1 34 Discontinuifies
For each discontinuity intersected by a scanline of trendlplunge as/&,
measure dip directionldip angle alp, and then tabulate the calculations:
Total no.of discons. = N Direction cosines of scanline = I,, m,, ns~ ~ ,-. ,E=N w- E-N &=r E=r E=rL
Direction cosines *%le +
of normal between Weighted
each normal direction cosines160' !"q = 0 +
q = 180-lq = 180'"Figure 7.20 Evaluation of the mean orientation of a discontinuity set.
By introducing the direction cosines of the scanline l,, m,, n, we can
calculate the corresponding value cos 0,. The reciprocal of this value is the
weighting factor wi, which is then scaled to w'~ in order that the overall
measured discontinuity frequency is maintained. Via this procedure, we
arrive at the last three columns, the weighted direction cosines. These
values may then be summed, and the mean orientation of the normal
computed. Obviously, if the aim of the analysis is to determine the mean
orientation of a discontinuity set, the procedure should only be attempted
on data likely to belong to a specific set of discontinuities.
These last three topics of the Poisson process, central limit theorem, and
sampling bias and mean orientation have illustrated the power and
necessity of applying basic standard statistical techniques to manipulating
discontinuity geometry and other rock property data. Indeed, it may be fair
to say that no other techniques are available for answering the questions
posed at the beginning of Section 7.2.6 and yet these have been solved
directly and elegantly as illustrated.
The use of statistical methods should always be an essential part of
the rock engineer's analytical capabilities, because we will never have
complete knowledge of the geometrical, mechanical and hydraulic
properties of rock masses. Readers interested in a wider treatment of
discontinuities are referred to Priest (1993).
7.3 Mechanical properties
7.3.7 Stiffness
In Chapter 6, we discussed the stiffness, strength and failure of intact rock
via the complete stress-strain curve. We can consider the equivalent
properties when a discontinuity is loaded in compression, tension or shear.
These are illustrated in Fig. 7.21, with an indication of the type of complete