A spectral analysis of a typical multi-tower gravity platform is carried out considering soil-structure interaction. The modal frequency response function and the linear hydrodynamic load transfer functions are determined taking into account diffraction effects. The displacement and wave loading spectra are evaluated for sea states described by the JONSWAP wave height spectrum relevant to the North Sea environment. Considerable simplification is achieved by a reduced interaction model together with complex notation for wave forces. A detailed parametric study using various values of soil shear modulus yields r.m.s. values of deck displacement and tower elastic deformation.
With the increase in the rate of world oil consumption, exploration and production has moved into deeper and environmentally more hostile waters. The first phase of this development favoured fixed platform with concrete gravity structures being designed for water depths up to 150m and the steel jacket for water depths up to 300m. The first concrete gravity platform, Ekofisk I, was installed in the North Sea in June 1973 and by the end of 1977 there will be more than 12 concrete platforms in operation. These are generally of a multi-tower (2, 3 or 4 towers) configuration with a large base caisson of cellular construction extending up to 1/3 of the height of the platform, or a manifold type of construction with a large diameter base raft up to 150m in diameter.
In designing a gravity platform it is necessary to consider the effect of wave forces on both the towers and the caisson in order to calculate the structural and foundation stresses. A detailed analysis of a rigid four tower gravity platform supported on a rigid foundation under deterministic and random wave forces is given by the authors in ref l.
The present paper gives a random dynamic analysis of a typical multi-tower gravity platform (Condeep Brent 'B') taking into account flexibility and damping of the towers and of the foundation The random wave forces are calculated for a fully developed sea state represented by the J.O.N.S.W.A.P. wave height spectrum11, which is typical of the North Sea. Due to the relatively large diameter of the towers hydrodynamic drag forces are small compared with the inertial forces on the towers and the diffraction forces on the caisson and can be neglected, enabling a linear spectral analysis to be used. The fluid inertia loading on the towers is evaluated using Morison's equation and diffraction theory where relevant. The wave forces and moments on the caisson are computed using the results of wave diffraction analysis2,10
The spectral analysis is carried out by formulating the wave force transfer function for unit wave height using complex notation, taking account of the phase differences of the waves due to spatial separation of the towers. The frequency response function is based on a real eigenvalue analysis through a modal formulation of the soil-structure dynamic model.