Random Finite Element and Limit Equilibrium Methods-Based Probabilistic Stability Analyses of a Cut Slope

This paper elucidates the efficacy of advanced Random Finite Element Method (RFEM) to assess the excavation induced slope instability over the conventional Limit Equilibrium Method (LEM). Both the studies have been carried out in a probabilistic framework in which the shear strength parameters of the slope material are considered as random variables. While the probabilistic LEM is used for the conventional one-dimensional (1-D) spatial variation with pre-assumed failure surfaces, the adopted probabilistic RFEM incorporates a more realistic two-dimensional (2-D) spatial variation of soil properties with the evolution of failure surfaces during the progress of the analysis. In absence of any previous studies employing RFEM to investigate the toe-excavation induced hillslope instability, the present study illustrates the importance of considering uncertainty and two-dimensional spatial variability in soil properties for a safe and economical cut slope design for hill-road constructions. The outcomes suggest that the chances of a cut-slope failure are strongly influenced by the coefficient of variation (CoV), cross-correlation coefficient between the shear strength parameters (rho(c phi)) and the non-dimensional correlation length (Theta) governing the spatial variability of soil properties. For a specific rho(c phi) = +0.5 and CoV varying between 0.2 and 0.4, the probability of failure (P-f) of the cut slope exhibits a variation of approximately 6%. Based on the various possible correlation types exhibited by the soil parameters (rho(c phi): - 0.5, 0, + 0.5), for a specific CoV = 0.4, a similar variation in P-f of approximately 6% is observed. Based on comparative study with 2-D RFEM-based spatial variability, it is deciphered that adoption of 1-D LEM-based spatial variability can significantly undermine the failure probability of the cut-slope, especially when the Theta ranges in 0.5-0.7. In this range, a cut slope section may even be adjudged safe ('above average' performance level) through 1-D spatial variability, while in reality the slope may have substantially higher chances of failure with a 'poor' performance level. The outcomes of the reported study indicate the inadvertent requirement of obtaining an appropriate site-specific spatial variation of soil parameters for the successfully assessing the probabilistic failure of cut slopes.