A Physics-Informed Deep Learning Approach Using Different Free Surface Approximation Strategies for Steady Seepage in Dams

Investigating soil seepage considering free surface conditions under complex geological conditions is of great significance to ensure the safety of dams. In recent years, physics-informed deep learning (PINN) has become a cross-disciplinary hotspot for solving forward and inverse problems based on partial differential equations. However, the challenges in free surface simulation have confined the majority of current PINN research to seepage problems under fixed boundary conditions. To address the above issues, we propose a physics-informed deep learning-based approach for steady seepage in dams. In the proposed method, two different free surface approximation strategies are introduced to accommodate varying boundary conditions in the dam seepage problem. The first strategy approximates the free boundary by sampling points, while the second strategy approximates the free boundaries by an additional deep neural network. To validate the proposed methods, three benchmark cases with different boundary conditions have been conducted. The results indicate that the proposed approach effectively simulates steady seepage in dams. Both point-sampling and deep neural network-based free surface approximation strategies demonstrate high accuracy in predicting the location of the phreatic surface and the discharge of the seepage. Specifically, the prediction results are comparable in accuracy to analytical solutions and advanced numerical simulation methods.