Soil properties used to determine the stability of soil structures are variable in nature. Uncertainty in soil can be attributed to its inherent variability, as well as sources of error encountered while estimating the magnitude of its properties. The modelling of these uncertainties will produce more meaningful solutions when evaluating stability. This is especially relevant when quantifying the probability and risk associated with a rare event of failure.

An uncertainty framework is implemented in this report to evaluate improbable slope failure. A slope stability program using a modified subset simulation approach is expanded to account for cross-correlation between cohesion, friction angle and unit weight of soil. The mean of the three soil properties and their correlation coefficients are treated as random variables in the analysis. A parametric study is performed to evaluate the influence of the mean and correlation coefficients of these properties on the probability of failure. The influence of randomising these properties is also evaluated in the analysis. The implemented method is applied for a practical slope example, based on values reported in literature for the expected variability in the mentioned soil properties.

Results demonstrate that modelling the mean of C, phi and gamma as a random variable leads to a significant increase in the probability of failure for a slope. While treating the correlation coefficients as random in the analysis will lead to very little changes in the outcome, some generated correlation matrices may lead to a notable decrease in probability of failure. The stability of the slope is heavily influenced by the input parameters used in the analysis. Furthermore, a proper choice for coefficient of variation of each property and the horizontal and vertical scales of fluctuation is necessary to avoid inaccurate results in the analysis. Other inputs investigated include the type of distribution for each soil property and the range of possible values for their means. Different distribution types are tested in the analysis to identify which of these properly model the variability in the parameter.

By evaluating generated samples within each subset level, it is evident that a combination of low mean values for C and positive correlation between phi and gamma is required for failure at low probability of failure levels. Although the influence of set means of C, phi and gamma on the calculated probability of failure is similar, the same conclusion cannot be made when the means of the properties are random. At low probability of failure levels, the outcome is very sensitive to changes in the minimum possible value for C and less to changes in phi and gamma. Furthermore, it is demonstrated that the mode of failure may be overestimated when analysing stability by reducing the strength of the slope. Shallow failures are encountered when slope is failing under a strength reduction factor of 1, which is a more likely mode of failure in spatially variable soil.