Prediction Of Large Amplitude Motions And Stability Of Intact And Damaged Mobile Platforms
Authors: Söylemez M. , Incecik A. 
Published: October 2008

ABSTRACT
In this paper the development of generalised non-linear motion equations to study the intact, progressive and post-flooding behaviour of a floating structure in waves is presented. The motion response predictions obtained using non-linear large motion equations are illustrated to indicate the behaviour of a semi-submersible platform in waves during intact, flooding and post-flooding conditions. The results of the parametric studies to determine the effects of flooding rate and of the size of damaged compartment on motion response characteristics are also summarised.

INTRODUCTION
A number of papers published after the extensive research on the stability of semi-submersibles following the Alexander Kielland disaster concluded that stability calculations performed by the designers and the recommendations of the regulatory bodies should take the effect of waves and dynamic wind forces into account (Ref.1) and that dynamic analysis should be performed for both intact and damaged platform conditions in order to evaluate proper locations of floodable openings (Ref.2). However, very few reported studies exist on the prediction of behaviour of a semi-submersible undergoing large motions in intact, progressive flooding or post-damage conditions. In (Ref.3) a non-linear time domain simulation method to predict the motions of a platform with large list angles (post-damage behaviour) was presented. The transient (progressive flooding or sudden breaking of mooring lines) behaviour of a semisubmersible was studied both theoretically and experimentally (Ref. 4). The theoretical part of the study reported in (Ref. 4) showed the importance of the transient behaviour through a simple mathematical model and recommended that the transient motions should be considered by regulatory bodies. The post-damage behaviour of a semi-submersible type platform was also reported in (Refs.5&6). The general methodology in predicting the behaviour of a damaged platform in progressive and post-flooding conditions is also reported by Moncarz et. al. in (Ref.7).
The study reported in this paper is based on non-linear large motion equations which were derived using three dimensional generalised wave loading formulations to simulate the motions in six degrees of freedom during intact, transient and post-flooding conditions. In the paper a summary of the systematic study performed to illustrate the effects of non-linear terms on the solution of the motion response equations is given. The results of the parametric studies to show the effects of flooding rate and of the size of damaged compartment on motion response characteristics are also discussed.

THE DERIVATION AND SOLUTION OF MOTION RESPONSE EQUATIONS
In order to select a suitable hydrodynamic model to formulate wave excitation forces which will be implemented in non-linear large amplitude motion equations a pilot study was carried out. In this study a semi-submersible geometry as shown in Fig.l (Available in full paper) was considered to predict the wave exciting forces and resulting linear motions using the Morison approach and the two dimensional source distribution technique. Comparisons between the wave excitation forces and motion responses as obtained from the two different models show fairly close agreement Figs.2–5(Available in full paper).