Engineering Rock Mechanics

1 26 Discontinuities

two-dimensional piece of paper. There are many possible techniques for
this. In fact, the problem of plotting lines on the Earths surface on a sheet
of paper has been a problem since the early days of navigation.
During the development of rock mechanics and rock engineering, there
has been almost total acceptance of equal-angle lower-hemisphere
projection. Here we will give a basic description of the plotting method,
sufficient to allow the reader who is not familiar with the method to
follow the discussion; a monograph on the subject has been produced by
Priest (1985) and more detail is given here in Appendix 8.
In Fig. 7.12, we show the dip direction plotted as the compass bearing
and the dip angle plotted inwards from the perimeter of the projection. This
defines a point on the projection representing the line of maximum dip of
the plane being plotted. As is also shown in Fig. 7.12, another line in the
plane is the strike line, i.e. the line with zero dip: this is plotted as two
diametrically opposed points on the perimeter of the projection. In the
same way, all lines in the plane can be plotted using their particular cu'p
values, resulting in the great circle shown in the figure. Thus, a line in the
plane is plotted as a point, and the plane itself is plotted as a curve (for
equal-angle projection, it is an arc of a circle).
An alternative method of uniquely specifying the plane is to plot the
position of a line which is perpendicular to the plane: this line is known
as the normal and the associated point plotted on the projection is known
as the pole. The pole of the plane is also plotted in Fig. 7.12. Note that the
following two relations exist between the line of maximum dip and the
normal:

Generally, we wish to plot many discontinuity planes, which means that

plotting poles is preferred to plotting great circles. Also, once many poles

have been plotted on the projection, the basic rock structure can be

considered in terms of the clustering of these normals: this is conventionally

studied by contouring the projection to locate the densest regions. More

advanced techniques involve various clustering algorithms, based either on

surface ' k\, \maximum

Figure 7.12 Discontinuity plane and the associated hemispherical projection.