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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. RÃ©thÃ¡ti (2012) found that for the angle of shearing resistance of granular soils, the coefficient of variation increase with the decreasing grain size, 112