Engineering Rock Mechanics

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spaces may be studied concurrently. A 'spherical projection' is shown in
Fig. 20.14, with the extensions of the great and small circles into the upper
half-space being clearly identifiable.
The rock blocks in a rock mass are identified by numerical codes,
according to how they are composed in terms of the upper and lower half-
spaces produced by the various discontinuity planes in the rock mass. For
example, consider the block 010-which is formed by the great circles
associated with planes 1,2 and 3 shown in Fig. 20.15. The first digit of zero
means that the block is formed by the upper half-space defined by plane
1, i.e. is outside great circle 1 in the figure. Similarly, the second digit of 1
indicates that the block is formed by the lower half-space defined by plane
2, and hence is within great circle 2 in the figure. Finally, the third digit of
zero represents the upper half-space defined by plane 3. In Fig. 20.15, all
of the blocks defined by the three planes are shown, and it is clear from
this diagram that block 111 resides within all three great circles, whereas
block 000 resides outside all three great circles.
In the preceding discussion, the specific locations of the discontinuity
planes are not considered, and so it is convenient to consider the geometry
of the block as it would be defined if all of the planes intersected at a point.
Under these conditions, blocks would exist as pyramidal shapes called 'joint

Design and analysis of underground excavations

Figure 20.14 Composite upper- and lower-hemispherical projection, i.e. the

spherical projection.