Page 125 - Rock Mechanics For Underground Mining

STRENGTH CRITERIA FOR ISOTROPIC ROCK MATERIAL

Figure 4.24 Coulomb strength en-
velopes with a tensile cut-off.

If the Coulomb envelope shown in Figure 4.23b is extrapolated to 1 = 0, it will
intersect the 3 axis at an apparent value of uniaxial tensile strength of the material
given by

2c cos
T = (4.17)
1 + sin
The measurement of the uniaxial tensile strength of rock is fraught with difficulty.
However, when it is satisfactorily measured, it takes values that are generally lower
than those predicted by equation 4.17. For this reason, a tensile cutoff is usually
applied at a selected value of uniaxial tensile stress, T 0 , as shown in Figure 4.24. For
practical purposes, it is prudent to put T 0 = 0.
Although it is widely used, Coulomb’s criterion is not a particularly satisfactory
peak strength criterion for rock material. The reasons for this are:

(a) It implies that a major shear fracture exists at peak strength. Observations such
as those made by Wawersik and Fairhurst (1970) show that this is not always
the case.
(b) It implies a direction of shear failure which does not always agree with experi-
mental observations.
(c) Experimental peak strength envelopes are generally non-linear. They can be
considered linear only over limited ranges of n or 3 .
For these reasons, other peak strength criteria are preferred for intact rock. How-
ever, the Coulomb criterion can provide a good representation of residual strength
conditions, and more particularly, of the shear strengths of discontinuities in rock
(section 4.7).

4.5.3 Griffith crack theory
In another of the classic papers of engineering science, Griffith (1921) postulated
that fracture of brittle materials, such as steel and glass, is initiated at tensile stress
concentrations at the tips of minute, thin cracks (now referred to as Griffith cracks)
distributed throughout an otherwise isotropic, elastic material. Griffith based his deter-
mination of the conditions under which a crack would extend on his energy instability
concept:

A crack will extend only when the total potential energy of the system of ap-
plied forces and material decreases or remains constant with an increase in crack
length.
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