Geotechnical Evaluation of Gradient-Based Neural Networks for Factor of Safety Prediction in Homogeneous Soil Slopes Under Hydraulic Variability

An Empirical Express Method for Clay Slope Stability Assessment Based on Slip Surface Geometry and Factor of Safety Prediction

Clay slopes are particularly sensitive to variations in soil strength, groundwater conditions, and slope geometry, making their rapid and reliable assessment essential for geotechnical design, landslide prevention, and infrastructure risk management. This study develops and evaluates an empirical express method for estimating the stability of clay slopes based on the relationship between soil mechanical parameters, slip surface geometry, and the factor of safety. The proposed approach derives empirical dependencies for the radius of the potential circular slip surface and the coordinates of its centre as functions of slope height, cohesion, internal friction angle, and water-related conditions. The method is supported by long-term field observations and geotechnical investigations of clay slopes, including dry and water-affected scenarios. Two representative stability conditions are considered: dry slopes and slopes influenced by an elevated depression curve. The method was evaluated for 45° clay slopes with heights up to 60 m, using eight representative cases: four dry scenarios and four water-affected scenarios. The calculated factors of safety were compared with GEO5 SLOPE results obtained using Bishop’s simplified method. The comparison showed that most analysed cases presented differences below 5% between the proposed express method and the Bishop-based numerical benchmark, with larger deviations occurring only in selected boundary cases. The results demonstrate that the proposed method can provide a rapid preliminary assessment of clay slope stability, supporting early-stage geotechnical diagnosis, risk screening, and decision-making in regions where clayey formations and slope instability are recurrent.

Deterministic, Reliability-Based and Risk-Based Design Optimization of Earth Slopes Using ANN-Based Surrogate Modeling

Expanding road and railway networks in developing countries is essential for economic growth and reducing regional disparities. However, such projects often face significant geotechnical stability and risk management challenges. This study presents a three-phase optimization framework consisting of: (1) deterministic, probabilistic, and risk analyses; (2) Random Variable (RV)-based optimization; and (3) Random Field (RF)-based refinement. Soil variability is modeled using both RV and RF approaches. Two Artificial Neural Network (ANN) surrogate models are employed to improve computational efficiency by predicting failure probabilities and associated costs. Two application cases are presented to demonstrate the integrated framework for optimizing earth slopes in transportation infrastructure using Deterministic Design Optimization (DDO), Reliability-Based Design Optimization (RBDO), and Risk Optimization (RO). The application cases further demonstrate the model’s potential for early-stage roadway design under limited geotechnical data. Overall, the framework supports more reliable, cost-effective, and sustainable infrastructure development.

Reliability-Based Slope Stability Analysis Using Particle Swarm-Optimized Neural Network: Benchmarking Against Conventional Probabilistic Methods Using a Lebanese Case Study

Probabilistic slope stability analysis requires tools that are both computationally efficient and accurate for uncertainty propagation. This study develops a reliability-oriented surrogate framework coupling a multilayer perceptron artificial neural network with particle swarm optimization (ANN–MLP–PSO). The model was trained on 2014 homogeneous slope cases drawn from literature records and mechanics-based simulations. PSO identified a best-performing six-hidden-layer architecture achieving a coefficient of determination of R2 = 0.95 on the held-out test set. The trained surrogate was embedded in a probabilistic sampling framework to estimate the probability of failure (Pf), reliability index (β), and factor-of-safety quantiles, then applied to the Mansourieh slope near Beirut, Lebanon, under dry and wet conditions. Outputs were benchmarked against the First-Order Second-Moment method (FOSM), the Point Estimate Method (PEM), and Monte Carlo simulation (MCS). The comparison showed that the ANN–MLP–PSO surrogate reproduced the dry-to-wet changes in factor-of-safety distributions, probability of failure, and reliability index obtained from the conventional reliability methods under the same probabilistic assumptions, with wet-scenario failure probabilities ranging from approximately 86% to 99%. Despite quantitative differences, all four methods identified the same reliability trend and engineering interpretation. Once trained, the surrogate enabled rapid probabilistic evaluation without repeated deterministic calculations, providing an efficient tool for slope stability screening and uncertainty-aware geotechnical decision support.

The Evolution and Future of Machine Learning in Rock Slope Stability: A Systematic Review and Meta-Analysis

Physics-informed neural networks for predicting ultimate bearing capacity of layered soils under complex loading conditions

A hybrid ANN–FEM framework for high accuracy slope stability prediction

Purpose. To develop a hybrid methodology that integrates Artificial Neural Networks (ANN) with Finite Element Method (FEM) simulations for the rapid and accurate prediction of slope stability. Methodology. A dataset of 1,000 FEM simulations was generated by systematically varying seven key input parameters: slope geometry (height and angle) and soil properties (cohesion, friction angle, unit weight, pore water pressure ratio, and reinforcement type). An ANN model with a (7-10-1) feedforward architecture was trained on this data. Findings. The model demonstrated exceptional predictive performance, achieving a near-perfect correlation coefficient (R  0.999997) and an extremely low mean squared error (MSE = 3.6828  10-6), showing close agreement with the FEM-computed factors of safety (FOS). A comprehensive sensitivity analysis based on analysis of variance identified the pore water pressure ratio as the dominant controlling parameter, contributing approximately 77 % to the variability of FOS, followed by cohesion with a contribution of about 13 %. Complementary correlation analysis revealed that cohesion exhibits the strongest linear correlation with FOS (r = 0.83), whereas the pore water pressure ratio shows a relatively weak linear correlation, highlighting its pronounced nonlinear and interaction-driven influence on slope stability. These results demonstrate that the proposed ANN–FEM hybrid framework provides a powerful, efficient, and reliable tool for slope stability assessment and parametric analysis. The methodology is particularly well suited for engineering applications requiring rapid decision-making, large-scale evaluations, and uncertainty analysis. Originality. The core originality of this research is its development of a robust ANN–FEM hybrid framework applied to a large, systematically generated dataset of 1,000 slope simulations. Unlike many studies, it comprehensively incorporates seven critical input variables, including the often underrepresented pore water pressure. Furthermore, its scientific rigor is enhanced by a dual interpretability strategy that combines analysis of variance for quantifying parameter contribution and correlation heatmaps for distinguishing linear effects from nonlinear ones, providing deeper insight into slope stability mechanisms. Practical value. This study provides engineers with a fast and reliable tool to predict slope safety in seconds instead of running time-consuming FEM simulations, making it highly valuable for real-time decision-making and large parametric studies. Practically, it also shows that controlling pore water pressure (through drainage) is the most effective risk-reduction strategy, while cohesion offers a predictable way to improve slope stability in design.