Engineering Rock Mechanics

1 08 Fractures and hemisphericul projection

The frequency is then 10.115 m-l, and the reciprocal of this is the mean
length of the recovered pieces (because X = l/A), i.e. 0.10 m.

For a horizontal tunnel heading north

Set A Angle between set normal AI cos 6 I

1 7.72 68 2.892

2 3.07 48 2.054

3 5.34 80 0.927

Sum 5.873

and required direction

The frequency is then 5.873 m-l, and the mean length of the recovered

pieces is 0.17 m.

For a borehole trending 280/35

Set A Angle between set normal AI cos 6 I

and required direction

1 7.72 47 5.265

2 3.07 92 0.107

3 5.34 20 5.01 8

SUm 10.390

The frequency is then 10.390 m-l, and the mean length of the recovered

pieces is 0.10 m (coincidentally similar to the vertical borehole value).

The engineering ramifications of the results are that, firstly, the fracture

frequency in different directions through a rock mass can be sigruficantly

different. Secondly, this variation can be calculated if the set orientations

and frequencies are known. Thirdly, measurements of fracture frequency

in a vertical borehole will probably not correctly predict the fracture

frequency in a horizontal tunnel (although the difference will depend on

the properties of the fracture sets present).

(b) In order to use the equation for the threshold value that maximizes

the RQD range, we need to know the maximum and minimum values

of fracture frequency in the rock mass for the directions considered. On

the basis of the results obtained earlier, we can say A- = 10.39 m-l and

Ami,, = 5.87 m-l, from which we find

2 2 10.39

In (2) = 10.39 - 5.87 In (=) = 0'25

t* =

hmax - Amin

We can now construct a table of frequency values and corresponding

RQD values, using the relation RQD = 100(ht + l)e-". The results are as

follows:

Frequency, rn-l RQD, % (t = 0.1)

5.87 88.2 56.9

10.39 72.1 26.8

Range 16.1 30.1

RQD, o/o (t = 0.25)