عنوان مقاله [English]
Soil strength properties are inherently variable, due to the nature of their formation. Slope stability problems are among the most important issues in geotechnical engineering, and they are investigated in this study considering the effect of heterogeneity and anisotropy of soil strength properties in long term behavior. To this aim, the random field theory combined with the finite difference method has been adopted in the frame of Monte-Carlo simulations. The factor of safety of the slope has been calculated by the $C-phi$ reduction method and the probability of failure has then been investigated through Monte-Carlo simulations.
Different stochastic parameters were considered in order to study their effect on the stability of natural slopes in long term schemes or under drained conditions. The coefficient of variation of the cohesion and internal friction angle representing strength properties, scale of fluctuation of the parameters, cross correlation between strength parameters and heterogeneity anisotropy, are among all stochastic parameters investigated in this study. Three different values of 10, 50 and 90 for the CoV of parameters were considered, in order to cover both low and high variability. Different vertical correlation lengths, ranging from 0.1 to 50m, are considered to cover a wide range, from fully uncorrelated to fully correlated parameters.
The First Order Second Moment (FOSM), the First Order Reliability Method (FORM), and the Random Finite Difference Method (RFDM) were adopted to investigate the probability of failure. The latter was invoked by a combination of random field theory with the finite difference method through Monte-Carlo simulations by FISH programming in FLAC software.
The results show that considering heterogeneity causes variability in results. The coefficient of variation and the scale of fluctuation have been found to have the most effect on the probability of failure. When the coefficient of variation of shear strength parameters increases, the mean factor of safety decreases, and the probability of failure increases. The vertical scale of fluctuation of parameters induces an increase in variance function, due to its increase up to a critical value. Furthermore, it seems that cross correlation has less effect on variations of the factor of safety of natural slopes.