Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 47

(3.19)

σ is the absolute value of the corres-

ponding shear stress in the failure state. The shear parameters c IR and

is the normal stress acting on the shear plane and τ

φ IR are referred
to as “cohesion” and “angle of internal friction” or simply “friction angle”, respectively.
This failure criterion is based on the hypothesis that shear failure occurs on a plane
inclined at an angle of φ IR /2 to the horizontal. Furthermore, it is assumed

that the shear strength is independent of the intermediate principal normal stress

α = 45° +

σ 2 .

Consequently, the failure stress state can be represented in a diagram in the form of

a Mohr's circle defi ned by the maximum and minimum principal normal stresses

τ - σ

σ 1 and

σ 3 . The failure criterion (3.19) represents a straight line in the τ - σ diagram (Fig. 3.5).

Figure 3.5 Mohr-Coulomb failure
criterion with tension cut-off
(Wittke et al. 2006)