An analytical solution has been presented for the vertical buckling of submarine pipelines laid on seabed with initial stress-free geometric out-of-straightness of arbitrary shape. The arbitrary imperfection shape as well as the deflection in the buckled portion is expressed in terms of Fourier series. The coefficients of the Fourier terms for the deflection under the action of axial force and submerged weight are obtained through energy principles. The relation between the compressive forces in the buckled portion and far away from it are obtained using both constant and deformation dependent friction models for axial friction at the pipeline-seabed interface. The obtained series solution is found to yield the same results as the classical exact solution of governing differential equations for a perfect (zero imperfection) pipeline. Numerical results are presented to illustrate the effects of the magnitude and the shape of initial imperfections on the instability temperature and the post buckling equilibrium path of imperfect pipelines. The maximum deflections and the stresses associated with the post-buckling states are also determined. The effects of the nature and the magnitude of axial friction on the buckling characteristics are investigated.
In-service buckling of submarine pipelines under the action of axial compressive forces has received significant attention in recent years in view of their increasing economic importance and high repercussions of any failure during service. Such failures are even more unwanted in case of deeper water because of the difficulty and high cost involved in the rectification works in deep sea. Axial compression can build up in pipelines laid on sea bed as the longitudinal expansions due to temperature and internal pressure changes are constrained by the frictional resistance developed in the pipe-soil interface.
