Physics-Informed Neural Networks (PINNs) have shown considerable potential in solving both forward and inverse problems governed by partial differential equations (PDEs) for a wide range of practical applications. This study leverages PINNs for modeling nonlinear large-strain consolidation of soft soil, including creep behavior. The inherent material and geometric nonlinearities associated with soft soil consolidation pose challenges for PINNs, including precision and computational efficiency. To address these issues, we introduce self-adaptive physics-informed neural networks (SA-PINNs), featuring an adaptive loss function weighting and a slope scaling method for the activation functions. Additionally, a sensitivity analysis exploring the influence of monitoring data on the parameter inversion accuracy is presented. Two engineering case studies are used to benchmark the settlement prediction capabilities of the present SA-PINN method with traditional techniques, demonstrating the superior prediction accuracy and consistency of the SA-PINN approach. The findings highlight the significant potential of SA-PINN in practical geotechnical engineering problems.

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.

An approach based on a Physics-Informed Neural Network (PINN) is introduced to tackle the two-dimensional (2D) rheological consolidation problem in the soil surrounding twin tunnels with different cross-sections, under exponentially time-growing drainage boundary. The rheological properties of the soil are modelled using a generalized viscoelastic Voigt model. An enhanced PINN-based solution is proposed to overcome the limitation of traditional PINNs in solving integral-differential equations (IDEs) equations. In particular, two key elements are introduced. First, a normalization method is employed for the spatio-temporal coordinates, to convert the IDEs governing the consolidation problem into conditions characterized by unit-duration time and unit-area geometric domain. Second, a conversion method for integral operators containing function derivatives is devised to further transform the IDEs into a set of second-order constant-coefficient homogeneous linear partial differential equations (PDEs). By using the TensorFlow framework, a series of PINN-based models is developed, incorporating the residual adaptive sampling method to address the 2D consolidation equations of soft soils surrounding tunnels with different burial depths and cross-sections. Comparative analyses between the PINNbased solutions, and either finite element or analytical solutions highlight that the aforementioned normalization stage empowers PINNs to solve the PDEs across different spatial and temporal scales. The integral operator transformation method facilitates the utilization of PINNs for solving intricate IDEs.

Hydromechanical behaviour of unsaturated expansive soils is complex, and current constitutive models failed to accurately reproduce it. Different from conventional modelling, this study proposes a novel physics-informed neural networks (PINN)-based model utilising long short-term memory as the baseline algorithm and incorporating a physical constraint (water retention) to modify the loss function. Firstly, a series of laboratory tests on Zaoyang expansive clay, including wetting and drying cycle tests and triaxial tests, was compiled into a dataset and subsequently fed into the PINN-based model. Subsequently, a specific equation representing the soil water retention curve (SWRC) for expansive clay was derived by accounting for the influence of the void ratio, which was integrated into the PINN-based model as a physical law. The ultimate predictions from the PINN-based model are compared with experimental data of unsaturated expansive clay with excellent agreement. This study demonstrates the capability of the proposed PINN in modelling the hydromechanical response of unsaturated soils and provides an innovative approach to establish constitutive models in the unsaturated soil mechanics field.