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THE HEMISPHERICAL PROJECTION
of observations made for each orientation interval are plotted as radii. Dips and dip
directions may be added at the periphery of the circular diagram. This method of
presenting discontinuity orientation data is much less useful and versatile than the
hemispherical or stereographic projection which will be discussed in the following
section.
3.6 The hemispherical projection
3.6.1 Hemispherical projection of a plane
The hemispherical projection is a method of representing and analysing the three-
dimensional relations between planes and lines on a two-dimensional diagram. The
method was first developed as a tool for use in structural geology but has been ex-
tended and used to solve engineering problems. The basis of the method and its classic
geological applications are described by Phillips (1971). Rock engineering applica-
tions are described in detail by Goodman (1976, 1989), Hoek and Brown (1980),
Hoek and Bray (1981) and Priest (1985, 1993). Application of the technique to the
problem of structurally controlled failures around underground mining excavations
will be discussed in Chapter 9.
Imagine a sphere which is free to move in space so that it can be centred on an
inclined plane as illustrated in Figure 3.22. The intersection of the plane and the
surface of the sphere is a great circle, shown at the perimeter of the shaded area in
Figure 3.22 The great circle and its
poles which define the orientation of
a plane.
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