Engineering Rock Mechanics

S/ope instobilify 297

5

4

a

Stable block

$<+

b/h >tan $

Sliding & toppling

b/h < tan 6

Toppling only

IIIIII

Base plane angle +-degrees

10 20 30 40 50 60 70 80 '

Figure 17.10 Sliding and toppling instability of a block on an inclined plane (from
Hoek and Bray, 1977).

Flexural toppling instability. In Chapter 16, the stability of underground
excavations was discussed in relation to the potential for inter-layer slip,
the @j theory (see Figs 16.11 and 16.12). Here we adopt an analogous
approach to the potential for slope instablity.
Remembering that the creation of a new excavation surface results in the
principal stresses being parallel and perpendicular to the excavated face,
we consider the potential for inter-layer slip given the geometry
illustrated in Fig. 17.11(a). An analysis of instability will include these
geometrical parameters as well as the angle of friction. In Fig. 17.11(b), the
@j theory is applied directly to inter-layer slip along the slope surface. The
geometrical construction, which includes the normal to the discontinuities

(4 (b)

Figure 17.11 Flexural toppling: (a) geometry and (b) Qj analysis.