Page 262 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN BLOCKY ROCK

(a)

(b)

Figure 9.3 (a) A finite, non-tapered
block formed by two joints and two
free surfaces; (b) a joint pyramid and
an excavation pyramid for a two-
dimensional removable block (after
Goodman, 1989).

which can be formed around an excavation boundary. They are described as infinite,
finite and tapered, and finite and non-tapered. Of these three block types, inspection
shows that only the finite, non-tapered block is kinematically capable of displacement
into the excavation.
The general determination of movability of a block into an adjacent excavation is
derived from the schematic shown in Figure 9.3(a). In it, a typical block is defined
by four half-spaces, which are the upper surface of joint 1 (denoted U 1 ), the lower
surface of joint 2 (L 2 ) and the upper surfaces U 3 and U 4 of the linear segments 3 and
4 of the excavation surface. To test the movability of the block, suppose the bounding
surfaces 3 and 4 are moved without rotation towards the centre of the block, as shown
in Figure 9.3(b). Under this translation, the block becomes progressively smaller until
it shrinks to a single point. This contraction to a point contact cannot be achieved for
an infinite block or a finite but tapered block. In Figure 9.3(b), all of the faces have
been moved without rotation to pass through a single point O. The intersection U 1 L 2
is called the joint pyramid, JP, a prism with its apex at O. The intersection U 3 U 4 is
called the excavation pyramid, EP, and is also a prism with its apex at O. The prisms
touch at O without intersection. The theory of block topology due to Goodman and
Shi posits that a block is finite and non-tapered if and only if JP and EP have no
intersection.
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