Page 134 - Applied Petroleum Geomechanics

126 Applied Petroleum Geomechanics

0
In p eq plane the CSL, similar to the shear failure envelope in the
MohreCoulomb failure criterion, is a straight line passing through
the origin with the slope equal to M, one of the characteristic of the ma-
0
terial (see Fig. 3.30). The size of the yield surface is determined by p 0 and
M. The Cam-Clay model has been widely used to simulate pore-collapse
related reservoir compaction and surface subsidence analysis.

3.4.9 Tensile and Griffith failure criteria

It is commonly assumed that the tensile failure in rock will occur when
the effective stress becomes tensile and equals or exceeds rock tensile
strength, i.e.,

0 (3.77)
s ¼ T 0
3
0
where T 0 is the uniaxial tensile strength; s 3 is the minimum effective prin-
0
cipal tensile stresses (s 3 is negative when it is tensile).
Griffith (1921) proposed that fractures are caused by stress concentration
at the tips of minute Griffith elliptical cracks supposed to pervade the
material. A fracture is initiated when the maximum stress near the tip of
most favorably oriented crack reaches a critical value of the material. The
Griffith failure takes place if the following equations are satisfied for a dry
material:
If s 1 þ 3s 3 0,
2
ðs 1 s 3 Þ ¼ 8T 0 ðs 1 þ s 3 Þ (3.78)
If s 1 þ 3s 3 < 0,
(3.79)
s 3 ¼ T 0
When s 3 ¼ 0, it is uniaxial compression, so that the UCS predicted by
Eq. (3.78) (s 1 ¼ UCS) is:
(3.80)
UCS ¼ 8T 0
From Eq. (3.80), the Griffith theory predicts that a ratio of uniaxial
compressive to tensile strengths is 8. It should be noted that for some rocks,
Eq. (3.80) underestimates the UCS. An extension of the Griffith criterion
examines the stresses induced around open penny-shaped cracks in a semi-
infinite body subjected to triaxial compressive stresses s 1 , s 2 , and s 3 .Itis
shown that the intermediate principal stress s 2 has no significant influence
on the tensile failure initiation. Hence, this extended Griffith criterion is