Pipeline element for upheaval buckling analysis of submarine pipelines with geometric-imperfections under high temperature high pressure

Submarine pipeline is used for transporting oil from wells to resource storage facilities. The oil inside the pipeline is heated and pressured for long-distance transportation, making the pipeline under high temperature and high pressure (HTHP). The pipeline is usually placed inside a trench where surrounding soil restraints its longitudinal expansion. The pipeline is not perfectly straight, but with geometric imperfections, so the upheaval buckling may be triggered when the accumulated compression force has reached its buckling strength. It is not easy to conduct a geometrically nonlinear analysis for the pipeline because of the nonlinear soil–pipeline interactions (SPIs). This paper proposes a new line element aiming for the geometrically nonlinear large deformation analysis of the pipeline under HTHP. The axial expansion force due to high working temperature and pressure is included in the element formulation. Furthermore, a Gauss–Legendre integral method is employed to consider continuously distributed nonlinear SPIs in both lateral and longitudinal directions. Since the pipeline might exhibit large deflections, the analysis adopts the Updated-Lagrangian approach to establish the equilibrium conditions. A Newton–Raphson procedure is developed to execute the analysis. Detailed element formulations are given. Six groups of examples are provided to examine the robustness of the numerical method.