Background Accurate estimation of soil bearing capacity is fundamental for safe and economical foundation design. Conventional analytical approaches often rely on simplified assumptions regarding soil behavior and failure mechanisms, leading to significant variability in predicted capacities. This study presents a comparative evaluation of traditional bearing capacity theories and advanced machine learning (ML) approaches for shallow foundations on granular soils in Dhangadi, Nepal. Three boreholes were drilled to 15 m depth, and Standard Penetration Tests (SPT) together with laboratory testing were performed to characterize the silty sand deposits. Traditional analytical methods (Terzaghi, Meyerhof, Hansen, and Vesic) were compared with Artificial Neural Network (ANN), Physics-Informed Neural Network (PINN), Gaussian Process Regression (GPR), and Polynomial Chaos–Kriging (PC-Kriging) models. Results Classical analytical methods predicted allowable bearing capacities ranging from 290 to 435 kN/m2 for footing widths of 2–5 m and embedment depths of 1.5–2.5 m, with Meyerhof producing the highest estimates and Terzaghi the most conservative. However, SPT-based settlement analysis yielded a much lower allowable capacity of approximately 115 kN/m2, indicating that settlement governed the foundation design. Among all predictive models, the PINN achieved the best performance with MAE = 8.9 kN/m2, RMSE = 13.5 kN/m2, and R2 = 0.96, outperforming the ANN model (RMSE = 18.7 kN/m2; R2 = 0.91) and all traditional methods (RMSE = 28.9–34.1 kN/m2; R2 = 0.72–0.81). Probabilistic surrogate models also demonstrated strong predictive capability, with GPR achieving RMSE = 14.8 kN/m2and R2 = 0.95. Statistical analysis confirmed significant differences among prediction methods (ANOVA: F(5,66) = 89.47, p < 0.001, η2 = 0.871). Tukey HSD testing showed that the PINN predictions aligned closely with the intermediate Hansen and Vesic methods while maintaining substantially lower prediction errors. Conclusions The results demonstrate that machine learning approaches, particularly physics-informed frameworks, significantly improve the accuracy and reliability of bearing capacity prediction compared with traditional analytical methods. Incorporating physical constraints within the PINN framework enhanced generalization capability and reduced physically inconsistent predictions. The study further highlights that settlement considerations govern shallow foundation performance in granular soils and should not be neglected in design. A hybrid framework integrating traditional analytical verification, settlement-based empirical assessment, and physics-informed machine learning is therefore recommended for more reliable geotechnical foundation design.

Comparative analysis of traditional and machine learning approaches for estimating the bearing capacity of granular soils

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2026年6月22日

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Mahendra Acharya,
Diwash Bhattarai

摘要

Background

Accurate estimation of soil bearing capacity is fundamental for safe and economical foundation design. Conventional analytical approaches often rely on simplified assumptions regarding soil behavior and failure mechanisms, leading to significant variability in predicted capacities. This study presents a comparative evaluation of traditional bearing capacity theories and advanced machine learning (ML) approaches for shallow foundations on granular soils in Dhangadi, Nepal. Three boreholes were drilled to 15 m depth, and Standard Penetration Tests (SPT) together with laboratory testing were performed to characterize the silty sand deposits. Traditional analytical methods (Terzaghi, Meyerhof, Hansen, and Vesic) were compared with Artificial Neural Network (ANN), Physics-Informed Neural Network (PINN), Gaussian Process Regression (GPR), and Polynomial Chaos–Kriging (PC-Kriging) models.

Results

Classical analytical methods predicted allowable bearing capacities ranging from 290 to 435 kN/m² for footing widths of 2–5 m and embedment depths of 1.5–2.5 m, with Meyerhof producing the highest estimates and Terzaghi the most conservative. However, SPT-based settlement analysis yielded a much lower allowable capacity of approximately 115 kN/m², indicating that settlement governed the foundation design. Among all predictive models, the PINN achieved the best performance with MAE = 8.9 kN/m², RMSE = 13.5 kN/m², and R² = 0.96, outperforming the ANN model (RMSE = 18.7 kN/m²; R² = 0.91) and all traditional methods (RMSE = 28.9–34.1 kN/m²; R² = 0.72–0.81). Probabilistic surrogate models also demonstrated strong predictive capability, with GPR achieving RMSE = 14.8 kN/m²and R² = 0.95. Statistical analysis confirmed significant differences among prediction methods (ANOVA: F(5,66) = 89.47, p < 0.001, η² = 0.871). Tukey HSD testing showed that the PINN predictions aligned closely with the intermediate Hansen and Vesic methods while maintaining substantially lower prediction errors.

Conclusions

The results demonstrate that machine learning approaches, particularly physics-informed frameworks, significantly improve the accuracy and reliability of bearing capacity prediction compared with traditional analytical methods. Incorporating physical constraints within the PINN framework enhanced generalization capability and reduced physically inconsistent predictions. The study further highlights that settlement considerations govern shallow foundation performance in granular soils and should not be neglected in design. A hybrid framework integrating traditional analytical verification, settlement-based empirical assessment, and physics-informed machine learning is therefore recommended for more reliable geotechnical foundation design.