Stability of Deepwater Pipelines Under Combined Loading
Authors: Karamanos S.A. , Tassoulas J.L. 
Published: October 2008

ABSTRACT
The paper investigates the response of relatively thick tubes under external pressure and bending, using a nonlinear finite element formulation. Results from two-dimensional as well as three-dimensional analyses show good agreement with the available experimental data. A stability criterion applicable to any loading path is adopted and results for three loading paths are presented. Finally, results of three-dimensional calculations indicate that curvature reported in previous experimental studies may be an ambiguous measure of bending. Some useful suggestions are made, concerning this matter.

INTRODUCTION
This work was motivated by the design of deepwater offshore pipelines. During the installation process, pipes are subjected to both external pressure and bending that may lead to buckling. The stability analysis of relatively thick tubes under such loading is treated in this paper.
The first analytical work on pure bending of tubes is due to Brazier3 who examined the elastic case. Further work was conducted by Ades1 and Reissner and Weinitschke18, who considered the inelastic behavior of pipe material. Reissner17 was first to analyze tubes under bending and pressure.
Towards safe deep-water pipeline installation, Shell Development Company and Battelle Columbus Laboratories performed analytical and experimental investigations of the phenomenon. Results gave rise to the well-known "Shell" (Murphey and Langner15) and "Battelle" (Johns and McConnell10) formulas, widely used in offshore-pipeline design:Mathematical equations (1) and (2) (Available in full paper)
Sherman19presented extensive experimental work for a variety of D/t values and showed that for D/t less then 35, limit-moment instability, rather than bifurcation instability, controls the behavior. Stephens et al.20 reported a finite-difference treatment of the pure bending case of thin elastic tubes. Gellin9 investigated the bending of pressurized pipes using a Garerkin formulation with trigonometric functions for both limit moment and bifurcation instability. Notable analytical studies of the phenomenon were also presented by Fabkn6, who treated elastic buckling and, later, extended his formulation to include inelastic effects 7.
Extensive experimental and analytical results were reported by Kyriakides and Shaw13 and Corona and Kyriakides4,5. The experiments were small-scale tests on relatively thick aluminium and steel tubes, whereas the analytical technique made use of a Galerkin formulation with trigonometric functions. Analytical results and experimental data were found to be in good agreement. The main contribution of these papers was the observation that collapse under combined pressure and bending is sensitive to the loading path. The path dependence of pipe response was also verified in the recent work of Fowler8, who performed large-scale tests on pipes which are used in deep-water applications.
The purpose of the present study is the analytical support of concurrent experimental work at The University of Texas at Austin. The technique developed in the course of this investigation accounts for geometric and material nonlinearities, and is capable of simulating pipes of arbitrary thickness. Moreover, it permits examination of loading paths where both loading parameters are simultaneously increased (such as the radial loading case).