Engineering Rock Mechanics

Geometrical properties OF discontinuities 1 1 9

Frequency

Of

occurrence

f(X: Discrete

Fc.

Spacing, x

Continuous

I- I

I

, x= I,

Spacing, x

Figure 7.5 The negative exponential distribution of discontinuity spacing values.

is that, although there are more small spacing values than large spacing

values, a single large spacing value can be a greater proportion of the

scanline length than many small spacing values added together. However,

the discontinuity frequency (or mean spacing value) does not give any

indication of this phenomenon. For this reason, Deere (1963) developed,

for borehole core, the concept of the Rock Quality Designation,

universally referred to as RQD. This is defined as the percentage of the

sampling line (or borehole core) consisting of spacing values (or intact

lengths of rock) greater than or equal to 4 inches (or 100 mm). Expressed

mathematically,

RQD = 1002 5%

1=1 L

where x, = spacing values greater than 0.1 m, and n is the number of these
intersected by a borehole core or scanline of length L.
We are now in a position to relate the discontinuity frequency to the
RQD utilizing the negative exponential distribution of spacing values. In
Fig. 7.6 the shaded area shows those spacing values above the RQD
threshold value. We can find the RQD by establishing the percentage of
the sampling line that is represented by the spacing values in the shaded
area. This is not represented just by the shaded area expressed as a percentage of
the total area under the curve, because we must take into account the
different contributions made by the different spacing values, as presented
below.
The probability of the length of a piece of intact core being between x
and x + 6x isf(x)6x. Given that the total number of pieces of core is N, then
the total number of pieces of core in this interval is Nf(x)6x and the length
of all of these pieces is Nxf(x)6x. We can find the total length of all pieces
with all values of x by summing: