Modelling soil stiffness in FEM

You could try locating a text on foundation dynamics by "Richart, Hall, and Woods" which might give some info on soil properties for a first run approximation, but I'm not to sure about that. These properties can be determined from tests of the shear wave velocity but I'd be concerned about the validity of standard soil dynamics when under water. Not much of an answer I guess.

-Mike

It's going to depend on the type of footing and the geotechnical characteristics of the sea bed.

Discussing concrete pad-type footings (above water), D.D.Barkan, in his book "Dynamics of Bases and Foundations" (McGraw-Hill, 1962), shows that in practical footings the soil's equivalent effect never exceeds 23% of the mass of the footing, because the amplitude of its vibrations is rapidly dying down with increasing distance from the footing. Thus even to ignore it altogether will only cause an error never exceeding 12% in the calculation of the natural frequency.

On damping, and depending again upon the geotech situation, it could be quite high if radiation damping (aka "geometric damping") is applicable.

Meant to add the following.

An excellent reference for pad-type footings, inter alia, is "Design of Structures and Foundations for Vibrating Machinery", by Suresh Arya, Michael O'Neill and George Pincus. Published in ~1979 by Gulf Publishing Company, Houston. ISBN 0-87201-294-8. Whilst your problem is (presumably) concerned with wave-induced vibrations rather than machine-induced vibration, the book will still contain much of relevance. In particular I would refer you to its Chapter 4 "Geotechnical Considerations". This presents a simple, tableau-style approach to the dynamic analysis of a (rigid) pad footing sitting on (or partially embedded in) an isotropic elastic halfspace. The approach is readily spreadsheetable, and among its intermediate results are the natural frequencies for the five (uncoupled) vibration modes.