In design practice, the two limit equilibrium methods of Fellenius and Bishop’s simplified methods are commonly employed for assessing slope stability. However, recent research indicates that the safety levels of sand slopes estimated using Fellenius’ method may be underestimated compared to those obtained using Bishop’s simplified method when random variables are applied to soil properties. Considering the natural spatial variability of soil properties, which was not considered in previous work, this study investigates the probabilistic safety of slope stability by incorporating soil strength variability. Two representative slopes, one composed of clay and the other of sand, are analyzed in this study. Soil strength properties are represented as random fields to incorporate spatial variability. Monte Carlo simulations with 50,000 samples are then used to determine the system failure probabilities of the two slopes. Investigations indicate that the safety factors and probabilistic safety levels are relatively similar when using both the simplified Bishop and Fellenius methods for the clay slope. However, for the sand slope, the safety factor estimated by Fellenius’ method is approximately 17% lower than that obtained using Bishop’s simplified method, even though the probabilistic results are relatively identical. As a result, Fellenius is recommended for practical use in probabilistic analyses due to its lower computational requirements. Furthermore, it is revealed that the reliability index has an inverse relationship with the scale of fluctuations used in random field simulations. This inverse relationship is more pronounced for the clay slope than for the sand slope.

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Probabilistic Safety Assessments of Slopes Estimated by Fellenius and Bishop’s Simplified Method Considering Spatial Variability of Soil Properties

  • Nhu Son Doan

摘要

In design practice, the two limit equilibrium methods of Fellenius and Bishop’s simplified methods are commonly employed for assessing slope stability. However, recent research indicates that the safety levels of sand slopes estimated using Fellenius’ method may be underestimated compared to those obtained using Bishop’s simplified method when random variables are applied to soil properties. Considering the natural spatial variability of soil properties, which was not considered in previous work, this study investigates the probabilistic safety of slope stability by incorporating soil strength variability. Two representative slopes, one composed of clay and the other of sand, are analyzed in this study. Soil strength properties are represented as random fields to incorporate spatial variability. Monte Carlo simulations with 50,000 samples are then used to determine the system failure probabilities of the two slopes. Investigations indicate that the safety factors and probabilistic safety levels are relatively similar when using both the simplified Bishop and Fellenius methods for the clay slope. However, for the sand slope, the safety factor estimated by Fellenius’ method is approximately 17% lower than that obtained using Bishop’s simplified method, even though the probabilistic results are relatively identical. As a result, Fellenius is recommended for practical use in probabilistic analyses due to its lower computational requirements. Furthermore, it is revealed that the reliability index has an inverse relationship with the scale of fluctuations used in random field simulations. This inverse relationship is more pronounced for the clay slope than for the sand slope.