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This paper develops a combined method to predict the volume of sliding mass for homogeneous slopes in an efficient manner. Firstly, the failure surface with minimum factor of safety (FS) in Limit Equilibrium Method is equated to that one determined by Smoothed Particle Hydrodynamics algorithm to obtain the threshold displacement value for unstable and stable particles. Secondly, the threshold displacement value is used to identify the volume of sliding mass using SPH. Finally, a regression model is developed based on a finite number of SPH simulations for homogeneous soil slopes. The proposed LEM-SPH based method is illustrated through a cohesive soil slope. It is concluded that the use of failure surface with minimum FS in LEM tends to underestimate the volume of sliding mass and to give an unconservative risk value. The Coefficient of Variation (Cov) of volume of sliding mass are 0.14, 0.28, 0.4, 0.48, 0.53 for Cov of soil properties = 0.2, 0.3, 0.4, 0.5, and 0.6, respectively. The uncertainty of soil properties has a significant effect on the mean value of volume of sliding mass and therefore the landslide risk value. The proposed method is necessitated for cases where large uncertainties in soil properties exist. [ABSTRACT FROM AUTHOR]

The determination of slope failure areas plays an important role in slope stability problem. The previous studies evaluate the failure area either based on the slip surface with minimum factor of safety (FS) or using area failure probability method (AFPM). A user-defined displacement criterion is combined with smoothed particle hydrodynamics (SPH) to properly quantify the failure area and to rationally assess the average slope failure area using Monte Carlo Simulation (MCS). The proposed method is illustrated through two slope examples. It is found that although AFPM can identify the multiple slip surfaces, it tends to overestimate the area of failed soil mass due to its inability to consider the progressive behaviour of a slope failure. A wider search range for entrance and exit points in AFPM is highly recommended. The slip surface with minimum FS underestimates the area of failed soil mass because only initial slip surface is identified and used while neglecting the evolution of a slope failure. The proposed approach serve as an alternative tool for quantifying the average slope failure area accounting for the specific acceptable threshold displacement value, d, or dimensionless coefficient, ξ. As the d or ξ value increases, the average slope failure area decreases. [ABSTRACT FROM AUTHOR]

This paper develops a multiple response surfaces approach to approximate the limit state function for slope failure by second-order polynomial functions, to incorporate the variation of the most probable slip surfaces, and to evaluate the slope failure probability pf. The proposed methodology was illustrated through a cohesive soil slope example. It is shown that the pf values estimated from multiple response surfaces agree well with those pf values that have been obtained by searching a large number of potential slip surfaces in each Monte Carlo simulation (MCS) sample. The variation of number of the most probable slip surfaces is studied at different scale of fluctuation ( λ) values. It is found that when full correlation assumed for each of random fields (i.e., spatial variability is ignored), the number of the most probable slip surfaces is equal to the number of random fields (in this study, it is 3). When the spatial variability grows significantly, the number of the most probable slip surfaces or number of multiple response surfaces firstly increases evidently to a higher value and then varies slightly. In addition, the contribution of a specific most probable slip surface varies dramatically at different spatial variability level, and therefore, the variation of the most probable slip surfaces should be accounted for in the reliability analysis. The multiple response surfaces approach developed in this paper provides a limit equilibrium method and MCS-based means to incorporate such a variation of the most probable slip surfaces in slope reliability analysis. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]