Page 115 - Applied Petroleum Geomechanics

Rock strengths and rock failure criteria 107

Figure 3.16 Triaxial compressive test results for Tournemire shale showing the vari-
ation of peak principal stress difference (s 1 s 3 ) with the angle of inclination of the
major principal stress to the plane of weakness (a), for the confining pressures (s 3 )
indicated (Niandou et al., 1997).

rocks with roughly similar solidity, because the failure angles of isotropic

rocks are nearly a ¼ 30 in many cases.
The bedding planes in rock formations cause rock strength anisotropy.
Willson et al. (2007) presented the following equation to calculate rock
UCS variation relative to the bedding planes:
UCS w ¼ UCS max ðcos w þ k 1 sin wÞð1 sin w cos wÞ
(3.35)

4k 2
1 2 sin w cos w 1 p ffiffiffi
2ð1 þ k 1 Þ
where UCS w is the uniaxial compressive strength at w with consideration of
bedding effects; w is the angle between the stress concentration orientation
and the bedding plane, w ¼ 0 represents loading perpendicular to bedding;
and w ¼ 90 represents loading parallel to bedding; UCS max is the
maximum strength at any orientation; k 1 and k 2 are defined in the
following:

k 1 ¼ q == q t