Engineering Rock Mechanics

336 Design and analysis of surface excavations

Satisfies all three criteria

Exceeds minimum mean F but violates one or

both probabilistic criteria

Falls below minimum mean F but satisfies

both probabilistic criteria

Falls below minimum mean F and does not

satisfy one or both probablistic criteria

Category

of

slope

Stable slope

Operation of the slope presents a risk which may

or may not be acceptable. The level of risk can be

assessed by a comprehensive monitoring

programme.

Marginal slope. Minor modifications of slope

geometry are required to raise the mean F to a

satisfactory level.

Unstable slope. Major modifications of slope

geometry are required. Rock improvement and

slope monitoring may be necessary.

Consequences

of failure

Not serious

Moderately

serious

Very serious

Examples

Individual benches, small

(height<50m) temporary slopes

not adjacent to haulage roads.

Any slopes of permanent or

semi-permanent nature.

Medium sized (50m<height

<150m) and high (heighbl50m)

slopes carrying major haulage

roads or underlying permanent

mine installations.

Probabilistic slope design criteria

Satisfaction of above criteria I Interpretation

Slope performance interpretation

Figure 18.19 Interpretation of probabilistic design criteria (after Priest and Brown,

1983).

7 8.4.3 Fuzzy mathemutics

It may be that the parameters influencing the instability of a slope do not

conform to any known probabilistic distribution, or that the resources

necessary to determine the relevant distributions are unavailable. In such

circumstances, the application of probabilistic methods is inappropriate.

However, the analysis of 'uncertainty' (rather than probability) may be

performed using fuzzy mathematics, as described in Section 12.6.1.

The application of fuzzy mathematics to the analysis of slope instability

through the use of standard equilibrium analysis is straightforward, but the

interpretation of the resulting fuzzy factor of safety needs care. A

procedure for this interpretation has been outlined by Sakurai and Shimizu

(1987), who considered fuzzy cohesion and angle of internal friction in the

analysis of plane sliding. The analysis is mechanically identical to that

presented in Section 17.1.2, but in order to interpret the resulting