The critical aspect of the seismic bearing capacity of footings holds significant importance in the field of geotechnical engineering. Past research has primarily focused on deterministic analyses, mainly neglecting or ignoring the spatial variability of the soil. This study aims to address this gap by employing a probabilistic approach to assess the seismic bearing capacity of foundations while considering the seismic force effect by adopting the pseudo-static approach. To achieve this goal, this study utilizes the random adaptive finite element limit analysis technique and Monte Carlo simulations to cover a wide range of potential outcomes, taking into account the uncertainties in the parameters. This research investigated the influence of soil strength variability on three key factors: the horizontal seismic coefficient, coefficient of variation, and dimensionless correlation length. The study revealed that an increase in the coefficient of variation of the undrained shear strength (COVsu) and the dimensionless correlation length (Theta su) leads to a reduction in the mean of the random seismic bearing capacity factor (mu Nran). Conversely, the horizontal seismic coefficient (kh) negatively impacts the seismic bearing capacity, thereby diminishing the overall soil stability. Additionally, the factor of safety must be selected with caution to ensure that the probability of failure is less than a specified value, particularly when the coefficient of variation of the undrained shear strength (COVsu) is high. To establish surrogate models capable of predicting the random seismic bearing capacity, multivariate adaptive regression spline (MARS) models have been developed. Utilizing the proposed MARS surrogate models offers a more convenient and computationally efficient means of evaluating the impact of variability in soil strength properties on geotechnical stability calculations.

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.