Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet

This paper develops a Monte Carlo simulation (MCS)-based reliability analysis approach for slope stability problems and utilizes an advanced MCS method called "subset simulation" for improving efficiency and resolution of the MCS at relatively small probability levels. Reliability analysis is operationally decoupled from deterministic slope stability analysis and implemented using a commonly available spreadsheet software, Microsoft Excel. The reliability analysis spreadsheet package is validated through comparison with other reliability analysis methods and commercial software. The spreadsheet package is then used to explore the effect of spatial variability of the soil properties and critical slip surface. It is found that, when spatial variability of soil properties is ignored by assuming perfect correlation, the variance of the factor of safety (FS) is overestimated, which may result in either over (conservative) or under (unconservative) estimation of the probability of failure (P-f = P(FS < 1)). When the spatial variability of soil properties is considered, the critical slip surface varies spatially and such spatial variability should be properly accounted for. Otherwise, the probability of failure can be significantly underestimated and unconservative.