Engineering Rock Mechanics

Design against structurally-controlled instability 373

Figure 20.15 Illustration of rock blocks formed by the intersection of rock planes,
using block theory notation.

pyramids’, JP. Similarly, the planes that make up the boundary of an
excavation can be considered in the same way, except that these planes
divide space into rock and non-rock half-surfaces. By convention, when
these planes are considered as intersecting at a point, the rock side is
termed the excavation pyramid, EP. It follows that if the joint pyramid and
the excavation pyramid do not intersect, i.e. JP n EP = 0, then the block
is removable. Such a case is illustrated in Fig. 20.16.
At the left of Fig. 20.16, there are two discontinuity planes, 1 and 2, and
two excavation planes, 3 and 4, which together delineate a rock block. From
this diagram, and using the notation regarding upper and lower half-spaces
presented earlier, the block is coded as 0100. If the diagram is transformed
such that all of the planes intersect at a point, the diagram shown at the
right of the figure is obtained. The joint and excavation pyramids are clearly

4

i

TRANSFORMS

Figure 20.16 Example of block removability using the block theory concepts of joint
and excavation pyramids.