Structurally-controlled instability mechanisms 345Figure 19.6 Identification of kinematically admissible falling blocks at an inclined
surface.slide-either from an overhanging or a non-overhanging surface. Figures
19.7 and 19.8 illustrate the identification of blocks sliding from inclined
overhanging and non-overhanging surfaces, respectively. For the case of
a falling block, note the great circle, H, representing the horizontal plane
and the associated pole, Nhl, representing the vertical. The blocks
themselves and the vertical lines are also shown in the accompanying
sketches of the geometry. For overhanging surfaces, NhI is directed
downwards and for non-overhanging surfaces, NhI is directed upwards.
In order to use the method illustrated in Fig. 19.2, the friction circle has
to be included on the inclined projections. This circle is easily drawn, as it
represents a cone of semi-angle (90 - @)O around NhI for overhanging
surfaces and (90 + @)O for non-overhanging surfaces-as implied in Figs
19.7 and 19.8 by the arrowed lines.
Thus, for an overhanging surface, as shown in Fig. 19.7, if any point on
the perimeter of the spherical triangle lies between NHI (the downward
directed vertical) and the friction circle, sliding is kinematically feasible.
Similarly, for a non-overhanging surface, as shown in Fig. 19.8, if any point
Figure 19.7 Identification of kinematically admissible sliding blocks at an over-
hanging inclined surface.