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was not used for the undrained cohesion, then negative factors of safety would be calculated
resulting in low probability of failure which would not accurately represent the embankment.
The high probabilities of failure confirm the findings throughout this thesis that the undrained
analysis of baseline case 1 is not stable.
8.9
Probabilistic analysis of the case study
The case study tailings dam introduced in Section 7 is used again in this analysis to determine
the probability of failure. The embankment is analysed with a 2 m sandstone foundation as
this produced the highest factor of safety in Section 7. The embankment height, phreatic
surface and soil layer widths are assumed constant. In reality these values are likely to be
variable due to natural variability and construction techniques. Similar to the random
variables already discussed in this thesis, the variability can be observed from in situ tests that
would show differences in embankment height, phreatic surface and soil layer widths at
various locations around the embankment. It would be difficult to accurately model the exact
conditions or calculate suitable ranges for each variable for the case study without having
more information about the site and embankment (since only a single cross section is given).
Therefore the values at this cross section are assumed instantaneous and hence deterministic.
A more detailed analysis that includes using embankment height, phreatic surface and soil
layer widths are random variables could be undertaken to determine the effect these would
have on the factor of safety and probability of failure.
The bulk unit weight and angle of shearing resistance of each layer are considered random
variables. The rock armour layer is made up of cobbles, boulders and gravel with some silty
fines and sand. A coefficient of variation for the bulk unit weight is chosen as 7%, and for
angle of shearing resistance 13%, to represent the variability in the rock armour layer. These
values are from the upper end of the typical range specified in Table 8.1.
The earth fill layer is a highly variable mixture of gravelly clay with some pockets of clayey
sand and cobbles. Since this layer is highly variable, a higher coefficient of variation is
estimated. Due to the lack of data from the geotechnical observations, the coefficients of
variation are estimated based on the information provided. The PP (pocket penetrometer) test
results (Appendix D) show values varying from 200 to 600 kPa which highlight the variability
in strength. For these reasons, the coefficient of variation for the bulk unit weight is 8%, and
19% for the angle of shearing resistance. Rétháti (2012) found that for the angle of shearing
resistance of granular soils, the coefficient of variation increase with the decreasing grain size,
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