The use of probabilistic analysis (PA) of slopes as an effective method for evaluating the uncertainty that is so pervasive in variables has become increasingly common in recent years. This study presents a case study which was conducted to demonstrate the efficiency of an embankment which consists of an 11.693 m-high soil slope, placing emphasis on PA and reliability evaluation. The investigation employs Monte Carlo simulation (MCS) and subset simulation (SS) techniques, considering seismic coefficients (kh) of 0.12 for Zone-III and 0.14 for Zone-IV, along with varying pore water pressure ratios (ru=0.0, r u = 0 . 05 , and r u = 0 . 10 ). MCS with 10,000 samples was used to test the probabilistic response of the proposed embankment. This work also discusses the results of SS, in which 1,400 samples are generated from UPSS 3.0 Excel add-ins, which permits rapid PA in such a way that they progressively shift toward the failure zone in successive stages. The study delves into the impact of uncertainty on the probability of failure ( p f ) . Findings reveal an increased p f with rising coefficients of variation, r u , and kh values, underscoring the sensitivity to soil parameter variations. SS outperforms MCS in simulating low probabilities, demanding smaller sample sizes and less computational time. Furthermore, the machine learning technique has been used to optimize the worst p f condition. In this current research, three neural network-based models, namely recurrent neural network, long short-term memory (LSTM), and Bayesian neural network, have been used. Based on the performance of the models, the three neural network-based models were compared in the testing phase, and the proposed LSTM outperformed the other neural networks (R2 = 0.9962 and root mean square error = 0.0051).

The maintenance of safety and dependability in rail and road embankments is of utmost importance in order to facilitate the smooth operation of transportation networks. This study introduces a comprehensive methodology for soil slope stability evaluation, employing Monte Carlo Simulation (MCS) and Subset Simulation (SS) with the UPSS 3.0 Add-in in MS-Excel. Focused on an 11.693-meter embankment with a soil slope (inclination ratio of 2H:1V), the investigation considers earthquake coefficients (kh) and pore water pressure ratios (ru) following Indian zoning requirements. The chance of slope failure showed a considerable increase as the Coefficient of Variation (COV), seismic coefficients (kh), and pore water pressure ratios (ru) experienced an escalation. The SS approach showed exceptional efficacy in calculating odds of failure that are notably low. Within computational modeling, the study optimized the worst-case scenario using ANFIS-GA, ANFIS-GWO, ANFIS-PSO, and ANFIS-BBO models. The ANFIS-PSO model exhibits exceptional accuracy (training R2 = 0.9011, RMSE = 0.0549; testing R2 = 0.8968, RMSE = 0.0615), emerging as the most promising. This study highlights the significance of conducting thorough risk assessments and offers practical insights into evaluating and improving the stability of soil slopes in transportation infrastructure. These findings contribute to the enhancement of safety and reliability in real-world situations.