This paper introduces wave directionality into a joint environmental contour description that has been used previously in the study of extreme response behavior for uni-directional random seas. A modified cosine power-spreading model that accounts for the frequency dependence of the various waves in the design seastate was utilized. Data from the Gulf of Mexico was used to evaluate the coefficients needed to describe the coupled frequency dependent behavior of the wave spreading exponent and the mean direction of wave travel. To illustrate the methodology the dynamic behavior of a generic steel caisson platform was studied. A finite element model of the platform was subject to a joint environmental description of directional seas. The time domain simulation yielded the stress levels at specified platform elevations. Based upon these numerical predictions, fatigue life estimates were evaluated using a simplified Palmgren-Miner approach. Results for both uni-directional and multi-directional sea simulations were obtained and are compared.
The importance of directional wave behavior on the design of offshore platforms has not been fully recognized in current design practice, although there has been a considerable amount of research on the subject. The directionality of waves in shallow to intermediate water depths can be the result of the interaction of the waves with the seafloor bathymetry or from the interaction of several storms. In deeper water depths the directional behavior could also be the result of the generation process of the waves, the interactions of storms or the focusing of the wave field by larger objects, like islands. Earlier models of wave directionality viewed the process as separable and were reflected in the range of mathematical models that were proposed, see for example Borgman (1969). Measurement programs targeting the directionally of ocean waves have increased but a fair amount of uncertainty in describing the process still exists.
