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<p>This study introduces a Bayesian Neural Network trained via Markov Chain Monte Carlo (BNN–MCMC) to deliver robust probabilistic predictions of ultimate bearing capacity for footings on treated soil. Leveraging a dataset of 273 plate load tests on lime-treated and geotextile-reinforced silty sand, the framework provides full posterior inference over network weights, enabling a rigorous decomposition of predictive uncertainty. This approach is critically benchmarked against Gaussian Process Regression and deterministic neural network methods (Deep Ensembles, Monte Carlo Dropout), which offer only approximate uncertainty or face scalability issues. The BNN–MCMC model demonstrates superior predictive accuracy, achieving the highest Pearson correlation coefficient (0.984 ± 0.006), coefficient of determination (R² = 0.965 ± 0.011), and the lowest error metrics (RMSE = 0.022, MAE = 0.016). Crucially, for uncertainty quantification, BNN–MCMC yields optimally calibrated 95% prediction intervals with a coverage probability of 94.15%, effectively capturing the true value while maintaining a sharp mean interval width of 0.081. A parametric analysis utilizing the model’s mean predictions and uncertainty surfaces reveals critical geotechnical insights: epistemic uncertainty increases with geotextile embedment depth due to complex soil-reinforcement interaction, yet decreases with higher lime content, reflecting enhanced soil homogenization. By delivering both high-fidelity point estimates and reliable, adaptive uncertainty bounds, the BNN–MCMC framework establishes a new benchmark for trustworthy machine learning in geotechnical design, where quantifying confidence is as paramount as prediction accuracy.</p>

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Probabilistic Prediction and Uncertainty Quantification of Bearing Capacity of Lime-Treated, Geotextile-Reinforced Silty Sand Using Bayesian Neural Network

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Dhawal Kumar,
  • Parbin Sultana

摘要

This study introduces a Bayesian Neural Network trained via Markov Chain Monte Carlo (BNN–MCMC) to deliver robust probabilistic predictions of ultimate bearing capacity for footings on treated soil. Leveraging a dataset of 273 plate load tests on lime-treated and geotextile-reinforced silty sand, the framework provides full posterior inference over network weights, enabling a rigorous decomposition of predictive uncertainty. This approach is critically benchmarked against Gaussian Process Regression and deterministic neural network methods (Deep Ensembles, Monte Carlo Dropout), which offer only approximate uncertainty or face scalability issues. The BNN–MCMC model demonstrates superior predictive accuracy, achieving the highest Pearson correlation coefficient (0.984 ± 0.006), coefficient of determination (R² = 0.965 ± 0.011), and the lowest error metrics (RMSE = 0.022, MAE = 0.016). Crucially, for uncertainty quantification, BNN–MCMC yields optimally calibrated 95% prediction intervals with a coverage probability of 94.15%, effectively capturing the true value while maintaining a sharp mean interval width of 0.081. A parametric analysis utilizing the model’s mean predictions and uncertainty surfaces reveals critical geotechnical insights: epistemic uncertainty increases with geotextile embedment depth due to complex soil-reinforcement interaction, yet decreases with higher lime content, reflecting enhanced soil homogenization. By delivering both high-fidelity point estimates and reliable, adaptive uncertainty bounds, the BNN–MCMC framework establishes a new benchmark for trustworthy machine learning in geotechnical design, where quantifying confidence is as paramount as prediction accuracy.