The critical design case for a structure such as an ultra-deep water pipeline is a combination of an extremely large load and an extremely small structural resistance. Common practice to estimate the probability of these extremes, for example mechanical strength, is using a Gaussian distribution fit of the data. Even though this distribution is generally suitable for describing average behaviour, it fails to describe extreme behaviour. This paper adopts extreme value theory (EVT) to assess extreme behaviour of material strength. Evidence is found that the minimum possible material strength is bounded and that the degree of control of mechanical parameters by means of specific requirements can have a positive influence on the shortness of the distribution tail.
An engineering assessment of a structure typically relates an extremely large applied load to an extremely small structural resistance. Key is to define a reasonable combination of these extremes. In practice this is accomplished by designing for a certain return period of a critical event, e.g. 1 failure per 10,000 years or rather a failure probability of 10−4 each year. This is the basis for the safety factors used in modern design codes such as DNV-OS-F101. An alternative to this load and resistance factor design (LRFD) approach is performing a probabilistic assessment, for example by means of Monte Carlo simulation.
In a Monte Carlo simulation the relevant input parameters behave as random variables that are sampled from a certain distribution. The design safety can be estimated by performing repeated sampling where a failure criterion is checked for each set of samples. After sampling a sufficiently large number of times (in the order of 106), the probability of exceeding this criterion can be estimated from the failure quantiles. The reliability of such method hinges on the goodness of the distribution fit of each random variable at extreme values. Common practice is to use a distribution for fitting all samples taken from a random variable. This generally fits well for sampled values close to the sample mean; however, it does not necessarily describe the distribution's tail correctly.