Stochastic Crack Propagation in Offshore Structures: The Sensitivity of Component Lifetime to Wave Distribution Models

Abstract

Stress variations induced by wave loading can lead to fatigue crack growth in structural components of offshore structures. This paper is concerned with the influence of the form of the statistical distributions for wave height on the damage accumulation and lifetime of a structural component. Damage accumulation is modeled by a stochastic Paris-Erdogan equation in which the increase in crack size is proportional to a power (m) of the range of the stress intensity factor. Analytic expressions for the mean and variance of damage, and approximate mean lifetime, of a component are derived for the case in which m equals 2. It is seen that these depend on both the mean and variance of the stress distribution. The results are compared with those obtained by simulation, and the adequacy of the approximation is demonstrated. Simulation results using Rayleigh and Weibull distributions for wave heights are also given for the case in which m equals 3. It is shown that the Weibull distribution gives a better fit to empirical wave height distributions than does the Rayleigh distribution. Furthermore, when m equals 3, there is a substantial difference between results obtained by fitting Rayleigh and Weibull distributions to wave height data. The former leads to considerable overestimation of lifetimes. It is argued that Weibull distributions are more appropriate in determining lifetimes since the two parameters in the distribution allow more accurate representation of the mean and variance of the stress distribution.