A deep learning physics-informed neural network (PINN) for predicting drilled shaft axial capacity

Accurately estimating the axial capacity of drilled shafts remains a persistent challenge in geotechnical engineering, as evidenced by significant discrepancies between measured load-test results and theoretical predictions. To bridge this gap, a novel Deep Learning–Physics-Informed Neural Network (DL-PINN) framework is proposed. Employing Meyerhof's bearing capacity equations as a physics-based constraint, the developed PINN integrated soil and geometric parameters directly into its training loss function. By combining these first-principles relationships with empirical data, the model preserved fundamental geotechnical mechanisms while refining predictive accuracy through dynamic weight adjustments between data-driven and physics-based loss components. Comparative experiments with a standard artificial neural network (ANN), using a dataset derived from the loaded-to-failure in-situ pile test and subsequent numerical simulations, demonstrated that although the ANN may attain lower statistical errors, the PINN's adherence to physical laws yields predictions that better align with established geotechnical behavior. This balance between physics fidelity and data adaptability may nominate these PINN frameworks to address the “black box” nature of deep learning in geotechnical applications. The paper also suggested the future research needs to fulfill the scientific and practical gap.