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94 Reservoir geomechanics

s
150 3

INSCRIBED MOHR–COULOMB
100 DRUCKER–PRAGER

CIRCUMSCRIBED
50 DRUCKER–PRAGER

(MPa) 0

s y HYDROSTATIC
AXIS

−50
s
2 s
1
−100 MODIFIED HOEK–BROWN
WIEBOLS–COOK

−150 −100 −50 0 50 100 150
s (MPa)
x
Figure 4.6. Yield envelopes projected in the π-plane for the Mohr–Coulomb criterion, the
Hoek–Brown criterion, the modified Wiebols–Cook criterion and the circumscribed and inscribed
Drucker–Prager criteria. After Colmenares and Zoback (2002). Reprinted with permission of
Elsevier.

perpendicular to the straight line σ 1 = σ 2 = σ 3 . Figure 4.6 shows the yield surface
of the linearized Mohr–Coulomb criterion is hexagonal in the π-plane. Figure 4.7a
shows the representation of the linearized Mohr–Coulomb criterion in σ 1 −σ 2 space for
C 0 = 60 MPa and µ i = 0.6. In this figure (and Figures 4.8, 4.9 and 4.10b below),
σ 1 at failure is shown as a function of σ 2 for experiments done at different values
of σ 3 .

Hoek– Brown criterion
This empirical criterion uses the uniaxial compressive strength of the intact rock mat-
erial as a scaling parameter, and introduces two dimensionless strength parameters,