Buried pipelines with bends: Analytical verification against permanent ground displacements

Available analytical methodologies for the stress analysis of buried pipelines against large permanent ground displacements (PGDs) apply only to straight pipeline segments. Hence, a new methodology is proposed herein for the analytical computation of pipeline strains in bends of arbitrary angle and radius of curvature, located outside the PGD high-curvature zone, but within the pipeline’s unanchored length. The methodology is based on the equivalent-linear analysis of the bend, assuming that it will perform as an elastic arched beam subjected to uniformly distributed ultimate axial and transverse horizontal soil reactions. The end of the bend towards the PGD zone is subjected to an axial displacement, calculated on the basis of overall displacement compatibility along the pipeline, while the other end is restrained by the unanchored pipeline segment beyond the bend. Using this approach, the maximum axial force at the vicinity of the PGD zone can also be calculated and consequently used for the estimation of corresponding pipeline strains with any of the available numerical or analytical methodologies for straight pipeline segments. Parametric nonlinear finite element analyses are performed to verify the analytical methodology and also derive conclusions of practical interest regarding the effect of bends on pipeline design.