Physics-informed extreme learning machine (PIELM) for tunnelling-induced soil–pile interactions

Physics-informed machine learning has been a promising physics-informed and data-enhanced approach in geotechnical engineering. This study proposes a physics-informed extreme learning machine (PIELM) framework for analysing tunnelling-induced soil–pile interaction. The soil–pile interaction is formulated into a fourth-order ordinary differential equation that constitutes the physics-informed component, while measured data are incorporated into PIELM as the data-enhanced component. Then, combining physics and data yields a loss vector of the extreme learning machine (ELM) network, which is trained within 1 s by the least squares method. After validating the PIELM approach by the boundary element method and finite-difference method, parametric studies are carried out to examine the effects of ELM network architecture, data-monitoring locations and numbers on the performance of PIELM. The results indicate that data-monitoring locations should be sited at positions where the gradients of pile deflections are significant, such as at the pile tip/top and near tunnelling zones. Two application examples highlight the critical role of the physics-informed and data-enhanced approach for tunnelling-induced soil–pile interaction. The proposed approach shows great potential for real-time monitoring and safety assessment of pile foundations, and benefits for intelligent early-warning systems in geotechnical engineering.