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Rock strengths and rock failure criteria 117

3.4.3 Weak plane sliding failure criterion
Because most sedimentary and metamorphic rocks are anisotropic, the
effect of anisotropy on strength is of great importance. The simplest
situation is the planar anisotropy in which a rock mass has a set of parallel
planes of weakness, as shown in the experimental results (Fig. 3.15).
Using the MohreCoulomb failure criterion, Jaeger and Cook (1979)
gave the following equation to calculate the maximum and minimum
principal stresses associated with the weak plane sliding along preexisting
planes of weakness for a rock mass having a set of parallel planes of
weakness:
2ðc w þ m s 3 Þ
w
s 1 s 3 ¼ (3.49)
ð1 m cot bÞsin 2 b
w
where, b is the angle between s 1 and the normal to the planes of weakness,

and 4 w < b < 90 (refer to Fig. 3.26); it should be noted that the angle of b
is different from a in Fig. 3.15, and a ¼ 90 b; s 1 and s 3 are the

maximum and minimum principal stresses, respectively; c w is the cohesion
of the plane of weakness; 4 w , m w are the angle and coefficient of internal

(A) (B)

Figure 3.26 (A). Transversely isotropic specimen with a set of parallel weak planes in a
triaxial compression test; (B). Schematic rock peak strength variation with the angle, b,
in the triaxial test at a constant confining stress (s 3 ) inspired by experimental tests and
Eq. (3.49).