# Modelling Seabed Interaction in Frequency Domain Analysis of
Mooring Cables

## Paul Pang Awn Ong

*Abstract*:

With the increasing demand for energy, the supply of offshore oil and
gas has also beome increasingly important. The exploration and
production of such a reserve often require the use of a floating
vessel, anchored to the seabed by mooring cables for safe
operation. The analysis of these cables is therefore a
challenging one, and this is due in part to the cable's interaction
with the seabed.

This cable-seabed interaction can be resolved into two primary
actions. First, the interaction involves the axial stretching and
relaxation of grounded cable (i.e. the section of cable that lies on
the seabed). Second, it involves the lifting off and touching
down of the cable on the seabed, which we term here as catenary
action. Traditionally, it is believed that the latter can only be
modelled accurately by time integrating the cable's equations of
motion. This is far too computationally expensive for the many
load cases that have to be considered.

A more efficient alternative would be to analyse the cable in the
frequency domain, where the cable is assumed to undergo simple harmonic
motions. Such an assumption also means that seabed interaction
would have to be simplified. Up until now, this has been achieved
either by pinning the cable at its touchdown position, thus ignoring
the interaction altogether, or by modelling the grounded cable with an
equivalent horizontal spring. Neither of these methods offer a
proper way of modelling the catenary action mentioned above.

A new method is therefore proposed. In this new method, seabed
interaction is modelled by a system of coupled linear springs, rather
than a single spring. The cable is truncated at an optimum
position near the seabed and the truncated section replaced by a system
of springs. Static catenery equations are then linearised,
following a procedure routinely adopted in the linearisation of fluid
drag, to yield the stiffness values for the spring system. Doing
this, it is assumed that the spring system would replicate the
behaviour of the truncated line, and hence model the interaction
concerned.

The proposed method has shown to improve the accuracy of frequency
domain analysis in a number of cases. Cables of different
pretensions found in three broad categories of water depths - shallow,
deep and ultra-deep - have been analysed in both frequency and time
domains. Where available, model test solutions have also been
used as benchmark. The proposed method has shown the greatest
improvement for large excitations of low pretension cables, or those
deployed in shallow waters. For depths of 1000 m or more, seabed
interaction has no effect on the cable and can thus be modelled simply
by pinning the cable at its static touchdown.

[Cambridge University | CUED | Structures
Group | Geotechnical
Group]

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(last update 16 March 2005)