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8
PROBABILISTIC METHODS OF ANALYSIS
This thesis has until now focussed on analysing slope stability based on traditional methods of
analysis which output a single deterministic estimate as to whether, or not, an embankment is
stable. Limit equilibrium methods cannot neither quantify the level of risk, nor probability of
failure, associated with the slope: nor can they determine the criticality of the asset in the
event of a slope being seen, as a tailings dam would, in such terms. Probabilistic methods of
analysis produce a distribution of possible factors of safety rather than a single fixed value.
The parametric study in Section 6 has shown that the factor of safety changes when a single
variable changes for the same embankment. The study does not show how representative the
value was in terms of reliability or take into account the simultaneous variation of the input
variables. A reliability analysis allows the uncertainties to be identified, and quantified, to
determine how reliable the result is. It is therefore worthwhile to analyse the stability of a
tailings dam embankment using a probabilistic approach to account for the inherent variability
in a soil.
Probabilistic approaches were first applied to slope engineering in the 1970s (Alonso, 1976;
Ang and Tang, 1976). The methods have since developed and are well established and
documented in literature; however, probabilistic methods are not as commonly used by
practicing engineers. El-Ramly et al. (2002) suggest that this reluctance is attributed to four
factors:
1. Engineers’ training in statistics and probability theory is often limited to basic
information taught during the early years of their education.
2. A common misconception that probabilistic analyses require significantly more data,
time and effort than deterministic methods.
3. There are limited studies on the implementation and benefits of performing a
probabilistic analysis.
4. Acceptable probabilities of unsatisfactory performance are ill-defined, making it
difficult to understand the results of a probabilistic analysis.
A fifth reason why practicing engineers are reluctant to use deterministic methods could be to
do with insurance and indemnity issues. If an undesirable probability of failure were
calculated from back-analysis of an existing structure then this could be problematic with
regard to future insurance premium increases, or even a refusal to insure, and increases the
costs of maintaining the dam or result in its closure. More frequent maintenance inspections
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