Stability evaluation of gentle slopes in spatially variable soils using discretized limit analysis method: a probabilistic study

The stability of gentle slopes is rarely accessed in existing studies, which are at risk of below-toe failure in soils with low shear strength. The inherent spatial variability of soil shear strength poses a huge complication to the probabilistic stability evaluation of large-scale three-dimensional gentle slopes, which usually forces a trade-off between precision and efficiency. In view of this, a semi-analytical method is developed in the framework of discretized limit analysis, which gives a unified mathematical representation of toe failure and below-toe failure of slopes. The proposed method inherits the high efficiency of analytical methods and has the ability to integrate spatially variable shear strengths into the slope mechanical model. The model validation is conducted by comparisons with a widely recognized analytical method developed for uniform soils. The random fields are introduced to achieve a relatively accurate characterization of soil shear strength, and the Monte Carlo simulation is employed to obtain a sufficient number of factors of safety of slopes for the subsequent statistical analyses. In the parametric study, spatial variability-related parameters, including the coefficient of variation of soil cohesion cov_c or internal friction angle cov_φ, the autocorrelation lengths along vertical and horizontal directions ξ and k, the cross-correlation coefficient ρ_cφ, are varied systematically to reveal their influences on the slope stability from a statistical perspective. It is found that the ranking of the impact on the probabilistic stability of a gentle slope is given as: cov_c or cov_φ > ξ > k > ρ_cφ. Finally, the failure probabilities of the gentle slope are computed considering the variations of key parameters, which may have implications for practical slope designs.