耦合物理约束与深度学习的断层作用下管道力学响应求解改进方法

An improved method for solving mechanical responses of pipelines under fault displacement by coupling physical constraints and deep learning

  • 摘要:
    目的 走滑断层引起的永久性地面位移是埋地油气管道的重要威胁,会导致局部变形并可能引发拉伸断裂或屈曲破坏,从而严重威胁管道结构安全。因此,准确预测走滑断层作用下的管道变形至关重要,然而现有解析方法难以充分描述管土非线性相互作用与管材弹塑性行为,有限元方法建模复杂度高,难以有效兼顾计算精度与计算效率。
    方法 构建了一种基于物理信息神经网络(Physics-Informed Neural Network, PINN)模型的走滑断层作用下管道变形求解方法:搭建深度神经网络(Deep Neural Network, DNN)模型,建立管道轴向位移与侧向位移在管道轴向空间坐标下的映射关系;基于虚功原理与格林-拉格朗日应变,结合非线性土弹簧模型模拟管道与土壤的轴向及侧向非线性相互作用,采用线性强化本构模型表征管材的非线性特征,构建走滑断层作用下管道变形的物理信息损失函数;结合断层作用下的管道力学特征,并通过迪利克雷边界条件建立边界条件损失函数,实现受走滑断层作用管道变形的高精度预测。
    结果 以某穿越走滑断层区管径为1016 mm管道为例,对比穿越角为30° 、45° 、60° 、75° 及90° ,且走滑断层位移为2.5 m下PINN模型计算结果与有限元计算结果,发现PINN模型与有限元计算结果具有较高的一致性,PINN模型计算得到的管道轴向位移与侧向位移的均方误差范围分别为3.82×10−7~1.85×10−6与1.73×10−6~6.18×10−6, PINN模型计算结果求解管道轴向拉伸应变与轴向弯曲应变的均方误差范围分别为1.20×10−10~6.06×10−9与8.01×10−10~2.73×10−8。进一步扩展工况,对比国际典型走滑断层作用下管道应变峰值求解方法,结果表明在不同的载荷条件下PINN模型与有限元方法求解应变峰值保持一致,平均相对误差仅为2.88%,显著优于其他应变峰值求解方法。
    结论 PINN模型在计算效率、计算准确性方面有着显著的优势,为断层作用下管道完整性评价提供了一种新方法。

     

    Abstract:
    Objective Permanent ground displacement from strike-slip faults poses a serious threat to buried oil and gas pipelines. It can induce local plastic deformation that leads to tensile fracture or buckling failure, thereby compromising pipeline structural integrity. Accurate prediction of pipeline deformation under strike-slip fault displacement is therefore essential. Existing analytical methods struggle to capture the nonlinear interaction between pipelines and surrounding soil and the elastic–plastic behavior of the pipes. Finite element modeling (FEM) is complex and often fails to strike an effective balance between computational accuracy and efficiency.
    Methods Taking into account shortcomings of previous research, a method for solving pipeline deformation under strike-slip fault displacement based on a Physics-Informed Neural Network (PINN) is proposed. A Deep Neural Network (DNN) is constructed to map axial and lateral pipeline displacements within the axial spatial coordinates of pipelines. Using the principle of virtual work and the Green–Lagrange strain measure, a nonlinear soilspring model simulates axial and lateral nonlinear interactions between pipelines and the surrounding soil, while a linear-hardening constitutive model characterizes the pipe’s nonlinear material behavior. A physics-informed loss function is formulated to express pipeline deformation under strike-slip fault displacement. A boundary condition loss function is established, further integrating mechanical characteristics of pipelines under fault displacement and enforcing Dirichlet boundary conditions. The combined formulation enables high-precision prediction of pipeline deformation under strike-slip fault displacement.
    Results In a case study based on a 1,016 mm pipeline section crossing a strike-slip fault zone, the PINN calculation results for crossing angles of 30°, 45°, 60°, 75°, and 90° under a fault displacement of 2.5 m were compared with the reference values from FEM calculations and found to be closely aligned. Subsequent quantitative error analysis yielded the following ranges of mean squared errors (MSE) for the PINN calculations: 3.82×10−7–1.85×10−6 for axial displacement and 1.73×10−6–6.18×10−6 for lateral displacement. For strain metrics derived from the PINN results, the axial tensile-strain MSE ranged from 1.20×10−10–6.06×10−9, and axial bending-strain MSE ranged from 8.01×10−10–2.73×10−8. To broaden the comparison conditions, comparisons were also made with international representative methods for solving peak pipeline strain under strike-slip fault displacement. Results showed that the PINN results remained consistent with the FEM results under different load conditions, with an average relative error of 2.88%, demonstrating its significant superiority to other methods for solving peak strain.
    Conclusion The proposed PINN method exhibits significant advantages in computational efficiency and accuracy, providing a new approach to maintaining pipeline structural integrity under fault displacement.

     

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