Failure criteria 107traditionally regarded as the ‘cause’ and strain as the ’effect’ in materials
testing: as a consequence, early testing and standards utilized a constant
stress rate application. It was then natural to express the strength of a
material in terms of the stress present in the test specimen at failure. Since
uniaxial and triaxial testing of rock are by far the most common laboratory
procedures in rock mechanics and rock enpeering, the most obvious
means of expressing a failure criterion is
strength = f(q, 02, q).
With the advent of stiff and servo-controlled testing machines and the
associated preference for strain rate control, perhaps the strength could be
expressed in the form
strength = f(q, E~, E~).
We also discussed the possibility of more eclectic forms of control such
as constant rate of energy input, leading to more sophisticated possibilities
for strength criteria expressed in the form
Despite this possibility, the number and variation of the failure criteria
which have been developed, and which are in some degree of everyday
use, are rather limited. The Mohr-Coulomb criterion expresses the relation
between the shear stress and the normal stress at failure. The plane Griffith
criterion expresses the uniaxial tensile strength in terms of the strain energy
required to propagate microcracks, and expresses the uniaxial compressive
strength in terms of the tensile strength. The Hoek-Brown criterion is
an empirical criterion derived from a ’best-fit’ to strength data plotted in
01-03 space.
We will be presenting outlines of these criteria below; for a full derivation
and more complete explanation and discussion, the reader is referred to
the text by Jaeger and Cook (1979) for the Mohr-Coulomb and the Griffith
criteria, and to Hoek and Brown (1980), Hoek (1990) and Hoek et al. (1992)
for the Hoek-Brown criterion.
6.5.7 The Mohr-Coulomb Criterion
The plane along which failure occurs and the Mohr envelope are shown
in Fig. 6.18 for the two-dimensional case, together with some of the key
expressions associated with the criterion. From the initial principal
stresses, the normal stress and shear stress on a plane at any angle can be
found using the transformation equations, as represented by Mohr’s circle.
Utilizing the concept of cohesion (i.e. the shear strength of the rock when
no normal stress is applied) and the angle of internal friction (equivalent
to the angle of inclination of a surface sufficient to cause sliding of a
superincumbent block of similar material down the surface), we generate