A novel surrogate model for hydro-mechanical coupling in unsaturated soil with incomplete physical constraints

Abstract

Physics-informed neural networks (PINNs) are increasingly employed for surrogate modelling of soil behaviour. Existing surrogate models for unsaturated soil only account for seepage in rigid soil, neglecting the complex coupling between deformation and seepage in unsaturated soil. This study develops a new surrogate model for hydro-mechanical coupling in unsaturated soil using the PINN approach. Dimensionless governing equations, including mass balance and force balance equations, are derived and adopted for physical constraints. With absence of explicit constitutive relations, this new surrogate model utilises sparse measured data to identify pore water pressure, effective stress and deformation in unsaturated soil. Separate neural networks are employed to facilitate efficient back-propagation for coupled problem involving multiple outputs. The newly developed model is then applied to simulate two cases with sparse measurements in unsaturated soil. The results illustrate that the newly developed surrogate model successfully learns the elasto-plastic constitutive relation of suction-induced volume change from experimental data. Meanwhile, model predictions regarding both water flow and stress distribution align within the 95 % confidence interval of theoretical values, demonstrating interpretability of PINN model. Furthermore, by adhering to physical constraints, the relative error in predicting soil deformation from neural networks significantly reduces from 49 % to less than 10 %. These findings suggest PINN model with separate networks is capable to simulate unsaturated soil considering both deformation and seepage, even with sparse measured data and incomplete physical constraints.