Structurally-controlled instability mechanisms 34 1(a) (b)Figure 19.2 Kinematic identification of sliding blocks.
Fig. 19.2(a) and the lines of maximum dip, p1 and A, of planes 1 and 3 in
Fig. 19.2(b). In each of these cases, the planes, although dipping at angles
greater than the friction angle, are not candidates for the sliding direction
because the line of maximum dip is not included within the block. The spherical
triangle represents the region of kinematically admissible directions of
movement and any other direction represents directions directed into the
rock surrounding the block. There are no restraints on the azimuth of slid-
ing direction from the horizontal roof: there will naturally be constraints
on the azimuth when sliding is considered from the side walls.
Hence, the shaded blocks in Figs 19.2(a) and 19.2(b) represent plane
sliding along p2 and wedge sliding along AI, respectively. Only one friction
circle has been used because all discontinuities are assumed to have the
same friction angle, but in the plane sliding case the analysis could easily
be extended to cater for different friction angles with associated friction
circles on the projection. In the case of wedge sliding, which may be
regarded as plane sliding on two planes simultaneously, the direction of
movement is parallel to the direction of the line of intersection of the planes
themselves. If the two planes have different angles of friction, the line
of intersection must lie within both friction circles for wedge sliding to
occur.
Stable. The final possibility, that the block is stable, is shown in Fig. 19.3.
This occurs when a spherical triangle lies completely outside the friction
circle. Again, a line of maximum dip which exceeds the angle of friction is
not in itself sufficient to cause instability: it must lie on the perimeter of the
spherical triangle under consideration to be part of a kinematically feasible
block.
7 9. I .2 Use of inclined hemispherical projection
methodsIn Section 19.1.1, it was assumed that the blocks would move from the
horizontal roof of an excavation. In order to use the simplicity and clarity
of these graphical methods for any blocks-which may be moving from