Prediction of Ultimate Bearing Capacity of Shallow Foundations Using Physically Constrained Neural Networks

In the evolving landscape of geotechnical engineering, the integration of data science has become increasingly critical for enhancing analytical capabilities, improving prediction accuracy, and optimizing design processes. This study underscores the importance of adapting machine learning (ML) models to the specific challenges of the field, particularly in terms of data scarcity and the necessity for reliable predictions. Using the bearing capacity of shallow foundations as a case study, this research demonstrates how the incorporation of domain knowledge into ML models can alleviate challenges associated with limited data availability while leveraging the inherited flexibility of ML models for high performance and reliable predictions. A novel physically informed monotonicity constraint was proposed and applied to ensure that the model predictions adhere to the fundamental principle that larger foundation areas should logically result in higher bearing capacities. A simulated data set with a limited sample size generated by Vesic’s method was used to benchmark the model performance. Results showed that both ML models, with and without the proposed monotonicity constraint, could predict well on the testing data set with an R² of 0.99. However, when applied over the entire input space, the baseline ML model without constraint showed unexpected behavior and failed to capture the nonlinear relationships between foundation area and bearing capacity despite having a high testing R² score. On the other hand, the ML model with the proposed constraint consistently adhered to geotechnical principles across the input space. This paper highlights the utility of domain-specific enhancements in ML models and advocates for their essential role in enhancing the robustness and reliability of predictive models in geotechnical engineering.