Continuum Modelling Framework for Local Buckling Response of Plain and Girth Welded Pipes
Authors: Fatemi Ali , Kenny Shawn 
Published: May 2011

Abstract
In this paper, the significance of boundary conditions (L/D ratio), initial geometric imperfections, anisotropic material properties, and material constitutive model on the local buckling response of plain and girth welded pipes was evaluated using continuum finite element modelling procedures. A numerical model was developed, using the finite-element simulator ABAQUS/Standard, to predict the local buckling and post-buckling response of high strength pipelines subject to combined state of loading. The numerical procedures were calibrated using test data from large-scale experiments examining the local buckling of high strength linepipe. The moment and strain response estimates, predicted by the numerical simulation tool, was consistent with the experimental data well into the post-yield range. As the models with high L/D ratio exhibit global Euler-type response, a numerical algorithm was developed to calculate the local section moment response based on FE predictions.

Introduction
Arctic pipelines may be subject to large deformation geohazards such as ice gouging, frost heave, thaw settlement, seismic fault movement and lateral spreading due to liquefaction. The imposed ground displacement field and load transfer effects will develop a pipe bending and axial feed-in response that may result in local pipeline buckling response. For these design conditions, mechanical performance criteria are generally based on strain limits in order to develop practical and cost-effective engineering solutions.
Although there have been a significant number of investigations on the bending and local buckling response of pipelines over the past 80 years, which include analytical, physical and computational modelling studies, there remains some areas of uncertainty [1–11]. Some of these areas include parameter characterization and quantification on effects of capacity reduction associated with initial geometric imperfections of the pipe body, residual stress and geometric imperfections associated with girth welding processes, material anisotropic behavior and discontinuous yielding [6,12,13].
This paper will address these issues through discussion of studies conducted by the authors, using continuum finite element modelling procedures, and reference to other publications.

Numerical Modelling Procedures
The numerical modeling procedures were developed using the commercial software package ABAQUS/Standard. These numerical modeling procedures were calibrated with full scale tests conducted on linepipe segments with a 3.5 L/D ratio. Zimmerman et al. [14] presented a generalized description of the experimental apparatus and test procedure. The FE modelling procedures simulated experimental tests on a linepipe segment subject to end rotation, internal pressure and axial force. A typical FE model is illustrated in Figure 1.
The pipeline was modeled using a reduced integrated shell element (S4R). The mesh topology was an element length of 20 mm on the pipeline length and circumference, which was based on a mesh convergence study [15]. The mesh density was selected to maintain a consistent topology across the range the two segment lengths examined.
In the experimental test program, for pipeline segment lengths of 3.5 D, end support collars were used to mitigate the effects of boundary conditions on the local buckling response. In this study, the support collars were assumed to have perfect contact with the pipeline segment. The support collars were modeled with a nominal wall thickness equal to the nominal pipeline wall thickness and a length of 0.5D.