Engineering Rock Mechanics

Techniques for incorporating variations in rock and site 337

';'[A 'If,s\ ~[y--\ 'r ~i\

43

8: I I I I I

E0 I .n 0 I .o 0 1 .0 0 1 .o

Factor of safety Factor of safety Factor of safety Factor of safety

(a) Unstable (b) Poor (c) Fair (d) Stable

Figure 18.20 Class of slope stability based on fuzzy analysis (after Sakurai and

Shimizu, 1987).

trapezoidal fuzzy number representing factor of safety, Sakurai and

Shimizu defined a 'Stability Index', S.I., as

where fi and f2 are as indicated in Fig. 18.20, which shows four classes of
slope stability based on the stability index.
Using fuzzy mathematics to accommodate uncertainty in slope analysis
presents no additional difficulty in an ordinary instability analysis, and so
it is likely that its use will increase in the future together with experience
of assessing instability in terms of the stability index or some similar
measures.