On The Dynamics And The Arrest Of The Propagating Buckle In Offshore Pipelines
Authors: Kyriakides S. , Babcock C.D. 
Published: October 2008

ABSTRACT
An investigation has been carried out in an effort to understand the dynamics of a propagating buckle and to find a basis for designing efficient and effective arresting devices. The velocity of propagation was measured as a function of diameter to thickness ratio and pressure, Tests were carried out in different pressure media. It was found that the propagation velocity is affected by the pressurizing medium used as well as the pressure. It was also found that for buckles "initiated" near the buckling pressure a unique "flip-flop" mode occurs. Quasistatic buckle arrest experiments were carried out to determine the parametric dependence of the pressure at which "slowly" propagating buckles penetrate the arrestors.

INTRODUCTION
The propagating buckle is one of the new problems that has appeared as a result of the increased interest in offshore natural resources. The problem can occur during offshore pipelaying operations when the pipe is under combinations of loads such as external pressure and bending moment. A local buckling initiated by these loads can propagate down the pipeline if the external pressure is above a critical pressure known as the propagation pressure. This phenomenon was first discovered and studied by Mesloh, Johns and Sorenson at Battelle. Their studies resulted in an empirical expression for the propagation pressure as a function of the pipe material and dimensions as well as tests on various buckle arrestor designs. Work on buckling interaction was also carried out.
From these results it became clear that the design of deepwater pipelines could be seriously affected by the propagating buckle phenomenon since the propagation pressure is much lower than the buckling pressure of the pipe (Pc). The buckling pressure is proportional to Young's Modulus, E, and the propagation pressure is proportional to yield stress. The ratio of these two pressures depends on the yield strain. This is shown in Fig. 1 as a function of the diameter to thickness ratio.
The propagating buckle profile takes the form of a transition from a circle to a dog bone type shape. This is depicted along with the parameters of the problem in Fig, 2 and an actual buckle is shown in Fig. 3. The final collapse shape depends upon the pressure and the length of the transition section, L, depends upon the velocity of propagation, U, as will be discussed in subsequent sections. The dependence of velocity on the pressurizing medium was the primary motivation for the present work. This dependence was ignored in previous investigations and it will be shown that this leads to considerable errors in velocity.
Once the consequences of a propagating buckle were fully understood, the focus of attention shifted to the problem of arrest. Buckle arrestors similar to previously devised crack arrestors were proposed and studied by Battelle. This was done on an empirical basis and design parameters were not clearly defined. In an effort to elucidate these parameters, one of the arrestor designs proposed by Batelle has been studied experimentally in greater detail.