Geometrical properties of discontinuities 1 27statistical or fuzzy-set methods (Harrison, 1993). In Fig. 7.13, we show an
example of plotted data, the resulting contoured plot and the main set
directions.
It is common to idealize a set of discontinuities as a collection of parallel,
persistent and planar features. It is clear from Fig. 7.13 that in practice not
only might a set consist of sub-parallel discontinuities, but also there might
be difficulty in even distinguishing to which set a particular discontinuity
belongs. Moreover, each discontinuity will have other geotechnical para-
meters of interest apart from its geometry, and it is likely that in the future
a more comprehensive analysis of the clustering will evolve.
One subject where the concept of discontinuity sets is important is in the
formation of rock blocks and the distribution of their sizes. With the
knowledge of the fracture frequency and orientation of the discontinuity
sets in a rock mass, it is possible to determine a three-dimensional block
volume distribution and associated two-dimensional block area distribu-
tions encountered on any plane through the rock mass. An example of the
area size distribution is shown in Fig. 7.14, which has been generated by
assuming that in one case the discontinuities are randomly orientated and
positioned, and in the other case that there are two orthogonal sets, each
with negative exponential spacing distributions.
In both cases, it is possible to calculate the probability density function
for the tessellated area as illustrated. Note that for these two cases, with
the same two-dimensional fracture density, the block area distributions are
very similar, indicating that, for this particular case, the orientation of the
discontinuities does not significantly affect the sizes of the blocks.
This type of analysis is important in rock engineering design, bearing in
mind the earlier discussion on the significance of the scale of the engi-
neering project in relation to the rock mass geometry, whether this be
considered along a line (i.e. a borehole or scanline), on a plane (i.e. one of
the walls of an excavation) or within the rock volume. (Block volume
distributions in the context of excavation are discussed in Chapter 15.)
7.2.5 Persistence, roughness and uperture
To some extent, the parameters of persistence, roughness and aperture
reflect the deviation from the assumption of the idealized discontinuities
discussed in Section 7.2.4. Note that even the plotting of a single great circle(a) Raw data (b) Contoured data (c) Main discontinuity sets
Figure 7.13 Discontinuity orientation data plotted on the lower-hemispherical
projection.