A Dedicated Finite-Element Model for Analyzing Upheaval Buckling Response of Submarine Pipelines
Authors: Klever F.J. , van Helvoirt L.C. , Sluyterman A.C. 
Published: October 2008

ABSTRACT
Offshore developments, for example, in the North Sea, are showing a clear trend towards the use of satellite technology, associated with an increasing number of small-diameter pipelines and flowlines transporting multiphase fluids at high temperatures and pressures. Upheaval buckling of a pipeline at a critical foundation undulation may occur when thermal expansion is axially restrained and lateral movement is restricted (burial). Classical design of protective covers is often over-conservative. More recently, models have been developed that take realistic imperfections and theactual, non-linear response of the cover into account. However, only idealised, symmetric foundation imperfections were considered, thus rendering these models unsuitable for fitness-forpurpose assessments of actual cases. Therefore, a computer model has been developedthat takes all the relevant non-linear parameters into account, such as elastic/plastic material behaviour, axial friction and sand/clay/rock cover uplift resistance. Furthermore, both idealised imperfections and arbitrary foundation profiles are possible. In the paper the theoretical formulation will be described and results will be shown of the analysis of a characteristic North Sea pipeline using both the conventional design method and the newly developed numerical model. The effects of the most important parameters will be demonstrated and the potential benefits of using such an advanced tool illustrated. This new PC-based computer program enables the engineer to analyse the buckling response of a pipeline accurately and fairly quickly. Various design options can be assessed at different levels of complexity, as can be the analysis of fitness-forpurpose and integrity during service using condition assessment techniques.

NTRODUCTION
Offshore developments, for example, in the North Sea, are showing a clear trend towards the use of subsea completion technology and minimum facilities concepts. This trend is associated with an increasing number of small-diameter pipelines and flowlines transporting untreated hydrocarbons from deep wells into adjacent facilities. These lines may operate at high temperatures (even beyond 100°C) and pressures. Recently, several upheaval buckling failures of small-diameter flowlines that were designed for high temperatures have occurred in the North Sea, this amplifying the need for research into this phenomenon and the development of effective protective measures against it. When a pipeline, after its installation, is operated at higher than ambient temperatures and pressures, it will try to expand. If the line is not free to expand, but axially restrained by friction, the pipe will be subjected to an axial compressive load. When in such a case, at a critical foundation undulation, the force exerted by the pipe on the soil cover exceeds the vertical uplift restraint created by the pipe's submerged weight, its bending stiffness and the soil cover, the pipe will tend to move in the vertical plane (or along the trench side slope when the pipe is not covered), and considerable vertical displacements may result. This phenomenon is called upheaval buckling (offshore) or overbend instability (onshore) and shown in Fig. 1. The pipeline response (see, for example, Fig. 8) might then be unacceptable in terms of vertical displacements (the pipe protruding through the cover or moving out of the trench), excessive yielding of the pipe material, or local buckling.