Towards Robust and Adaptive Bearing Capacity Prediction for Dry Shallow Foundations Using Physics-Informed Machine Learning

This study proposes a physics-informed machine learning (PIML) framework for geotechnical engineering applications that combines the strengths of traditional physics-based methods and data-driven machine learning (ML) models. Bearing capacity prediction of shallow foundations is used as a case study to demonstrate the applicability of the proposed framework. The PIML framework integrates Vesić's bearing capacity method as an embedded differentiable physics module to improve model generalization and robustness. A benchmark data set was created using finite element analysis (FEA), consisting of 3,500 samples with randomly generated values for soil properties, foundation geometries, and loading conditions. To evaluate the effectiveness of the proposed framework, the data set was divided into non-overlapping clusters based on input features, followed by cross-cluster validation. Results show that both the baseline neural network (NN) and the PIML model outperform Vesić's method. Notably, the PIML model showed superior generalization performance and faster convergence, as evidenced by higher R² and lower RMSE values. The proposed PIML framework presents a hybrid approach that effectively addresses the limitations of standalone physics-based and ML methods, providing a scalable and interpretable tool for geotechnical and other engineering challenges under various environmental conditions.