Page 131 - Rock Mechanics For Underground Mining

STRENGTH CRITERIA FOR ISOTROPIC ROCK MATERIAL

Table 4.1 Constants in Bieniawski’s empirical strength criterion
(after Bieniawski, 1974).
Rock type A B
norite 5.0 0.8
quartzite 4.5 0.78
sandstone 4.0 0.75
siltstone 3.0 0.70
mudstone 3.0 0.70

Using a boundary element analysis to calculate the elastic stresses induced around the
raise as the pillar was progressively mined, he found that fracture of the rock could be
accurately modelled using equation 4.23 with A = 3.0, k = 0.75 and c = 90 MPa
which is approximately half the mean value of 170 MPa measured in laboratory
tests.
Hoek and Brown (1980) found that the peak triaxial compressive strengths of a
wide range of isotropic rock materials could be described by the equation

2 0.5

1 = 3 + m c 3 + s (4.25)
c
where m varies with rock type and s = 1.0 for intact rock material. On the basis of
analyses of published strength data and some interpolation and extrapolation based
on practical experience, Marinos and Hoek (2000) have suggested that the constant
m for intact rock, m i , varies with rock type in the manner shown in Table 4.2.
A normalised peak strength envelope for sandstones is shown in Figure 4.30. The
grouping and analysis of data according to rock type has obvious disadvantages.
Detailed studies of rock strength and fracture indicate that factors such as mineral
composition, grain size and angularity, grain packing patterns and the nature of ce-
menting materials between grains, all influence the manner in which fracture initiates
and propagates. If these factors are relatively uniform within a given rock type, then it
might be expected that a single curve would give a good fit to the normalised strength
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data with a correspondingly high value of the coefficient of determination, r . If, on
the other hand, these factors are quite variable from one occurrence of a given rock
type to another, then a wider scatter of data points and a poorer fit by a single curve
might be anticipated. For sandstones (Figure 4.30) where grain size, porosity and
the nature of the cementing material can vary widely, and for limestone which is a
2
name given to a wide variety of carbonate rocks, the values of r are, indeed, quite
low.
Despite these difficulties and the sometimes arbitrary allocation of a particular
name to a given rock, the results obtained initially by Hoek and Brown (1980) and
updated by Marinos and Hoek (2000), do serve an important practical purpose. By
using the approximate value of m i found to apply for a particular rock type, it may be
possible to carry out preliminary design calculations on the basis of no testing other
than a determination of a suitable value of c made using a simple test such as the
point load test. A value of c is required as a scaling factor to determine the strength
of a particular sample of rock. Thus although the same value of m i may apply to
granites from different localities, their strengths at different confining pressures may
differ by a factor of two or three.
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