Elastoplastic Analysis of Tunnels Using the Energy‐Based Physics‐Encoded Deep Learning Framework

ABSTRACT As an innovative deep learning method, physics‐informed neural networks (PINNs) have shown remarkable success across diverse science and engineering domains. However, employing physics‐informed neural networks to solve problems in geotechnical engineering, especially those involving elastoplastic mechanical behaviors, has significant challenges due to the intricate and nonlinear characteristics of geomaterials. In this work, the novel energy‐based physics‐encoded neural networks are proposed to investigate the elastoplastic mechanical responses of tunnels. The proposed deep learning method employs potential energy as the physics‐encoded loss function of the neural networks, which accelerates the training efficiency of neural networks by avoiding the use for residual‐based loss function expressed in strong form partial differential equations. To validate the effectiveness of the proposed method, we analyze the impact of activation functions and optimizers on network training and conduct a numerical analysis of a classic example with a closed‐form solution. Finally, we extend it to the excavation of small‐interval tunnel. This research contributes to improving the training efficiency of physics‐informed neural networks, and opens up new possibilities for leveraging deep learning in geotechnical engineering.