What question did this study set out to answer?

The research aims to predict the random bearing capacity factor for shallow foundations on Bolton sand, incorporating spatial variability and optimization.

April 17, 2026Open Access

Optimized LightGBM-Based Prediction of Foundation Bearing Capacity on Spatially Variable Bolton Sand

Key Points

The research aims to predict the random bearing capacity factor for shallow foundations on Bolton sand, incorporating spatial variability and optimization.
Examined random bearing capacity factor using random field theory and finite element limit analysis.
Employed adaptive meshing techniques to analyze spatial variability.
Developed hybrid LightGBM models optimized with Equilibrium Optimizer and Archimedes Optimization Algorithm.
Utilized SHAP analysis to interpret model predictions and assess feature importance.
Findings show that increasing the vertical correlation length improves predictions toward the deterministic bearing capacity factor.
Higher coefficients of variation in friction angle systematically reduce mean bearing capacity factor.
AOA-LightGBM outperformed other models, evidenced by higher R² values and better performance metrics.

Abstract

This study examines the random bearing capacity factor ( N γran ) of shallow foundations on spatially variable Bolton sand using random field theory, adaptive meshing technique, and finite element limit analysis. The analysis focuses on the variability of the critical-state friction angle ( ϕ cv ) and its spatial correlation. Results indicate that increasing the vertical dimensionless spatial correlation length ( Θ Y ), causing the mean random bearing capacity factor ( μN γran ) to converge toward the deterministic bearing capacity factor ( N γdet ), whereas increasing the coefficient of variation of the critical-state friction angle ( COVϕ cv ) leads to a systematic reduction in μN γran . To enhance predictive performance, a hybrid machine learning framework was developed using the Light Gradient Boosting Machine (LightGBM), optimized through both the Equilibrium Optimizer (EO) and the Archimedes Optimization Algorithm (AOA). Among the models, AOA-LightGBM demonstrated superior accuracy, as indicated by higher R 2 values and improved performance metrics. Additionally, SHapley Additive exPlanations (SHAP) were employed to interpret model predictions, offering insights into the relative importance of input features. The analysis revealed that the factor of safety (F.S.) and COVϕ cv had the most significant impact on the model’s predictions. These findings highlight the importance of considering spatial variability in geotechnical design to ensure reliable foundation performance under uncertain conditions. • Developing new limit state solutions for the random bearing capacity factor of shallow foundations on spatially variable Bolton sand using random field theory and finite element limit analysis. • Constructing hybrid XGBoost models integrated with the Equilibrium Optimizer (EO) and the Archimedes Optimization Algorithm (AOA) • Assessed the performance of the proposed machine learning models for predicting the probability of failure using SHAP analysis and various performance metrics.

Optimized LightGBM-Based Prediction of Foundation Bearing Capacity on Spatially Variable Bolton Sand

Key Points

Abstract

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