Time Domain Estimation Of Structural Loading Due To Irregular Waves: Two Case Histories
Authors: Duncan P.E. , Reid D.L. , Drake K.R. 
Published: October 2008

ABSTRACT
This paper discusses time domain simulations of irregular wave loading on offshore structures, highlighting diffraction and nonlinear wave effects. Two design applications are presented: an investigation into the 'ringing' behaviour of the deepwater Draugen monotower, and evaluation of the strength of the unconventional 'plated' foundation being designed for a North Sea jacket.

INTRODUCTION
The global strength of steel jacket structures for moderate water depths (to 150m, say) is generally assessed by considering the Morison equation loading from a single design crest and then allowing for the modest structural dynamic effects with a simple dynamic amplification factor. For large volume structures, where nonlinear viscous effects are small but diffraction is important, a linear frequency domain spectral analysis incorporating a fuller description of the structural dynamics is the more common approach. When both nonlinearities and dynamics are important - as is often the case, for instance, when structural concepts are extrapolated for use in deeper waters - neither of these approaches adequately represents all of the important loading effects. Time domain simulation of the loading and response in realistic wave trains is a useful tool in these cases, and this is the topic discussed and illustrated in this paper.
The paper outlines the basic steps required for such simulations, and then discusses in more detail the incorporation of diffraction effects and the numerical simulation of realistic wave trains. Applications of the method, involving two radically different offshore structural design problems, are then presented.

BASIC CALCULATION PROCEDURE
As illustrated in Figure 1(Available in full paper), different physical effects are important for different types of structure, and clearly the numerical simulation procedure must be adapted for different structural forms. In this section the objective is to outline the basic method as required for calculating the loads on the slender vertical column in Figure 1(a).
Figure 2(Available in full paper) is a schematic of this basic calculation procedure: for the present the items in dashed lines, which refer to diffraction effects, should be ignored. The inputs are shown across the top of the figure, and comprise the surface elevation time history together with various representations of the structure. The surface elevation record could represent an actual wave train, measured either at full scale or in a model tank, or it could be itself the result of numerical simulation.

Water Particle Kinematics
The standard approach for estimating irregular wave kinematics is to assume that the incident wave train comprises a large number of independent sinusoidal waves or 'wavelets'; the overall kinematic field beneath the wave train is then approximated by superposing the Airy wave kinematics for each wavelet. A practical concern is that Kinematics up to the instantaneous water surface are required and various heuristic methods have been suggested to achieve this. More fundamentally, this procedure ignores nonlinear interaction between the waves; for example, attributing Airy kinematics to all the higher frequency components of a truly representative wave record is questionable.