Deflection of foundation pit retaining wall in heterogeneous soil strata: Intelligent prediction methods based on physics-informed machine learning

Excavation-induced retaining wall deflection (RWD) significantly influences the safety of surrounding built environment. To predict the three-dimensional RWD in heterogeneous strata, a new partial differential equation (PDE) is derived in this study, and two prediction models are proposed, i.e. the physics-informed neural network (PINN) model and the data-driven PINN model. As a physical constraint, the new PDE is crucial to the loss functions of these models. Then, the validity of the models is verified and analysed using a subway deep-foundation pit. The results show that the training times of both models are controlled within 900 s, which is a significant reduction compared to that of the conventional numerical model. In addition, the prediction accuracy of the data-driven PINN model is higher than that of the numerical model, while that of the PINN model is slightly lower than that of the numerical simulation. However, in contrast to the data-driven PINN model, the PINN model can identify irregular soil interfaces in heterogeneous strata to learn the deflection continuity conditions at irregular interfaces and realize RWD prediction in non-uniform distributed strata. In practical applications in foundation pit engineering, the selection of the PINN and data-driven PINN models can be conducted according to the in situ distribution conditions of the strata to enable the early prediction of potential RWD, thereby providing a reliable basis for the further optimisation of retaining structures design.