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<p>Seismic loading significantly reduced the ultimate bearing capacity of shallow strip footings due to inertial forces from both the soil mass and the superstructure. This study developed a unified machine learning framework to accurately predict the seismic bearing capacity factors while explicitly accounting for both soil inertia and superstructure inertia effects. A high-quality dataset of 1498 data points was compiled from three independent pseudo-static studies using distinct rigorous numerical methods. Three advanced algorithms, including Gradient Boosting Trees (GBT), Extreme Gradient Boosting (XGBoost), and Artificial Neural Networks (ANN), were optimized using grid search and 5-fold cross-validation. The optimal model, a simple ANN with a single hidden layer of six neurons and hyperbolic tangent activation, achieved outstanding performance on an independent test set: R² ≈ 0.999, RMSE = 1.02–1.55, and MAE = 0.75–1.12 across all factors, clearly outperforming XGBoost, GBT, and traditional numerical solutions. Shapley Additive exPlanations (SHAP) analysis confirmed the dominant positive influence of the friction angle (<i>φ</i>) and the detrimental effect of the horizontal seismic coefficient <i>k</i><sub>h</sub>. Closed-form equations derived from the trained ANN weights and biases were provided for instant hand calculations in routine design. Extensive validation against the original benchmark datasets yielded average relative errors of approximately 5% for smooth and rough interfaces, both inertia types, with no overfitting. The proposed surrogate model offers highly accurate, transparent, and practically implementable predictions for seismic foundation engineering.</p>

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Advanced Machine Learning Models for Predicting the Seismic Bearing Capacity Factors of Shallow Strip Footings Considering Soil and Superstructure Inertia Effects

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • L. Nguyen-Son,
  • T. Thai-Phuong,
  • T. Vo-Minh

摘要

Seismic loading significantly reduced the ultimate bearing capacity of shallow strip footings due to inertial forces from both the soil mass and the superstructure. This study developed a unified machine learning framework to accurately predict the seismic bearing capacity factors while explicitly accounting for both soil inertia and superstructure inertia effects. A high-quality dataset of 1498 data points was compiled from three independent pseudo-static studies using distinct rigorous numerical methods. Three advanced algorithms, including Gradient Boosting Trees (GBT), Extreme Gradient Boosting (XGBoost), and Artificial Neural Networks (ANN), were optimized using grid search and 5-fold cross-validation. The optimal model, a simple ANN with a single hidden layer of six neurons and hyperbolic tangent activation, achieved outstanding performance on an independent test set: R² ≈ 0.999, RMSE = 1.02–1.55, and MAE = 0.75–1.12 across all factors, clearly outperforming XGBoost, GBT, and traditional numerical solutions. Shapley Additive exPlanations (SHAP) analysis confirmed the dominant positive influence of the friction angle (φ) and the detrimental effect of the horizontal seismic coefficient kh. Closed-form equations derived from the trained ANN weights and biases were provided for instant hand calculations in routine design. Extensive validation against the original benchmark datasets yielded average relative errors of approximately 5% for smooth and rough interfaces, both inertia types, with no overfitting. The proposed surrogate model offers highly accurate, transparent, and practically implementable predictions for seismic foundation engineering.