Fatigue Free Span Analysis

Nowadays, offshore pipelines have asignificant role in development of oil and gas industry in different parts of the world. This crucial industry is laid on seabed by various methods either embedded in a trench (buried

method) or laid on uneven seabed (unburied method). Construction of unburied pipeline is the most common method for its rapid and economic performance. In this method, however, the pipelines are subjected to various lengths of free spanning throughout the route during its life time, which may threaten the pipelines safety. Free spanning in offshore pipelines mainly occurs as a consequence of uneven seabed and local scouring due to flow turbulence and instability; hence, with no doubt, free spanning occurrences for unburied pipelines are completely inevitable. 

Fredsoe and Sumer (1997) assessed the role of free spans in unburied offshore pipelines. They acknowledged the previous studies and mentioned that resonance is the main problem for offshore pipelines laid on the free spanning. Pipelines resonance happens when the external load frequency as a result of vortex shedding becomes equal to the pipe Natural Frequency. This phenomenon may burst the pipe coating and may lead to develop more fatigue on the pipelines. Different design guidelines, e.g. DNV (1998) and ABS (2001), have accepted a less stringent approach and recommend the free spanning to be reduced to the allowable length to avoid fatigue damage. These guidelines proposed a simple formulation to calculate the first Natural Frequency based on the pipelines specifications and seabed conditions; however, all of the guidelines encourages using modal analysis at the final phase of design.

Choi (2000) studied the effect of axial forces on free spanning of offshore pipelines. The results indicated that the axial force has a significant influence on the first Natural Frequency of the pipe. In this research, the different seabed condition has been broken down into three main types and the general beam equation for the boundary conditions was analytically solved. He also compared his result with Lloyd’s approximate formula which estimates the first Natural Frequency of the beam considering axial load effect. Xu et al. (1999) applied the modal analysis to incorporate the real seabed condition to assess pipelines fatigue and Natural Frequency (NF). Later, Bai (2001) approved Xu et al. (1999) approach and emphasis on applying the modal analysis to determine the allowable length of free span for offshore pipelines.

In practice, a considerable amount of works have been applied to determine the allowable free span length, however, there is still lack of knowledge in assessing the role of all effective parameters in determination of allowable free span length. The objective of this paper is two folds: (i) to assess the role of main effective parameters on Natural Frequency; and (ii) to present a simple formula for allowable free span length with accounting for the seabed condition. To do so, first the approaches of DNV (1998) and ABS guidelines are discussed and then the modal analysis is outlined to have a useful tool to assess the role of all involved parameters. Finally, a case study on the Qeshem pipelines is performed to evaluate the free span allowable length.

DNV and ABS ApporximationFormula

DNV (1998) and ABS (2001) guidelines determine the allowable length of free span with the following equations:

in which  

E = modulus of elasticity;

I = bending moment of inertia of pipeline;

C= coefficient of seabed condition; and

VR= reduced velocity defined according to Fredso and Sumer (1997) by

in which  

U= streamwise flow velocity (normal to the pipe); 

D = outer diameter of pipe;  

me  = effective mass (including structural mass, mass of content and added mass); and 

fn = Natural Frequency of the pipe

free span. In order to solve Eq. (1), fn should be replaced by vortex shedding frequency to avoid resonance. In other words, the pipe Natural Frequency based on these codes is expressed as:

In practice, employing the above-mentioned formula for estimation of pipelines free span length is not very applicable due to the difficulties in determination of the exact seabed conditions: therefore, alternative approaches including modal analysis usually will be adopted.

Reference:

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