Engineering Rock Mechanics

Slope instability 295

The various forces and angles used in these formulae are shown in the
individual parts of Fig. 17.7. Consolidating these formulae results in

F=- sin p X- tan @

sin 1 6 tan w,

which provides a simple method of evaluating the effect of the main
parameters on the factor of safety for wedge sliding.
A direct insight into the fundamental mechanism of wedge instability is
achieved by abbreviating the equation to

i.e.

wedge factor of safety = wedge factor x plane factor of safety.

In Fig. 17.6, the factor of safety varied with two of the main parameters.

For wedge sliding, we can study the effect of k,, the wedge factor. This is

a purely geometrical parameter, concerning how upright and how sharp

the wedge is.

In Fig. 17.8, we show how the factor of safety varies with the parameter

6, the sharpness of the wedge, and p, the verticality of the wedge. Again,

the utility of the application of a simple model to a complex problem is

clearly demonstrated. Considering the suite of curves in Fig. 17.8, it is not

obvious that thin, upright wedges would have a higher factor of safety than

thin, inclined wedges; nor, indeed, that the verticality of the wedge will be

more critical for thin wedges than for thick wedges (remembering that in

the diagram constant angles of friction and intersection line plunge have

been used).

Wedge verticality

(measured from

the horizontal)

P

90"

Note: drawn for angle of friction 0 800

intersection of 45" throughout 600

o 40"

+ 30"

of 30" and plunge of line of A 70"

A 50"

_- FoS = I

0 10 20 30 40 50 60 70 80 90

Included wedge angle (8)

Figure 17.8 Simplified analysis of wedge failure demonstrating variation in factor

of safety with included wedge angle and wedge verticality.