Walking of long pipelines with multiple buckles is usually self-limiting. The buckles break the ‘long’ pipeline into multiple ‘short’ ones that are prone to walk. However, as temperature decays over the length of the pipeline, the ‘short’ sections further downstream might become cyclically constrained and eventually anchor the full pipeline length. Walking of the hot end would then slow down and cease.

This tapering down can take a large number of cycles, and not seem obvious when after a fair number of cycles, a small value of accumulated axial displacement per cycle is still observed in FEA. Often, designers would stop the analyses at some stage and assume the small rate will continue indefinitely. This can be overconservative, as a limit will often exist — which is demonstrated using first principles in the paper.

On the other hand, extrapolating without full understanding of the underlying processes can be dangerous. For some particular conditions, the trend can suddenly change after continuing unaltered for many cycles. This paper illustrates such change in behavior with the example of a fictitious pipeline seeing a gentle, gradual increase in operational temperature over time. The exercise shows that, after the trend has apparently settled, at a given point the rate of walking can increase again. The conditions that trigger it are shown to be predictable.

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