Physical Information Neural Network-Based Seepage Behavior Analysis of Earth and Rock Dams - XUE binghan; HUANG zhenhua; LEI Jianwei; FANG Hongyuan (工程科学与技术)
ObjectiveAccurate determination of key parameters in earth-rock dam seepage analysis—specifically, pore water pressure distribution and free surface position—is fundamental to ensuring reliable stability assessments and long-term safety evaluations. However, simulating seepage in earth-rock dams involves highly nonlinear free boundary problems. Traditional numerical methods encounter significant challenges, including pronounced mesh dependency, difficulties in locating the seepage exit point, and limited adaptability to heterogeneous materials. To address these limitations, this study proposes a novel seepage field solution method based on Physics-Informed Neural Networks (PINNs).MethodsThe core of the proposed method lies in transforming the free-boundary seepage problem into a fixed-boundary optimization problem. This is achieved by leveraging the inherent capability of PINNs to embed the governing differential equations, enabling weakly constrained solutions for the seepage field. Specifically, the problem domain is first discretized spatially using uniform sampling to obtain nodal coordinates. These coordinates serve as both input features and training points for the PINN. Subsequently, an initial free surface position is defined and discretized into nodal coordinates, which are incorporated into the training set. Impermeable boundary conditions are imposed on these initial free-surface nodes, while other boundaries are assigned conditions according to the physical model. This fixation of the initial free-surface position effectively converts the movable boundary problem into a fixed-boundary formulation. Solving this fixed-boundary seepage field with the PINN yields the full field distribution, including hydraulic head values at free-surface nodes. The convergence error is computed based on hydraulic head values from two successive iterations at these nodes. Suppose the solution fails to meet preset convergence criteria. In that case, the free-surface nodal positions are updated using computational results (e.g., hydraulic head values or related criteria), with corresponding adjustments to the impermeable boundary conditions. The PINN resolution is then repeated. This iterative process continues until convergence in the free-surface position is achieved, ultimately determining the steady-state seepage field.Results and Discussions　To validate the effectiveness of the proposed algorithm, a homogeneous rectangular earth dam (10 m×10 m) with upstream and downstream water levels of 10 m and 2 m, respectively, and an impermeable bottom boundary is selected as the study case. After five iterations, the computed free surface demonstrates significant convergence: the mean square error (MSE) between the initial and first-iteration free surfaces is 0.10303, while the MSE between the fourth and fifth iterations reduces to 0.00105, indicating stable convergence toward the theoretical solution. Systematic comparison with existing studies reveals that: 1) the free surface position obtained by the present method exhibits high consistency with other approaches; 2) equipotential lines within the dam body display characteristic layered distribution with normal gradients strictly corresponding to the upstream-downstream head difference; 3) pore water pressure above the phreatic surface follows a nonlinear decay pattern, where zero-pressure contours align precisely with the free surface position. These results collectively verify the algorithm's accuracy. Further validation is performed using a classic earth-rock dam case study under both homogeneous and heterogeneous conditions. For the homogeneous case, the computed seepage exit point (8.401 m) shows merely 3.7% relative error relative to experimental measurements, representing a significant accuracy improvement (>45%) over literature-reported values. Moreover, maximum relative deviations at other characteristic free-surface locations remain below 3%, demonstrating the algorithm's high precision throughout the computational domain. Under heterogeneous conditions, the equipotential lines exhibit distinct upstream tilting characteristics, with tilt angles strictly governed by the permeability anisotropy ratio. The distribution patterns align with established literature, confirming the algorithm's capability to effectively handle material heterogeneity and accurately capture permeability anisotropy effects on seepage field distribution.ConclusionsThe results demonstrate that the proposed algorithm achieves significantly enhanced precision in locating the seepage escape point. Furthermore, for complex earth-rock dam problems involving non-homogeneous materials, the algorithm maintains stable solutions with high accuracy, confirming its adaptability to intricate engineering challenges. As a meshless method, the algorithm operates directly on training set sample points, effectively circumventing the mesh quality sensitivity inherent in traditional numerical approaches. More importantly, it requires only a single discretization of the problem domain, eliminating the need for dynamic adjustment of meshes or sampling points during iterations—a necessity in methods like moving mesh techniques. This substantially enhances computational efficiency.