Combined Environmental Loads Design Criteria for Marine Structures
Authors: Defu Liu , Yan Song , Shuqing Wang , Shuqin Wen 
Published: October 2008

Abstract
The joint probability design method based on stochastic simulation technique is proposed to determine the combined environmental design criteria of wave, current and wind. For template platform, the maximum wave height with simultaneous current and wind should be taken as initial data series for stochastic simulation; Similarly, for jack-up platform and riser in shallow water, maximum wind or current with simultaneous other factors are taken for simulation.

Introduction
The conservative defect often exists in conventional design practice because it usually takes the maximum individual environmental factor under a certain return period as the design criteria. It neglects the joint probability effect and might bring great uncertainty because the maximum winds, waves and currents are not necessarily to occur at the same time. The conventional design approach based on simultaneous occurrence of 50 or 100-year return period values of metocean parameters leads to different probabilities of occurrence at different sites. This is because there are places where wind, wave and current are closely dependent, and others where they are not. In theory, the actual return period of the "design storm" can therefore lie somewhere between a hundred years and a million years[1].
In order to improve the design criteria, some researchers developed different methods and estimated the overturning moment on a platform in the Gulf of Mexico from a simple algebraic function of wave height, surface current and wind velocity. The response probabilities were calculated. They showed that applying the individual design level oceanographic conditions simultaneously overpredicted the design overturning moment by 30%[2,3,4].
Forristall accounted for the effect of the joint occurrence of wind, wave and current on a rigid platform, a compliant tower, and a tension leg platform in the northern Gulf of Mexico. For the fixed platform, the 100 year base shear by this method was approximately 15% less than that which resulted from applying the 100 year oceanographic conditions for winds, waves and currents simultaneously[5].
The work described above demonstrates the importance of considering the joint probability of environmental factors. But they all belong to structure variable approach. It can transform the multivariate problem to univariate solution using univariate extreme value theory to carry out probabilistic analysis. But the structural response is difficult to determine as a simple function of wave, current and wind.
In this paper, the joint probability method is proposed. It uses ISPUD (Importance Sampling Procedure Using Design Point) method to solve the multidimensional joint probability of non-Gaussian correlated multivariate random variables. As examples, the joint probability method is applied to template platform, jack-up platform and riser, and obtaining the "100- yr. return period storm" with simultaneous wave, current and wind as the design criteria. At the same time, comparison among different methods is made and some suggestions are given about the design criteria.

Stochastic Simulation Technique Of Joint Probability
In order to solve the multidimensional joint probability, that is, to get the combination of simultaneous factors (wind, wave, current, etc.) under a certain probability level, the mathematical model must be built firstly.