| 摘要: |
| 针对有限点位参考信息条件下土石坝压力水头场和等效渗透系数场连续重构困难，以及复杂材料分区饱和渗透参数难以稳定表征的问题，构建了一种基于物理信息神经网络的二维饱和-非饱和稳态渗流分析框架。框架以计算域坐标为输入，以压力水头和当前水力状态下的等效渗透系数为输出，将渗流控制方程、边界条件与有限点位参考数据共同纳入损失函数，实现压力水头场和等效渗透系数场的连续重构；在此基础上，结合非饱和渗透关系对材料分区饱和渗透系数进行反算与统计表征。以均质坝算例和复杂工程断面算例进行验证，并采用相同工况下的有限元稳态渗流结果构造有限监督样本和全域评价基准。结果表明，物理约束能够提高模型在未参与监督区域的空间泛化能力，且小样本条件下优势更为明显。均质坝典型工况中，PINNs全域最大压力水头误差为0.597 m，明显低于纯数据驱动模型的2.726 m。工程断面验证中，模型能够复现复杂防渗体系、多材料分区及坝体-坝基耦合条件下的主体压力水头分布，96.07%的全域参考节点压力水头误差位于±0.2 m范围内；除混凝土防渗墙外，主要材料分区反算饱和渗透系数中位数与参考值之比约为0.95~1.10。研究表明，所构建框架可为有限点位参考信息条件下土石坝渗流状态场重构和区域渗透参数表征提供有效方法。 |
| 关键词: 土石坝 饱和-非饱和渗流 物理信息神经网络 渗流场重构 等效渗透系数识别 |
| DOI： |
| 分类号:TV641 |
| 基金项目:2025年度浙江省水利工程带科研“揭榜挂帅”项目(RA+202506) |
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| Physics and Data Driven Analysis of Seepage Behavior in Earth-Rock Dams |
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FAN Zhendong1, XIA Hanqiu2, JIN Hongjie1, HE Yong3, YANG Lei1
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1.Power China Huadong Engineering Corporation Limited,Zhejiang Hangzhou;2.College of WaterResources and Hydropower Engineering,Hohai University,Jiangsu Nanjing;3.Hangzhou Reservoir Management Service Center,Zhejiang Hangzhou
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| Abstract: |
| This study addresses the challenge of reconstructing continuous seepage-state fields and characterizing regional seepage parameters for earth-rock dams when only sparse pointwise reference data are available. A physics data driven framework is developed for two dimensional steady saturated unsaturated seepage analysis based on physics informed neural networks (PINNs). The network takes spatial coordinates within the computational domain as inputs and outputs two coupled quantities: the pressure head and the effective hydraulic conductivity under the current hydraulic state. The loss function simultaneously incorporates the seepage governing equation, hydraulic boundary conditions, and limited reference data, thereby constraining field reconstruction by both physical consistency and reference information. A distinctive feature of this framework is the explicit separation between effective hydraulic conductivity and the intrinsic saturated hydraulic conductivity of dam materials. Rather than directly outputting saturated hydraulic conductivity, the model first reconstructs the effective conductivity field required by the seepage equation, and then statistically infers the saturated conductivity of each material zone by combining the predicted pressure head with a prescribed unsaturated permeability function. In this manner, field reconstruction and regional parameter characterization are integrated into a single coherent procedure.
The proposed framework is validated against both a homogeneous dam benchmark and a complex engineering cross section, using finite element steady seepage solutions to generate reference samples and provide full domain evaluation benchmarks. In the homogeneous dam case, the PINNs based model and a purely data driven neural network are trained with identical architecture, reference points, and hyperparameters, allowing the contribution of physical constraints to be isolated. Results demonstrate that the physics data driven model is less sensitive to sparse reference data and yields more stable predictions in unobserved regions. For the representative case with 20 reference points, the maximum full domain pressure head error of the PINNs model is 0.597 m, substantially lower than the 2.726 m obtained by the data driven counterpart. The reconstructed phreatic surface also exhibits better agreement with the finite element benchmark, with the vertical coordinate RMSE reduced from 0.148 1 m (DNN) to 0.030 4 m (PINNs). Error frequency statistics further reveal that PINNs errors are more concentrated around zero and exhibit fewer large error tails for both pressure head and effective hydraulic conductivity. These findings confirm that the embedded governing equation and boundary conditions serve as effective regularization terms under limited data, enhancing spatial generalization beyond mere fitting of supervised points.
The framework is then extended to a complex engineering section featuring an anti seepage wall, multiple material zones, and dam foundation coupling. This section poses a more demanding test, as material hydraulic conductivities span several orders of magnitude and thin low permeability structures introduce sharp hydraulic gradients. Results indicate that increasing the number of reference points from 50 to 400 rapidly reduces the full domain pressure head RMSE, after which further improvement gradually plateaus. In the representative case selected for detailed analysis, the model reproduces the main pressure head distribution and captures the dominant head loss around the anti seepage system. Approximately 96.07% of the full domain reference nodes have pressure head errors within ±0.2 m, and the RMSE of the reconstructed phreatic line elevation is 0.181 5 m. The residual larger errors are spatially localized near the concrete anti seepage wall and the upstream core wall top, corresponding to thin low permeability layers and high gradient regions, which highlights that interface resolution and sampling coverage remain critical for practical engineering applications.
For regional saturated hydraulic conductivity characterization, the inferred median values for the main saturated or near saturated material zones are generally consistent with the reference values. Except for the concrete anti seepage wall, the ratio between the inferred median and the reference saturated conductivity falls within approximately 0.95~1.10, demonstrating that the method can identify order of magnitude differences in seepage capacity across material zones. The concrete anti seepage wall yields a higher inferred value, primarily because its small geometric scale, strong conductivity contrast, and localized pressure head errors amplify the uncertainty in back calculation. Overall, the proposed PINNs based physics data driven framework offers an effective pathway for reconstructing pressure head fields, identifying effective hydraulic conductivity distributions, and characterizing regional saturated hydraulic conductivity under finite point information. |
| Key words: earth-rock dam saturated-unsaturated seepage physics-informed neural network seepage field reconstruction equivalent permeability coefficient identification |
