Helical structures such as subsea control umbilicals and flexible pipes are commonly used in oil and gas industry, often the helical structures twist during handling and installation, and cause undesirable consequences. In this paper an analytical method is presented to calculate the helical structure twisting angles under tensile and bending loads. First, the helical structure was simplified as a bundle of helix coils, which are parameterized as three-dimensional space curves. Then the curve length equation is differentialized to study the twisting angles generated by tensile and bending loads, and analytical formulas were derived. The method was then applied to a practical umbilical load out case, and obtained good agreement with field measured date. It is found the helix pitch length variation may generate significant twisting angle, and relevant mitigation measures could be implemented by using the calculation results as guidance. This method can also be used to assess helical structure stress and strain, and cross section deformation and structure stability.


Subsea control umbilicals and flexible pipes are key equipment for offshore oil and gas field development. Both of them are helical structures, and exhibiting strong twisting tendency (i.e. pig tailing) during handling and installation. Authors have been personally involved in many industrial projects with flexible pipes and umbilicals, and experienced severe undesirable twisting, especially during load out and transpooling.

There have been many publications on umbilical and flexible structure analysis, most of the work is concerned on the stress and strain analysis, as discussed in Lu (2021). There is other research work concerned about torsional effect, and included the helical structure coupling effect through analytical method, as presented by Alkharisi (2019) and Ramos (2004). The former used a three-dimensional elasticity theory to study the coupled axial-torsional modes of vibration. And the latter presented an analytical model comprising equilibrium equations, constitutive equations, and geometrical constraints, to solve for the component deformation. Similar analytical method based on energy balance equations was presented by Saneian (2019). With different analytical models available, Tang (2015) summarized and assessed seven of them for helical wire analysis, and concluded that spring theory is the most recommended method. Besides analytical method, numerical modelling method was also used by many research teams. Rochinha (1996) simplified the helix wire as beam element to analyze helical structure, in his work an extension-torsion coupling finite element model was proposed and studied. Cheng (1997) and Chung (1997) presented coupled bending, axial and torsional displacement FEA method for long vertical mining pipe analysis. Savik (2005) also presented a finite element formulation to predict the umbilical behavior under tension, torque, internal/external pressure, and external contact bodies. Zhang (2021) studied a marine flexible pipeline twisting near the touch down area, and assessed the twisting induced instability using a moment method. Komperod (2014) presented an algorithm for torsion balancing umbilical design, which focused on the twisting induced torque balance calculations. Liu (2020) presented testing results on flexible pipe, mainly on axial strain under tensile load. Munoz (2016) presented a method for coupled extensional-torsional response of a flexible pipe, with no bending effect included. Maincon (2017) explained some of the observed phenomenon of the torsion in flexible pipes, umbilicals, and cables under loadout to installation vessel, which provides some insights to the reason of the twisting. While all the aforementioned publications presented work that considered torsional effect, the research work were mainly concerned on tension, bending and torsion coupling effect in pipe global dynamic response, and is not efficient to assess the pipe twisting under static tension and bending. In this paper, we present an efficient analytical method based on helix coil theory, with primary goal to calculate the helical structure twisting angle under static tensile and bending loads, and the solution is explicitly expressed using helix coil parameters.

This content is only available via PDF.
You can access this article if you purchase or spend a download.