Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 49

brought about the formulation of polyaxial failure criteria that consider the infl uence
of σ 2 on intact rock failure (Drucker & Prager 1952, Murrell 1963, Mogi 1967, Mogi

1971, Ewy 1999, Haimson & Chang 2000, Kulatilake et al. 2006, You 2009). However,
the evaluation of test data with different failure criteria led to the result that polyaxial
failure criteria do not, in every case, give a better fi t of test data than the Mohr-Cou-
lomb criterion or the Hoek-Brown criterion (Colmenaries & Zoback 2002). Thus, in
most cases, the shear strength of isotropic intact rocks at least at low to moderate σ 2

levels, which are relevant for rock engineering structures, can reasonably be described
by failure criteria that are independent of

σ 2 .

Figure 3.6 Results
of triaxial compression
tests on granite
(Franklin & Hoek 1970)

For tensile failure it is assumed that cracking of isotropic intact rock occurs perpendicu-
larly to the direction of the minimum principal normal stress σ 3 if the latter exceeds

the tensile strength σ tIR . Thus, the criterion for tensile failure can be represented in the

τ - σ diagram as well as in the σ 1 - σ 3 diagram by a vertical line (Fig. 3.5)

(3.23)