On the Influence of Environmental Contour Method in Estimating Extreme Structural Response

Environmental contours are often applied in probabilistic structural reliability analysis in order to identify extreme environmental conditions that may give rise to extreme loads and responses. The perhaps most common way of establishing such environmental contours are based on the Rosenblatt transform and the IFORM approximation (Inverse First Order Reliability Method), but recently an alternative approach based on direct Monte Carlo simulations with importance sampling has been proposed. A recent comparison study revealed that there might be rather large differences in certain parts of the contours and for certain joint environmental models. In particular, the alternative contour method yields convex contours by design, whereas the traditional contours may be convex or non-convex. In this paper, comparison studies that include applications on a few structural examples are presented. Comparing the contours with known response surfaces, one may investigate how large the differences between the contour methods may be, and compare this to the correct extreme response estimated by simulation studies. These case studies clearly illustrate the influence of the environmental contour calculation method on the estimated extreme response. Whereas the different methods yield comparable results for some structural problems, they may give very different estimates of the extreme response for other. It is demonstrated that in certain cases, the estimates from some of the contour methods are highly conservative, whereas they in other cases might be very optimistic. The reason for these results are discussed and some requirements on the response functions for obtaining conservative estimates will be stated.