Research on Safety of Pipelines with Defects in Frozen Soil Regions Based on PDE

Buried pipelines in permafrost areas are affected by harsh environments, especially those with defects and damages, which are prone to failure or even leakage accidents. However, current research is limited to single-factor analysis and fails to comprehensively consider the interaction relationships among temperature fields, moisture fields, and stress fields. Therefore, based on the thermodynamic equilibrium equation and the ice–water phase transition theory, this paper constructs the temperature field equation including the latent heat of phase transition, the water field equation considering the migration of unfrozen water, and the elastoplastic stress field equation. A numerical model of the heat–water–force three-field coupling is established to systematically study the influence laws of key parameters such as burial depth, water content, pipe diameter, and wall thickness on the strain distribution of pipelines with defects. The numerical simulation results show that the moisture content has the most significant influence on the stress of pipelines. Pipelines with defects are more prone to damage under the action of freeze–thaw cycles. Based on data analysis, the safety criteria for pipelines were designed, the strain response surface function of pipelines was constructed, and the simulation was verified through experiments. It was concluded that the response surface function has good predictability, with a prediction accuracy of over 90%.