A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties

• A multiple response-surface method for slope reliability analysis is proposed.
• The proposed method efficiently solves slope reliability with spatial variability.
• Scales of fluctuation of soil shear strength parameters are extensively summarized.
• Single exponential autocorrelation function may underestimate probability of failure.
• Probabilities of failure for different autocorrelation functions differ slightly.

This paper proposes a multiple response-surface method for slope reliability analysis considering spatially variable soil properties. The scales of fluctuation of soil shear strength parameters are summarized. The effect of theoretical autocorrelation functions (ACFs) on slope reliability is highlighted since the theoretical ACFs are often used to characterize the spatial variability of soil properties due to a limited number of site observation data available. The differences in five theoretical ACFs, namely single exponential, squared exponential, second-order Markov, cosine exponential and binary noise ACFs, are examined. A homogeneous c–ϕ slope and a heterogeneous slope consisting of three soil layers (including a weak layer) are studied to demonstrate the validity of the proposed method and explore the effect of ACFs on the slope reliability. The results indicate that the proposed method provides a practical tool for evaluating the reliability of slopes in spatially variable soils. It can greatly improve the computational efficiency in relatively low-probability analysis and parametric sensitivity analysis. The extended Cholesky decomposition technique can effectively discretize the cross-correlated non-Gaussian random fields of spatially variable soil properties. Among the five selected ACFs, the squared exponential and second-order Markov ACFs might characterize the spatial correlation of soil properties more realistically. The probability of failure associated with the commonly-used single exponential ACF may be underestimated. In general, the difference in the probabilities of failure associated with the five ACFs is minimal.