3D finite element–based meta-models for evaluating the structural response of buried steel pipelines under Gaussian-shaped localized subsidence

This article investigates the vulnerability of buried steel gas pipelines subjected to Gaussian-shaped localized subsidence in cohesionless sands (c = 0). The study aims to assess both (i) the transmission of free-field ground curvature to the pipeline and (ii) the resulting structural responses. In this context, a comprehensive parametric investigation involving 1080 three-dimensional finite element simulations is conducted using PLAXIS 3D, covering wide ranges of sand stiffness and strength parameters, pipeline geometries, burial conditions, and subsidence-profile characteristics. A surrogate model (named meta-model) is developed to predict curvature transmission using a dimensionless relative stiffness coefficient R*. The regression formulation achieves a high coefficient of determination (R² = 0.9884) with a low residual standard deviation (σ = 0.0211). Validation against centrifuge and full-scale experimental datasets from literature supports the robustness of the model, while comparisons with existing meta-models from the literature position the present 3D-based formulation with respect to earlier simplified approaches. Three additional meta-models are developed to predict: (i) the peak axial stress, (ii) the maximum shear stress, and (iii) the cross-sectional ovalisation. These models show strong agreement with numerical results (R² > 0.88, mean relative error below 14%), enabling rapid predictions without further finite element analyses. Finally, a probabilistic application demonstrates how the framework can be embedded within a reliability-based approach, supporting the assessment of structural integrity and the prevention of failure in buried pipelines under Gaussian-shaped localized subsidence.