Vol.:(0123456789) 1 3 Engineering with Computers https://doi.org/10.1007/s00366-018-0623-5 ORIGINAL ARTICLE A novel probabilistic simulation approach for forecasting the safety factor of slopes: a case study S. Farid F. Mojtahedi 1  · Sanaz Tabatabaee 2  · Mahyar Ghoroqi 3  · Mehran Soltani Tehrani 4  · Behrouz Gordan 5  · Milad Ghoroqi 6 Received: 2 April 2018 / Accepted: 29 May 2018 © Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract Stabilization of slopes is considered as the aim of the several geotechnical applications such as embankment, tunnel, high- way, building and railway and dam. Therefore, evaluation and precise prediction of the factor of safety (FoS) of slopes can be useful in designing these important structures. This research is carried out to evaluate the ability of Monte Carlo (MC) technique for the forecasting the FoS of many homogenous slopes in the static condition. Moreover, the sensitivity of the FoS on the efective parameters was identifed. To do this, the most important factors on FoS, such as angle of internal friction (�), slope angle () and cohesion (C) were investigated and used as the inputs to forecast the FoS. Then, a regression analysis was performed, and the results were used for the FoS prediction using MC. The obtained results of MC simulation were very close with the actual FoS values. The mean of the simulated FoS by MC was achieved as 1.32, while, according to actual FoSs, it was 1.27. These results showed that MC is an acceptable technique to estimate the FoS of slopes with high level of accuracy. Moreover, based on the results of correlation and regression sensitivity analyses, it was concluded that angle of internal friction, was the most infuential one on the results of FoS in both types of sensitivity analyses. Keywords Factor of safety · Monte Carlo simulation · Regression analysis · Sensitivity analysis Abbreviations  Angle of internal friction AI Artifcial intelligent C Cohesion CPD Continuous probability distributions FoS Factor of safety FD Finite diference FM Finite element LA Limit analysis LEM Limit equilibrium method MC Monte Carlo MR Multiple regression PGA Peak ground acceleration RMSE Root mean squared error  Slope angle H Slope height  Unit weight VAF Variance account for * Mahyar Ghoroqi Mahyar.Ghoroqi@Gmail.com S. Farid F. Mojtahedi farid.fazel71@student.sharif.edu Sanaz Tabatabaee tsanaz2@live.utm.my Mehran Soltani Tehrani Mehranso35@gmail.com Behrouz Gordan bh.gordan@yahoo.com Milad Ghoroqi Milad.Ghoroqi@Gmail.com 1 Civil Engineering Department, Sharif University of Technology, Tehran, Iran 2 Faculty of Civil Engineering, Universiti Teknologi Malaysia (UTM), Skudai, Malaysia 3 Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iran 4 Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 5 Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia 6 Department of Civil Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran