Amplitude-Dependent Modes for VIV Fatigue of ZRB Pipeline Spans

Abstract

Thermal expansion of subsea pipelines often leads to lateral buckling. Zero-Radius Bend (ZRB) buckle triggers were invented by the first author around 2004, to ensure that lateral buckles form at a controlled spacing, so that no single lateral buckle absorbs the thermal expansion of an excessive length of pipeline and thereby becomes overstressed. (Not only maximum stresses and strains but also fatigue loading at lateral buckles must be addressed.) Since then, ZRB buckle triggers have been extensively used in the offshore pipelines and flowlines industry and proved very successful. However, the trigger also generates a span to each side of the support that can be subject to Vortex-Induced Vibrations (VIV). This paper addresses the nonlinearity and inelasticity in the in-line VIV response of such spans.
Although it is long been recognized that nonlinearities and inelasticity of the soil are important at typical VIV amplitudes, the current practice for VIV fatigue assessment is based on linear behavior, so that modal analysis and empirical VIV response functions can be used to estimate the amplitude of the response of each mode to VIV. Without abandoning this approximation, this paper provides a way to improve it by a solution-dependent linearization, leading to a nonlinear eigenvalue problem for the amplitude-dependent modes and vibration frequencies, for which an efficient algorithm is described and applied.
Geometric nonlinearity of the pipe response is accounted for as well as the nonlinearity of the springs used to model pipe-soil interaction. The inelastic energy dissipation of the soil springs and ZRB support are used to calculate amplitude-dependent modal damping ratios. The accuracy of the linearization is verified by time-domain analysis.
A limitation of the method is that it does not capture the nonlinear interactions that can develop between closely-spaced modes. However, it works well for the pure in-line VIV response of the ZRB span considered, and shows a strong effect the nonlinearity and inelasticity for that case.