Influence From Nonelastic Material Modelling in Computer Simulation of Flexible Riser System Verified by Full-Scale Measurements
Authors: Sødahl Nils , Hanson T.D. , OUeren Audun , Fylling I.J. 
Published: October 2008

ABSTRACT
Field measurements of flexible riser dynamics are compared to stochastic time domain simulations using a state of the art finite element program for analysis of flexible risers.
Discrepancies observed in earlier comparisons are explained by nonelastic behaviour of the flexible pipe. The nonelastic properties are in the present study modelled by a combination of nonlinear stiffness and internal friction. The resulting pipe model shows an amplitude dependent hysteretic effect, as well as a variable dynamic bending stiffness.
The simulations show that both the hysteretic damping and the variable dynamic stiffness have a considerable influence on the dynamic curvature. It is concluded that the nonelastic cross-section model corresponds well with the actually measured behaviour of the pipe, and previously reported discrepancies are to a large extent eliminated.

INTRODUCTION
Full scale measurements of the steep wave riser system used by Petrojarl 1 at the Oseberg field in the North Sea were carried out by Norsk Hydro from August 1986 until May 1988. A considerable discrepancy was reported in a previous comparison of field data to analysis using a conventional elastic stiffness model [1]. One possible explanation for the deviations is the presence of nonlinear stiffness and damping effects not included in previous analyses.
Flexible pipes are built up of several layers where each layer has a specific function. Due to the rather complex cross-sectional structure, it is convenient to describe the material stiffness properties of the pipe in terms of force/displacement relations such as axial force versus axial elongation, bending moment versus curvature and torsional moment versus twist angle. Full scale laboratory measurements show that a hysteretic behaviour is present in the force/displacement relations for flexible pipes. The hysteretic behaviour is most pronounced in the bending moment/curvature relation for unbonded pipes [2].
The characteristics other bending moment/-curvature hysteresis is governed by the material properties of each layer and the friction between the layers. A bending moment/curvature hysteresis can be idealized in terms of a friction moment, Ms. an initial bending stiffness, EI, and a sliding bending stiffness, EI.. as shown in Figure 1. The initial bending stiffness describes the bending stiffness of the flexible pipe before the friction has been overcome. The initial bending stiffness is rather high because the flexible pipe behaves as a solid cross-section before the friction moment is exceeded. The sliding bending stiffness experienced when the friction moment has been exceeded is much lower due to slippage between the layers in the crosssection. The friction moment is dependent on the contact pressures between the layers. Hence, the external/internal pressures and the axial force in the pipe are important parameters for the magnitude of the friction moment.

DYNAMIC FINITE ELEMENT ANALYSIS
Flexible risers are exposed to environmental loading from waves and current and forced support motions due to the floater motions. Both waves and floater motions are assumed to be adequately described as stationary Gaussian processes.