Reliability analysis and uncertainty quantification of clay and sand slopes stability evaluated by Fellenius and Bishop’s simplified methods

Abstract

Slope stabilities are mainly designed using the conventional design approach (CDA), where the limit equilibrium methods (LEMs) are performed. Fellenius and Bishop’s simplified methods are the two commonly LEMs adopted as recommended in most design codes. In the design process of CDA, the safety factors (FS) of slopes are checked with specified FSs to ensure stability. The CDA has inherent drawbacks because the design process does not account for uncertainties. Moreover, different LEMs using different assumptions to solve the safety factors might include some amount orders of approximations. This study conducts probabilistic analyses, i.e., Monte Carlo simulations (MCSs) and uncertainty quantification, to obtain insights into the two LEMs applied to clay and sand slopes. The results reveal that the reliability indexes (RIs) obtained from the two LEMs-based MCSs are relatively identical for the same slope. Concerning the soil types, however, the RIs of the clay slope are significantly lower than those estimated for the sand slope, regardless of the LEMs used. The uncertainty quantifications for the clay slopes reveal that the two LEMs have relatively similar bias factors regarding FSs. Nevertheless, using the Fellenius method underestimates the probabilistic safety (about 17% in terms of the mean of FSs) for the sand slope compared to Bishop’s simplified method. Moreover, the coefficients of variation of FS obtained from the clay slope are consistently larger than those from the sand slope. These observations imply that the clay slope is more uncertain than the sand slope, and the Fellenius method results in lower FSs for sand slopes. Therefore, the FSs specified in the design codes should be connected to the soil type or the LEMs used to achieve the same probabilistic safety levels. Finally, the equivalent FSs associated with a RI of 1.75 are derived for each slope and each LEM used.