Engineering Rock Mechanics

1 10 lntoct rock

a direct mechanical explanation of the size effect discussed earlier: the
tensile strength decreases with increasing crack length, and larger
specimens will tend to contain larger flaws (i.e. larger initial crack lengths).
The Griffith criterion enables a relation to be derived between the
uniaxial tensile strength and the triaxial compressive strength as

(0* - 03)2 = STO(0, + 03)

which for uniaxial compression with o3 = 0 gives 0, = 8To where To = -o~

This relation has been modified by various researchers for a variety of

factors, particularly friction across the crack surfaces.

6.5.3 The Hoek-Brown empirical failure criterion

This empirical criterion is derived from a best-fit curve to experimental

failure data plotted in 01-03 space as shown in Fig. 6.20. Hoek (1990) has

noted that "since this is one of the few techniques available for estimating

the rock mass strength from geological data, the criterion has been widely

used in rock mechanics analysis".

The criterion is expressed as

01 = 03 + (m0,g +

where q = the major principal stress, o3 = the minor principal stress, O,

= the uniaxial compressive strength of the intact rock, and rn and s are

constants for a specific rock type.

Although the constants m and s arise from the curve-fitting procedure,

there is an element of physical interpretation associated with them which

is helpful for the engineer to consider.

The parameter s relates to the degree of fracturing present in the rock

sample: it is a representation of the cohesion of the rock. For completely

intact rock, it takes the value 1 (which can be demonstrated by

substituting o3 = 0 into the criterion: crl = 0,O.' and hence s = 1, noting

that 0, is the intercept on the ol axis in Fig. 6.20) and, for rock which is

highly fractured, it reduces in value and tends towards zero as the strength

is reduced from peak to residual.

The parameter llz is related to the degree of 'particle interlocking' present:

for intact rock this is high, and reduces as the degree of brokenness

increases. There are no clear limits to this parameter; it depends on the rock

type and its mechanical quality.

This criterion also provides a relation between the tensile and

compressive strengths which can be found by substituting o1 =^0 and

0, = -03 in the criterion to give

0, = -oc(m - (m2 + 4~)'.~)/2.

Thus, the relation between the two strengths is a function of the rock's

mechanical properties: for example, if s = 1 and m = 20 (a good-quality