Physics-informed neural network for elastic–plastic mesh-free modelling of tunnelling-induced deformation

Abstract The complexity of engineering problems generally makes it challenging to obtain explicit physical formulations and sufficient monitoring data. For the issue of shallow tunnelling-induced deformation, it is difficult to obtain an explicit analytical solution due to the anisotropy of in situ stress, asymmetric free surface boundary, and complicated elastic–plastic response. Physics-informed neural networks (PINNs) have demonstrated excellent capability in resolving boundary value problems. In this context, a data-driven and physics-informed neural network is developed to predict tunnelling-induced deformation. The underlying elastic–plastic governing equations and boundary constraints of a shallow-buried tunnel are encoded into a deep neural network framework, which is divided into two independent regions according to the Mohr–Coulomb yield criterion, ensuring that constitutive relations are executed in elastic and plastic regions separately. To mitigate nonlinearity and stress concentration effects, a global adaptive sampling strategy guided by probability distributions is introduced, which ensures a more efficient approach to enforcing physics laws. Comparisons between the analytical and PINN-based solutions of deformation induced by deep tunnel excavation demonstrate the robust performance of the proposed model, especially with the implementation of a global adaptive sampling strategy. For the solution of shallow tunnelling-induced ground deformation, the adaptive PINN model can accurately reproduce the elastic–plastic ground settlement fields with sparse labelled data. The data mining and physical information exchange character of the proposed adaptive PINN model demonstrates the promising potential of the scientific machine learning method in addressing engineering issues.