Page 80 - Rock Mechanics For Underground Mining

ROCK MASS STRUCTURE AND CHARACTERISATION

be carried out in two orthogonal directions, usually horizontal and vertical. Ideally,
equal total horizontal and vertical scanline lengths should be used, but this is often
difficult to achieve in practice.
The value x i0 given by equation 3.6 will be the true normal spacing of the discon-
tinuities only when the face is normal to the discontinuities. If the scanline intersects
N sets of discontinuities, the discontinuity frequency measured along the scanline is
given by

N

= i0 cos i (3.7)
i=1
where i0 is the frequency of set i measured along the normal to the discontinuities
and i is the acute angle between the normal and the scanline.
Hudson and Priest (1983) showed that if i , i are the trend (the azimuth of the
vertical plane containing the line) and plunge (the acute angle measured in a vertical
plane between the downward directed end of the line and the horizontal) of the normal
to the ith discontinuity set and s , s are the trend and plunge of the scanline, the
discontinuity frequency measured along the scanline is

(3.8)
= A sin s cos s + B cos s cos s + C sin s
where

N

A = i0 sin i cos i
i=1
N

B = i0 cos i cos i
i=1
N

C = i0 sin i
i=1

Priest and Hudson (1981) have pointed out that there is also a natural variability in
the mean discontinuity spacing ¯ x computed as
n

x i
i=1
¯ x = (3.9)
n
where x i is the ith discontinuity spacing measurement along a scanline of length L
yielding n values. The question arises as to what value n should take in order that
the value of ¯ x can be estimated with acceptable precision. In theory, a plot of the
frequency of occurrence of values of ¯ x determined from several scanline surveys in
the one direction with different values of n, should have a normal distribution (Figure
3.16a). It is known that, in this case, a proportion (z) of the different scanlines
√
will yield a mean value within ± z / n of the population mean (Figure 3.16b)
where z is the standard normal variable associated with a certain confidence level
and is the standard deviation of the population of values. Tabulations of values of
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