The principal objective of this investigation is to develop a nonlinear continuum based finite element formulation to examine dynamic response of flexible riser structures with large displacement and large rotation. Updated Lagrangian incremental approach together with the 2nd Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor is employed to derive the nonlinear finite element formulation. The 2nd Piola-Kirchhoff stress and the Green-Lagrange strain tensors are energy conjugates. These two Lagrangian tensors are not affected by rigid body rotations. Thus, they are used to describe the equilibrium equation of the body independent of rigid rotations. While the current configuration in Updated Lagrangian incremental approach is unknown, the resulting equation becomes strongly nonlinear and has to be modified to a linearized form. The main contribution of this work is to obtain a modified linearization method during development of incremental Updated Lagrangian formulation for large displacement and large rotation analysis of riser structures. For this purpose, the Green-Lagrange strain and the 2nd Piola-Kirchhoff stress tensors are decomposed into two second-order six termed functions of through-thethickness parameters. This decomposition makes it possible to explicitly account for the nonlinearities in the direction along the riser thickness, as well. It is noted that using this linearization scheme avoids inaccuracies normally associated with other linearization schemes. The effects of buoyancy force, riser-seabed interaction as well as steady-state current loading are considered in the finite element solution for riser structure response. An efficient riser problem fluid-solid interaction Algorithm is also developed to maintain the quality of the mesh in the vicinity of the riser surface during riser and fluid mesh movements. To avoid distortions in the fluid mesh two different approaches are proposed to modify fluid mesh movement governing elasticity equation matrices values; 1) taking the element volume into account 2) taking both element volume and distance between riser centre and element centre into account. The formulation has been implemented in a nonlinear finite element code and the results are compared with those obtained from other schemes reported in the literature.

Realistic predictions of service life of steel catenary risers (SCR) require an accurate characterization of seafloor stiffness in the zone where the riser contacts the seafloor, the so- called touchdown area (TDA). This paper describes the key features of a seafloor-riser interaction model based on the previous experimental model tests. The seafloor is represented in terms of non-linear load-deflection (P-y) relationships, which are also able to account for soil stiffness degradation due to vertical cyclic loading. The P-y approach has some limitations, but simulations show good agreement with experimental data. Hence, stiffness degradation and rate effects during penetration and uplift motion (suction force increase) of the riser are well captured through comparison with previous experimental tests carried out at the Centre for Offshore Foundation Systems (COFS) and Norwegian Geotechnical Institute (NGI). The analytical framework considers the riser-seafloor interaction problem in terms of a pipe resting on a bed of springs, and requires the iterative solution of a fourth-order ordinary differential equation. A series of simulations is used to illustrate the capabilities of the model. Due to the non-linear soil springs with stiffness degradation it is possible to simulate the trench formation process and estimate deflections and moments along the riser length. The seabed model is used to perform parametric studies to assess the effects of stiffness, soil strength, amplitude of pipe displacements, and riser tension on pipe deflections and bending stresses. The input parameters include the material properties (usually pipe and soil), model parameters, and loading conditions such as the amplitude of imposed dis- placements, tension, and moment. Primary outputs from this model include the deflected shape of the riser pipe and bending moments along riser length. The code also provides the location of maximum trench depth and the position where the maximum bending moment occurs and any point where user is interested in.

Yes / The near-trapping effects on wave-induced dynamic seabed response and liquefaction close to a multi-cylinder foundation in storm wave conditions are examined. Momentary liquefaction near multi-cylinder structures is simulated using an integrated wave-structure-seabed interaction model. The proposed model is firstly validated for the case of interaction of wave and a four-cylinder structure, with a good agreement with available experimental measurements. The validated model is then applied to investigate the seabed response around a four-cylinder structure at 0° and 45° incident angles. The comparison of liquefaction potential around individual cylinders in an array shows that downstream cylinder is well protected from liquefaction by upstream cylinders. For a range of incident wave parameters, the comparison with the results for a single pile shows the amplification of pressure within the seabed induced by progressive wave. This phenomenon is similar to the near-trapping phenomenon of free surface elevation within a cylinder array. / Energy Technology Partnership (ETP), Wood Group

Yes / Stability and safety of offshore wind turbines with mono-pile foundations, affected by nonlinear wave effect and dynamic seabed response, are the primary concerns in offshore foundation design. In order to address these problems, the nonlinear wave effect on dynamic seabed response in the vicinity of mono-pile foundation is investigated using an integrated model, developed using OpenFOAM, which incorporates both wave model (waves2Foam) and Biot’s poro-elastic model. The present model was validated against several laboratory experiments and promising agreements were obtained. Special attention was paid to the systematic analysis of pore water pressure as well as the momentary liquefaction in the proximity of mono-pile induced by nonlinear wave effects. Various embedment depths of mono-pile relevant for practical engineering design were studied in order to attain the insights into nonlinear wave effect around and underneath the mono-pile foundation. By comparing time-series of water surface elevation, inline force, and wave-induced pore water pressure at the front, lateral, and lee side of mono-pile, the distinct nonlinear wave effect on pore water pressure was shown. Simulated results confirmed that the presence of mono-pile foundation in a porous seabed had evident blocking effect on the vertical and horizontal development of pore water pressure. Increasing embedment depth enhances the blockage of vertical pore pressure development and hence results in somewhat reduced momentary liquefaction depth of the soil around the mono-pile foundation. / Energy Technology Partnership (ETP), Wood Group Kenny, and University of Aberdeen; the National Science Fund for Distinguished Young Scholars (51425901) and the 111 project (B12032).