Modal response of short pipeline spans on partial elastic foundations

•Short pipeline spans relevant for river crossings, inlets and straits are studied.•A dimensional analysis is carried out for the free span problem.•Closed analytical formulae are derived for eigenfrequencies and modal stresses.•The accuracy is improved compared to expressions currently used in pipeline design.•Simplified boundary conditions are demonstrated to give non-conservative results.

Very short pipeline free spans in flooded areas, river crossings, straits and inlets have been given a lot of attention due to recent failures caused by vortex-induced vibrations (VIV). Performing VIV analyses of free spanning pipelines requires accurate prediction of modal response quantities. Currently, no simple analytical solutions are available for short free spans supported by soils with a finite stiffness. Based on the Buckingham Pi theorem, the solution space for short free spans is spanned in the present study. Closed form analytical solutions are determined based on surface fitting to the developed solution space. The novel analytical solutions are accurate, easily implementable and thoroughly verified, and represent a significant improvement to current approaches found in design standards. An accurate expression for the buckling load of short spans is also derived, and asymptotic properties of the buckling load and frequency equations as the span length approaches zero are explored.