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

TLDR

The study introduces a Monte Carlo simulation–based reliability analysis for slope stability, employing subset simulation to enhance efficiency at low probability levels. The method is implemented in Microsoft Excel, validated against other reliability tools, and used to assess how spatial variability of soil properties and slip surfaces influences failure probability. Results show that neglecting spatial variability overestimates the factor‑of‑safety variance and can lead to conservative or unconservative failure probability estimates, while proper accounting of variability prevents significant underestimation.

Abstract

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.