Extreme Forces in Short-Crested Seas

The overall wave force on a large structure in a real multidirectional sea does not occur in a single direction but is a vector randomly varying in magnitude and direction. Although existing theories enable us to calculate the extremes of the orthogonal components of force, the designer needs the extreme resultant or total force. A theory is presented for estimating the extremes of the resultant and is confirmed by experimental measurement. Introduction Recent development of offshore resources in deep water and severe environmental conditions has led to the use of monolithic concrete structures. These structures have members large enough to modify the wave field, and are regarded as being in the diffraction regime of wave loading. Thus, the induced forces and moments are considered linear responses to the incident waves. Estimation of the forces and moments on such structures is based on the linear diffraction theory of Havelock. Several numerical models are used to compute the transfer functions between the incident waves and resuring forces and moments on large structures of arbitrary shape. In general, such models give the magnitude and phase of the transfer function between the waves and the loading at a range of discrete frequencies and angles of wave incidence. In parallel with the numerical approach, analytical methods have been developed to give directly the transfer functions for force and moment on a vertical cylinder in long-crested random waves. This analytical approach has also been extended to real seas that are multidirectional (short crested). In such seas, forces and moments are induced on structures both in line with and at right angles to the principal wave direction. The method gives the transfer functions between the components of force and moment and the total wave spectrum for any particular angular distribution of wave energy. The validity of this direct approach in short-crested seas has been confirmed by laboratory model tests in multidirectional random waves. These two approaches are complementary in that the numerical method allows estimation for regular waves on arbitrarily-shaped real structures; the analytical and laboratory studies allows the extension of results to real multidirectional random seas using the principle of superposition. By using this method, it is possible to compute the spectra of force and moment in two horizontal component directions on a real structure in a real short-crested sea. Since linear superposition is used both in the frequency and angular domains, the calculated component forces and moments also are linear with respect to the waves. However, the spectra of force and moment on a structure are of little direct value to designers concerned with primary failure. They are interested in the possible extremes and will want to set design limits on the forces and moments that are unlikely to be exceeded during the lift of the structure. Since the component forces and moments are linear responses to the waves, the statistical technique used to describe extreme wave elevations can be used to describe the extremes of the components of the loading. This method requires only the gross parameters of the spectra. Since the total (vector) force or moment combines the components and their probabilities in a nonlinear manner, the vital extreme values cannot be derived from the standard theory. This paper presents an analytical solution to this vector problem. SPEJ P. 567＾