Impact of distribution laws on the stability factor with the application of Monte Carlo method

The purpose of this study is to compare approaches to the quantitative probabilistic assessment of homogeneous slope stability using Monte Carlo method, employing standard engineering software and advanced statistical analysis. Additionally, it aims to assess the impact of the chosen distribution laws on the final calculation of the probability of collapse.

Methods. The GeoStudio software package served as a primary tool for deterministic and probabilistic calculation of the stability factor FS using four methods: Fellenius, Bishop, Janbu, and Morgenstern – Price. For in-depth analysis, the Morgenstern – Price method was implemented using the @RISK add-in for MS Excel. Statistical processing of the results and identification of distribution laws were performed using the R Package (fitdistrplus package), and using the Cullen – Frey skewness – kurtosis plot.

Results. Statistical analysis of the empirical stability coefficient distribution revealed its positive skewness and proximity to exponential-type distributions (e. g., Weibull, gamma). Approximating the data with the Weibull distribution results in a collapse probability value 33.8 times higher than the estimate obtained assuming a normal distribution FS.

Conclusions. Standard engineering software offers a limited range of functions for adequate probabilistic analysis. Without additional statistical validation, their use can lead to a gross underestimation of the risk due to an unsubstantiated assumption of a normal distribution law for the stability factor. For an accurate assessment of collapse probability, it is essential to identify the empirical distribution of the stability factor using specialized statistical tools. When modeling slope stability, it is recommended to consider skewness distributions, such as the Weibull or lognormal distributions.

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