Engineering Rock Mechanics

Slope instability 293

Variation with

FoS = 1

0.8

0.6

0.4

0.2

• 
  


• 
  


• 
  

  ~
  I I I I 1 I I 1
  0 24 6 8 10 12 14 16
  Depth of water in 15m deep tension crack

  
  

0 00 I 1 1 I I I I I I I

5 IO 15 20 25 30 35 40 45 50

Angle of friction

Figure 17.6 Simplified analysis of plane failure demonstrating variation in factor
of safety with (a) depth of water in tension crack varying and (b) angle of friction
of sliding plane varying.

edge of the history of the site, the nature of any infilling and the hydraulic
conditions are required in order to determine whether total stress or
effective stress parameters are to be used.
To illustrate the utility of the equation presented above, Fig. 17.6(a)
shows how the factor of safety may vary for different depths of water in
the tension crack, indicating a possible significant effect of heavy and
prolonged rainfall. It can be seen from this graph that, as the depth of water
in the tension crack varies from 0 to 15 m (the overall depth of the tension
crack itself) and the angle of friction of the sliding plane remains constant
at 30°, the factor of safety reduces from 1.30 to 0.72.
In Fig. 17.6(b), we show the complementary case of variation of the
effective angle of friction along the plane of sliding, for the instance of a
dry slope and all other parameters remaining constant. In this case, the
factor of safety reduces from 2.36 to 0.45 as the angle of friction varies from
50" to 5" for the dry slope.
The curves in Fig. 17.6 show how, for even a simple model, the factor of
safety vanes dramatically with just two critical parameters. A more realistic
analysis would have to include the manifold aspects of a real plane instabdity,
such as the end restraints, the roughness and possible partial impersistence
of the sliding plane, water pressures in the discontinuity network, the nature
of any filling material in the discontinuities, and so on. It is unlikely though
that the general thrust of the factor of safety variation trends shown in Fig.
17.6 would be altered by the adoption of a more realistic model. In the
following chapter we will present more thorough methods of analysing the
instability of plane slides, both kinematically and statically.