Continuum FE Modeling of Lateral Buckling
Authors: Yu S. , Konuk I. 
Published: October 2008

Abstract
Results from a 2D continuum Finite Element (FE) model illustrate that the soil-pipe interaction process involved in lateral buckling is a chaotic process which is mainly governed by the soil properties, the pipe diameter as well as the pipe weight or the vertical force. The 3D model developed for snake lay and zigzag configurations show that the pipe responds in a three dimensional geometry (helix like) resulting with soil berms of varying height and size on both sides of the pipe.

Introduction
In recent years, design approaches promoting lateral buckling to overcome thermal expansion stresses for the elevated temperature pipelines have become popular [1, 2, 3]. Three major approaches to achieve this objective are laying pipe into a snake like geometry, placing sleepers under the pipe at certain intervals, and varying submerged pipe weight by the help of distributed buoyancy elements. These design approaches are motivated by the expectation that buckling response can be controlled by the as-build pipe geometry. As discussed in Cardoso et al. [1] and Bruton et al. [2, 3], in all three approaches, modeling of soil-pipe interaction is the biggest challenge in the prediction of the response of a pipeline laid exposed on the seabed. It is now recognized that simple Coulomb friction concept is inadequate to represent this process. This is due to two main interrelated processes. Firstly, the pipe penetrates into the seabed soil when it is placed on the seabed. The magnitude of the initial pipe penetration may vary depending on the soil properties, the pipe characteristics and the installation method. Secondly, when the pipe moves laterally, some of the soil is removed from the seabed forming a berm on the front face of the pipe. Repeated cyclic pipe movements result with progressive soil berms on both sides of the pipe. The resulting process is a highly nonlinear and path dependent process where the pipe response controls the berm configurations and the soil deformations, and the berms, in return, influence the pipe lateral and vertical displacements all along the pipe axis.
The complexity of this process was recognized by Cardoso [1] and Bruton [2]. However, the tendency to utilize Winkler models required these authors to simplify this complex process in several ways. The Winkler models require that the soil foundation be represented by a series of springs, rods, or Coulomb interfaces which react independently along the pipe length.
Figure 1 - Illustration of the buckling process. (available in full paper)
In reality, there is no inherent justification that this complex soil-pipe interaction process can be reduced to a Winkler like model. The Appendix A provides a simple example problem which illustrates that Winkler models do not necessarily lead to a correct solution for the soil-structure interaction problems. As a matter of fact, during the lateral buckling process, the soil-pipe interaction forces will depend on the initial penetration and the progressive formation of the soil berms resulting with different response at different cycles. In addition, there is no reason to assume that the initial penetration or the subsequent soil-pipe interaction forces will be the same along the pipe axis. Any variability alomg the pipe will likely cause the pipe response to be three dimensional. Pipe can be going down at one location while it may be going up at another location as illustrated in Figure 1. The berms will be bigger at locations where the pipe penetrates deeper into the seabed further restricting the lateral pipe movement.