Page 129 - Applied Petroleum Geomechanics

Rock strengths and rock failure criteria 121

If the internal cone envelope coincident at q ¼ p/6 is used, the con-
version equations of the material parameters from the MohreCoulomb
criterion to the DruckerePrager criterion become:
2 sin 4
a 0 ¼ p ffiffiffi (3.59)
3ð3 þ sin 4Þ
6c cos f
k ¼ p ffiffiffi (3.60)
3ð3 þ sin fÞ

3.4.5 Modified Lade failure criterion
The modified Lade criterion was presented by Ewy (1998) based on the
Lade strength criterion (Lade, 1984) for studying wellbore stability. In this
0
criterion, all three effective principal stresses (s 1 , s 2 , s 3 ) were considered.
0
0
The modified Lade can be expressed as the following form:
I 00

3
1 ¼ 27 þ h (3.61)
I 00
3
where
I ¼ s þ S þ s þ S þ s þ S

0
00
0
0
1 1 2 3
I ¼ s þ S þ s þ S þ s þ S

0
00
0
0
3 1 2 3
c
S ¼
tan 4
2
4 tan 4ð9 7 sin 4Þ
h ¼
1 sin 4
Compared to the MohreCoulomb criterion, the modified Lade crite-
rion considers the effect of intermediate principal stress (s 2 ) on rock failures.
The wellbore stability predicted by the modified Lade criterion has less
failure (therefore, needs to design a smaller mud weight) than that by the
MohreCoulomb criterion because the latter ignores the effect of inter-
mediate principal stress. Therefore, critical mud weight values predicted by
the modified Lade criterion are less conservative than those predicted by the
MohreCoulomb criterion. However, the modified Lade predicts a larger
wellbore failure than that predicted by the DruckerePrager criterion
because the DruckerePrager criterion predicts a greater strengthening ef-
fect from intermediate principal stress.