Stochastic longitudinal model of buried pipelines considering soil spatial variability and void geometric uncertainty

Buried pipelines are subjected to complex geological environments and thermo-mechanical loads, which threaten their longitudinal stability. This research study establishes a stochastic analytical model for longitudinal pipe–soil interaction under multi-source uncertainties. To capture soil heterogeneity, one-dimensional random field theory is used to characterise the spatial variability of the soil elastic modulus. Concurrently, specific probability distributions are introduced to define the geometric uncertainty of local soil voids. The framework rigorously incorporates thermal loads, internal operating pressures, and localised pipe–soil detachment. Monte Carlo simulation is then employed to evaluate the probabilistic displacement and stress responses. The proposed model is validated by degenerating the stochastic framework into deterministic scenarios and comparing the results against classical thermo-mechanical Winkler solutions. Further parametric analyses reveal a nonlinear coupling between material randomness and geometric uncertainty. First, void geometry dictates the overall response magnitude. As a void extends, the pipeline exhibits an inverse pattern: peak displacement increases greatly owing to support loss, whereas peak stress decreases owing to stress relaxation. Second, the coefficient of variation of the soil acts as the primary driver of extreme risks. High soil spatial variability minimally affects the mean response but significantly broadens the distribution range and elevates the 95th percentile. Finally, a dominance shift mechanism determines the variable that exerts greater influence on the structural response. For short voids, the structural response is highly sensitive to soil spatial variability. However, as void length increases, geometric uncertainty completely eclipses material randomness. These insights identify critical hazard combinations, providing a robust theoretical basis for the risk assessment and preventive maintenance of pipelines.