Engineering Rock Mechanics

1 20 Discontinuities

A

Probability

Figure 7.6 The contribution to the core length made by intact pieces of rock greater
than 0.1 m in length.

n

total length = ZNx, f (x)6x.

z=1

For RQD, we consider only those pieces of core with a length greater than
0.1 m and so, in the limit for the continuous case, we have
x=-
total length of pieces 2 0.1 m in length = 5 Nxf (x)dx.

Now, substituting this into the previous (discrete) expression for RQD, we

find that

x=O.l

x=oo

RQD* = 100(1/L) JNxf (x)dx

*=O.l

where we have used the notation RQD* to represent the theoretical RQD

calculated from the distribution of spacing values.

However, we know that NIL = A, the discontinuity frequency, so for the

general case with any distribution of spacing values we have

I=-

RQD* = 1OOA 5 xf (x)dx.

x=0.1

We can evaluate this integral explicitly for the negative exponential

distribution. Thus, for a negative exponential distribution of spacing

values,

RQD* = 100A2 I xe-h dx

x=0.1

which gives

RQD* = lOO(0.lA + l)e-'.la.