Page 128 - Applied Petroleum Geomechanics
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120 Applied Petroleum Geomechanics
Figure 3.29 The MohreCoulomb failure surface and different possibilities to corre-
spond to the DruckerePrager failure conditions.
The DruckerePrager failure criterion is an extended form of the
MohreCoulomb failure criterion. In the principal stress space, a section in
the deviatoric plane shows that it is possible in various ways to relate the
two failure criteria (Fig. 3.29). For the plane-strain condition it is recom-
mended that the inside cone tangent to the pyramid is used (Kovari, 1977).
In this case, the conversions of the material parameters from the Mohre
Coulomb criterion to the DruckerePrager criterion are:
tan 4
a 0 ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3.55)
2
9 þ 12 tan 4
3c
k ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3.56)
2
9 þ 12 tan f
When the external envelope is used, the conversion equations in the
material parameters from the MohreCoulomb criterion to the Druckere
Prager criterion are as follows:
2 sin 4
a 0 ¼ p ffiffiffi (3.57)
3ð3 sin 4Þ
6c cos f
k ¼ p ffiffiffi (3.58)
3ð3 sin fÞ
