Finite Element Analysis of Propagating Buckles in Deepwater Pipelines
Authors: Tassoulas J.L. , Katsounas A.T. , Song H-W. 
Published: October 2008

ABSTRACT
The paper presents a technique for the analysis of propagating buckles in deep-water pipelines. The development is based on the finite element method and takes into account the large deformation of the pipe, the elastoplastic behavior of the pipe material and the contact between regions of the interior wall of the pipe during buckle propagation. The results of the technique are in excellent agreement with experimental data. The propagation pressure, i.e., the minimum pressure required for buckle propagation, as calculated by the technique, is within 1% of the measured value. Perhaps, more interesting are the results with respect to the state of deformation and stress due to the propagating buckle. The indications are that the deformation in the tail of the propagating buckle is not nearly that ofa collapsed elastoplastic ring in plane strain, as believed in earlier analytical work. Furthermore, the pipe material undergoes considerable unloading and reloading in the course of buckle propagation.

INTRODUCTION
The phenomenon known as the propagating buckle is of critical significance in the design of pipelines subjected to external pressure, e.g., pipelines for offshore oil production. Its most common occurrence is during pipe-laying operations. The pipe is usually paid off a barge and is subjected to substantial bending, while under external pressure and axial force. The tension necessary for this operation is supplied and controlled by equipment on the barge. In the segment of the pipe near the seafloor, known as the sag bend, where the curvature reaches its maximum, the combination of bending moment, external pressure and axial force may become critical, as a result, for example, of inadequate tension, and local damage may occur. If the external pressure is sufficiently high, this local damage may be transformed into a characteristic mode of deformation which travels along the pipe causing collapse of a long segment. The propagation is terminated when the deformation enters a region where the external pressure is below the minimum level required, or, upon encountering an arrestor, usually a stiffening ring, on the pipe. This mode of deformation is known as the propagating buckle, a term apparently coined by Mesloh et al1 who first observed the phenomenon.
The minimum level of external pressure required for buckle propagation is referred to as the propagation pressure and most experimental studies to date have sought to determine its value for the pipes most widely used in practice and develop empirical formulas for practical use, e.g., Mesloh and Sorenson2 and Kyriakides and Babcock3Several analytical studies have been conducted as well. Palmer and Martin4 were first to derive an estimate of the propagation pressure, on the basis of the collapse analysis of an inxtensional ring of rigid-perfectly-plastic material. The deformation of a ring in plane strain, subjected to external pressure, at least at first glance, appears to be almost identical to that of a short segment of the pipe during passage of the propagating buckle.