Geometrical properties of discontinuities 1 2 1Note that by using the negative exponential distribution in this way, the
RQD* can be expressed solely in terms of the discontinuity frequency. In
Fig. 7.7, we have plotted the RQD* against both the mean spacing, R, and
the frequency, A. From these curves, it can be seen that the RQD" is most
sensitive for spacing values in the range 0-0.3 m: above a mean spacing
value of 0.3 m, the RQD* is always greater than 95%. It can also be seen,
from the plot of RQD* versus A, that the relation is approximately linear
in the range 6 < A < 16. This leads to the simplified approximate formulaRQD* = -3.68a+ 110.4.To overcome the lack of sensitivity of RQD for large spacing values, we
can use any threshold value, t, for calculating RQD, rather than 0.1 m. This
results in the general formula
RQD* = ioo(~t + 1)e-%.
We have plotted this relation for t=0.1 m (the conventional threshold
value), t = 0.3 m and t = 1.0 m in Fig. 7.7. For rock masses with large mean
discontinuity spacing values, it can be helpful to adopt a two-tier
approach to the RQD calculation, utilizing the conventional threshold of
0.1 m and a higher threshold of, say, 1.0 m.
7.2.3 Vuriution of discontinuity frequency with
sumpling line direction
From the definition of discontinuity frequency, as illustrated in Fig. 7.4, the
measured discontinuity frequency is expected to vary with the direction
of the sampling line relative to the orientation of the discontinuities.
Because of the complexity of all potential three-dimensional discontinuity
patterns, we introduce the method of calculating this variation, firstly with
reference to a single set of planar, parallel and persistent discontinuities,
and subsequently for any number of discontinuity sets.
t = 0.1lic = 0.30.1 0.2 0.3 - 0.4 0.5
Mean spacing, x m1 1 I I
IO 20 30 40
Frequency, A rn-'
Figure 7.7 The relation between RQD* and both mean spacing and frequency for
a negative exponential distribution of spacing values, with different RQD"
threshold values.