# Local buckling collapse of marine pipelines

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## Abstract

To keep up with the growing demand for oil and gas, the oil and gas industry ventures into deeper waters. For a deep water pipeline project, South Stream, a pipeline test program is developed. Part of this program is the investigation of the resistance of an externally pressurised pipeline against local buckling collapse. This is a decisive factor in design of marine pipelines. Local buckling of a pipeline is the buckling behaviour within its cross section. Buckling is defined as the state of a structure for which a relatively small increment in load leads to a relatively large increment in displacement. Generally this is reflected in a change in deformation shape and possibly a loss of stability. A perturbation theory, first developed by Koiter [1], is applied to model this behaviour. The response of a geometrically imperfect structure is obtained by using the response of an initially perfect structure, e.g. a straight beam or a perfect ring. From the principle of minimum potential energy an equilibrium state can be obtained. For a certain load, the bifurcation load, multiple equilibrium configurations are possible. The nature of this equilibrium state is investigated by expanding the load around this bifurcation load and expanding the displacement functions around their fundamental solutions. The value and sign of the post-bifurcation load coefficients determine the system’s initial post-bifurcation stability. Introduction of initial imperfections leads to modified post-bifurcation load coefficients. Generality is enhanced by using dimensionless identities. System collapse can occur in the elastic domain for unstable initial post-buckling behaviour or in the plastic domain due to material yielding. It is likely that collapse of a system with (small) initial geometric imperfections occurs due to an interaction of elastic and plastic buckling. Buckling leads to relatively large displacements that induce material yielding. This can lead to loss of stiffness and can induce collapse. Relatively thin walled rings and cylinders tend to collapse more in the elastic domain, while relatively thick walled rings and cylinders tend to collapse more in the plastic domain. This is due to the fact that thin walled structures require more deformation to induce yielding than thick walled structures. When performing a collapse test, end caps are attached to a pipeline specimen. This is modelled by boundary constraints. End caps are very stiff and modelled as being rigid. Their influence on the bifurcation and collapse behaviour of a cylinder is investigated. The constraints introduce boundary layer behaviour in the regions close the end caps. It is found that these constraints increase the buckling load of a cylinder with respect to an infinitely long cylinder (ring under plane strain condition). Besides, for relatively short cylinders, the buckling mode is altered. While a long cylinder prefers to collapse in an oval shape mode (described by 2 lobes), a short cylinder prefers to collapse in a mode shape described by a higher number of lobes. A collapse test is performed to estimate the collapse behaviour of a real life pipeline. Hence it is required that the collapse shape that is observed in the test matches the oval collapse shape of a long real life pipeline. This results to a minimum required length of a tested pipeline specimen. A relation for the required length is obtained. An analytical method has been developed to determine the buckling load and mode of a constrained cylinder. Finally, the analytically obtained results have been verified using finite element analysis (FEA) and experimental results obtained from literature. [1] W.T. Koiter. Over de stabiliteit van het elastisch evenwicht. PhD Thesis, TH Delft, 1945