Probabilistic Extreme Values And Their Implication For Offshore Structure Design

Abstract

ABSTRACT The concept of the probabilistic extreme value and its application for offshore structure design is outlined. In particular, a method to evaluate the design extreme value based on the long-term prediction approach using a family of wave spectra in each sea severity is discussed. Some results of numerical calculations made on a semi-submersible-type ocean platform are presented. INTRODUCTION For the design of offshore structures floating in a seaway, it is possible to assess the expected structural safety by applying recent technology developed on the probabilistic approach. The assurance of structural safety against the wave-induced loads may be expressed in terms of probability of occurrence of possible structural failure. One type of failure which the present study primarily concerns is that which takes place as soon as a single load exceeds the value critical for the structural strength. For the probabilistic evaluation of possible occurrence of such failures, the probability density functions for the loadings as well as structural resistance are required. If the probability density function of the structural resistance is not known or cannot be established precisely (which may be the usual case at an early design stage), then one way to determine the design value is to estimate the extreme load which an offshore structure may experience in a lifetime, and then design the structure to withstand this extreme load. For this approach, it has been common practice to consider the probable extreme value for the assessment of the design value. Here, the probable extreme value is defined as the modal value of the probability density function which is applicable for the largest load in a specified number of observations. The probable extreme value has a significant meaning in practice since the largest value which actually occurs in n-observations may be very close to this value. However, the probability that the largest value exceeds the probable extreme value is theoretically quite large, and hence it is not appropriate to consider the probable extreme value for design. For design consideration a certain margin above the probable extreme value is required as an assurance for safety, and this can be achieved by estimating the extreme value which is unlikely to be exceeded with a pre-assigned assurance. This paper discusses the principle and underlying concept for evaluating extreme values of offshore structures floating in a seaway specifically for design consideration, and a method of estimating extreme values based on the long-term prediction approach is presented. DESIGN EXTREME VALUE The probabilistic extreme value of waves, and responses of offshore structures thereto, is defined as the largest value of the maxima (peaks or peak-to-trough excursions) which will occur in a specified number of observations or in a specified period of time. Let X be the response of an offshore structure in a seaway, and let Yn be the extreme value of the response in n-encounters with waves.