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Chapter 10

Force Model and Wave Fatigue

10.1 Introduction
Free-spanning subsea pipelines subject to oscillating environmental loads may fatigue at the
welded joints. Remedial seabed intervention by trenching and rock dumping is intended to
ensure that the span lengths are acceptable, but often at great cost. Therefore, the spans have
to be carefully assessed with respect to fatigue due to vortex-induced vibrations and wave-
induced oscillations.

A considerable amount of work has been performed to develop methods for assessment of
vortex-induced vibrations, see Tura et al. (1994) and Mark et al. (1997).

However, there is a lack of comprehensive mathematical formulations specifically dealing
with wave-induced fatigue. In order to clearly present the theoretical background, a few
equations available from reference books (e.g. Blevins (1994), Sumer and Fredsoe, (1997))
are presented. However, the rest of the paper is devoted to a methodology to assess wave-
induced fatigue that the authors feel has not been given enough focus in the literature.

When calculating the fatigue damage due to transverse oscillations, it is first necessary to
determine the stress amplitudes. This chapter describes the methodology used to calculate the
stress amplitudes using a wave force model, based upon the well-known Morison Equation.

Two different approaches are developed to solve the equation of the motion of the free-
spanning pipeline:

to solve the non-linear equation of motion numerically. This solution is called a ‘Time
Domain Solution’;
to linearize the Morison equation and solve it analytically. This is called a ‘Frequency
Domain Solution’.