Page 82 - Rock Mechanics For Underground Mining

ROCK MASS STRUCTURE AND CHARACTERISATION

Figure 3.17 Sample number vs. pre-
cision of the mean discontinuity spac-
ing estimate for a negative exponen-
tial distribution of spacing (after Priest
and Hudson, 1981).

allowable proportionate error. Hence
z 2
z
ε = √ or n = (3.10)
n ε
Equation 3.10 can be used to estimate the sample size required to achieve a given
error bandwidth to a required confidence level in the estimate of the mean. For exam-
ple, if the mean spacing is required within an error bandwidth of ±20% at the 80%
confidence level, ε = 0.2, z = 1.282 and n = 41. If, on the other hand, the mean
spacing is required to within 10% at the 90% confidence level, n = 271.
Figure 3.17 shows the required number of spacing values versus the error band for
various confidence levels. It will be seen that the required sample size increases very
rapidly as the allowable error is reduced.
Priest and Hudson (1981), Villaescusa and Brown (1992) and others, have discussed
the bias in trace lengths measured in scanline surveys and developed methods for
estimating mean trace lengths from censored measurements made at exposures of
limited extent. These estimated trace lengths can serve as measures of persistence
(Table 3.2) which is an important engineering property of discontinuities. A detailed
consideration of these analyses is beyond the scope of this text. However, the reader
should be aware of the uncertainties involved in estimating mean rock mass properties
from scanline and other types of discontinuity survey.

3.4.2 Geotechnical drilling and core logging
Core drilling is the most reliable way of exploring the interior of a rock mass prior to
mining. As will be discussed later in this section, downhole geophysical and other in-
struments may be used in drill holes to investigate the structure and physical properties
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