page 135 - Applied Petroleum Geomechanics

Rock strengths and rock failure criteria 127

essentially equivalent to loading a penny-shaped crack in a biaxial stress field
(Hoek and Martin, 2014; Murrell, 1963). The equation governing tensile
failure initiation is:
12T 0 ð1 þ 2s 3 =s 1 Þ
s 1 ¼ (3.81)
2
ð1 s 3 =s 1 Þ
This penny-shaped crack version of the Griffith criterion predicts that
the UCS is 12 times of the tensile strength:

(3.82)
UCS ¼ 12T 0
The Griffith criterion can be presented by a parabolic Mohr envelope
(Whittaker et al., 1992) as given by the following equation:

2
s ¼ 4T 0 ðT 0 þ sÞ (3.83)
where s is the shear stress acting along the crack plane surface; s is the
normal stress acting perpendicular to the crack surface.
The Griffith criterion in Eq. (3.83) can be plotted in s s space, similar
to the nonlinear MohreCoulomb envelope, as shown in Fig. 3.31. This
figure shows that the Griffith envelope intersects the s axis at 2T 0 ; however,
the intercept in the MohreCoulomb envelope (Fig. 3.21) is the cohesion c.
If the Griffith and MohreCoulomb envelopes have the same intercept,
then the cohesion and tensile strength have the following relation:
(3.84)
c ¼ 2T 0

Figure 3.31 Griffith failure criterion Eq. (3.84) plotted in terms of the MohreCoulomb
envelope with tensile strength T 0 ¼ 10 MPa.