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Probability distribution curves
9
8
@RISK
Frequency (%)
7
SLOPE/W
6
5
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Factor of safety
Figure 8.17: Probability distribution curves for undrained conditions
Table 8.12: Output data from @RISK and SLOPE/W
Outputs
@RISK
SLOPE/W
Minimum factor of safety
0.113
0.334
Maximum factor of safety
3.941
1.467
Mean factor of safety
0.746
0.829
Standard deviation
0.304
0.215
Reliability index β
-
-0.794
82.7*
77.3
Probability of failure (%)
*value only given to one decimal place
The probabilities of failure were found to vary by approximately 7% in this analysis. The
same range of variables was used in both programs to limit any potential epistemic errors.
Even with this, @RISK calculated a much greater maximum factor of safety. This difference
is assumed to be due to default functions in the programs on how they treat lognormal
distributions. The mean factors of safety were approximately 10% different with @RISK
having a lower mean factor of safety, and therefore a greater probability of failure.
The failure distribution curves are lognormal since the input variable (cohesion) was
lognormal. This does not affect the probabilities of failure; the distribution can be easily
turned into a normal distribution by taking the log of x-axis values. If lognormal distribution
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