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This paper focuses on the calculation of probability of failure of simple unreinforced slopes and the influence of the magnitude of cross correlation between soil parameters on numerical outcomes. A general closed-form solution for cohesive slopes with cross correlation between cohesion and unit weight was investigated and results compared with cases without cross correlation. Negative cross correlations between cohesion and friction angle and positive cross correlations between cohesion and unit weight, and friction angle and unit weight were considered in the current study. The factors of safety and probabilities of failure for the slopes with uncorrelated soil properties were obtained using probabilistic slope stability design charts previously reported by the writers. Results for cohesive soil slopes and positive cross correlation between cohesion and unit weight are shown to decrease probability of failure. Probability of failure also decreased for increasing negative cross correlation between cohesion and friction angle, and increasing positive correlation between cohesion and unit weight, and friction angle and unit weight. Probabilistic slope stability design charts presented by the writers in an earlier publication are extended to include cohesive-frictional (c-[Formula: see text]) soil slopes with and without cross correlation between soil input parameters. An important outcome of the work presented here is that cross correlation between random values of soil properties can reduce the probability of failure for simple slope cases. Hence, previous probabilistic design charts by the writers for simple soil slopes with uncorrelated soil properties are conservative (safe) for design. This study also provides one explanation why slope stability analyses using uncorrelated soil properties can predict unreasonably high probabilities of failure when conventional estimates of factor of safety suggest a stable slope.

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Reinforced slopes with horizontal layers of geosynthetic reinforcement can have different mechanisms of failure. In this paper two major mechanisms of failure of reinforced slopes are investigated. External mechanisms occur when the critical slip surface passes beyond the reinforced zone. Internal mechanisms are characterised by failure surfaces that intersect all of the reinforcement layers. For a target value of the factor of safety and a specific value of the reinforcement length, there is a minimum value of the reinforcement tensile strength that will generate only external mechanism types. For greater reinforcement strength values, there is no change in the mechanism of failure and the value of the factor of safety. On the other hand, increasing the minimum reinforcement length, while keeping the reinforcement tensile strength equal to or less than the minimum value obtained for an external failure mechanism, will generate an internal mechanism type with the same mean value of factor of safety. In this study, probabilistic slope stability analysis of these two mechanisms is carried out using Monte Carlo simulation of slopes with different purely frictional and cohesive-frictional (c − ϕ) soils and different slope angles. Margins of safety are expressed in terms of a conventional factor of safety and in terms of maximum probability of failure. Cross correlation between soil strength parameters is also considered in this paper. It is shown that considering practical values of cross correlation coefficient reduces the maximum probability of failure for both internal and external failure mechanisms.

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The Random Limit Equilibrium Method (RLEM) is a relatively new method of probabilistic slope stability analysis which uses a combination of 2D random field theory, limit equilibrium methods, and Monte Carlo simulation. The Random Finite Element Method (RFEM) uses a combination of 2D random field theory, finite element method of analysis, strength reduction method, and Monte Carlo simulation. In this paper, the effects of mesh size, number of slices, and number of Monte Carlo simulations on computed probability of failure are investigated using both approaches. Computation times using both methods to solve the same slope problem are also compared. Recommendations for mesh size, number of slices, and number of Monte Carlo simulations, with respect to the spatial correlation length, using RLEM are presented.