Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 51

It should be noted that the shear strength of intact rocks with planar grain structure is
no longer independent of the intermediate principal normal stress σ 2 . If, for example,

the principal normal stresses σ 2 lie within the plane perpendicular to the isotro-

pic plane failure may also take place in the isotropic plane. In such cases, in (3.26) and
(3.27)

σ 1 and

σ 2 .
For a tensile failure normal to the isotropic plane the following failure criterion, as in
(3.23), is used:

σ 3 must be replaced by

(3.28)

The combination of failure criteria for shear and tension is illustrated in Fig. 3.7.

Figure 3.7 Criteria for shear and tensile failure in the isotropic plane S of an intact rock with
planar grain structure (Wittke et al. 2006)

The anisotropic shear strength of intact rock with planar grain structure can be de-
scribed by means of Equation (3.20) valid for the intact rock matrix and by transform-
ing

τ res and σ n in (3.25) into σ 1 and σ 3 using (3.26) and (3.27) and solving for σ 1 . Thus,

the maximum principal normal stress at failure is given by:

(3.29)

This model was fi rst proposed by Jaeger (1960) and referred to as “single plane of weak-
ness theory”. This model leads to a marked anisotropy of the unconfi ned compressive
strength of an intact rock with planar grain structure as shown in Fig. 3.8, where a
schistose rock is uniaxially loaded by a stress σ z with different orientations with respect

to the schistosity. The angle of inclination of the schistosity to the horizontal is denoted
by

β . Setting σ 1 = σ z and σ 3 = 0 in (3.29) yields the following expression for shear failure

on the schistosity:

(3.30)