Page 101 - Rock Mechanics For Underground Mining

PROBLEMS

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angle of 55 with a horizontal scanline. Large numbers of measurements give the
apparent mean spacings of sets A and B along the scanline as 0.450 m and 0.800 m,
respectively.

(a) Calculate the mean normal spacing of each set.
(b) What is the mean spacing of all discontinuities in the direction of the scanline?
(c) Assuming that the combined discontinuity spacings follow a negative expo-
nential distribution, estimate the RQD of the rock mass in the direction of the
scanline.

2 A preliminary borehole investigation of a sandstone produced 30 m of core that
contained 33 drilling breaks, 283 iron-stained joints and 38 other discontinuities of
uncertain origin.
(a) Calculate the bandwidths within which the overall mean discontinuity spacing
in the direction of the borehole axis lies at the 80% and 95% confidence levels.
(b) What approximate additional length of borehole is required to provide a value
in a bandwidth of ± 8% of the true spacing value at the 95% confidence
level?

3 Plot on the stereographic projection the great circle of the plane with the orientation
(dip direction/dip) 110/50. What is the apparent dip of this plane in the direction 090 ?
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4 What are the trend and plunge of the line of intersection of the planes 110/50 and
320/60?
5 Plot the great circles and poles to the planes 156/32 and 304/82. What is the acute
angle between these planes? In what plane is it measured?
6 A tunnel of square cross section has planar vertical sidewalls of orientation 230/90.
The lineation produced by the intersection of a planar joint with one sidewall plunges
at 40 to the north-west. The same joint strikes across the horizontal roof in the
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direction 005 − 185 . What is the orientation of the joint plane?
7 A reference line is scribed on drill core for use in correctly orienting discontinuities
intersected by the core. A certain planar discontinuity has the apparent orientation
120/35 measured with the reference line vertical. If the actual trend and plunge of the
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