Engineering Rock Mechanics

Natural, pre-existing fractures 97

Figure 7.8 Longer fractures are more likely to be intersected by a scanline, borehole or

underground excavation than shorter fractures.

A Negative exponential

distribution of actual

Distribution of sampled

Probabiii ty

density,

f( 0

t Tracelength, 1

Figure 7.9 Actual and sampled distributions of fracture persistence.

The hemispherical projection technique, used for the presentation

and manipulation of fracture data, is explained in Appendix B of ERM 1.

However, we have included the following example question and an-

swer as an aide-memoire to the technique. Note that a hemispherical

projection sheet is included at the back of this book in Appendix B.

Example question and answer

Question Two boreholes are drilled from the face of a quarry, one at

an orientation7 of 298/38, and the other at an orientation of 055/72.

On a sheet of tracing paper over a hemispherical projection, plot

the points corresponding to these boreholes, and then determine:

(a) the orientation of the plane containing the two boreholes;

(b) the acute and obtuse angles between the two boreholes;

(c) the orientation of a borehole which bisects the acute angle; and

(d) the orientation of a borehole which is perpendicular to the two

holes already drilled.

Answer In order to show the steps involved in solving typical hemi-
spherical projection problems, we present diagrams here showing each

The orientation is given as trend/plunge.