Stochastic Response Analysis of Mooring Systems with Emphasis on Frequency-domain Analysis of Fatigue due to Wide-band Response Processes

Abstract

Mooring systems are widely used in the offshore industry to limit the horizontal excursions of a floating structure from desired position in order for the structure to fulfill the required tasks. Safety of mooring systems is therefore crucial for successful marine operations.

Under the environmental actions of waves, wind and current, large dynamic tension in mooring lines can be excited at both wave frequency (WF) and low frequency (LF). Due to the nonlinearities of environmental loads and mooring systems, both WF and LF tension are non-Gaussian random processes. In this thesis, stochastic nonlinear mooring line tension has been modeled in an efficient way, by which, motion-induced WF tension is approximated by a simplified dynamic model, while LF tension is evaluated based on a quasi-static analysis. Especially, non-Gaussian fatigue of each frequency component has been explicitly estimated in the frequency domain, and fatigue induced by the combined tension, so-called bimodal fatigue problem, has been dealt with. The frequency-domain method for fatigue analysis has been exemplified by mooring analysis of a semi-submersible and validated by time-domain simulations and rainflow cycle counting method.

The degrading mechanism of e.g. corrosion has an influence on mooring system reliability, since mooring lines are normally submerged in sea water for a long period of interest. A time-variant reliability problem is formulated herein using a probabilistic analysis of corrosion. The problem is solved by a piece-wise constant model of line strength and the effect of corrosion on mooring safety has been analyzed in terms of annual failure probability increasing with time.

Another problem discussed in this thesis is mooring system responsein a partially damaged condition. Extensive mooring analyses have been carried out using varying long-term environmental conditions and considerable increases of tension loads in the neighboring mooring lines have been obtained due to failure of one line. Significant variations in the yearly and even seasonal wave conditions and the induced extreme and fatigue responses of mooring systems together with other marine vessels, like an FPSO and a semi-submersible, have been analyzed. These variations could have a notable effect on the safety assessment of these structures.

In addition, an efficient method for estimating the damping of LF vessel motions caused by mooring systems has been proposed based on the simplified dynamic model of mooring lines. The accuracy of the calculated damping coefficients in surge and sway including the cross terms has been verified by time-domain simulations using a finite element method.

As an interesting extension of bimodal fatigue analysis, a novel frequency-domain method for estimating trimodal fatigue damage has been developed considering the interaction between the high, intermediate and low frequency components. Such a process might occur for combined responses of moored structures involving vortex induced vibrations. The proposed method has been verified to be accurate and practically acceptable by rainflow counting algorithm based on time-domain simulations of a series of ideal trimodal Gaussian processes.

Furthermore, this method has been generalized and applied to Gaussian processes with general wide-band spectra. In this way, three equivalent processes have been first defined based on the division of the response spectrum into three parts with the same variances. The wide-band fatigue damage is then estimated using the same procedure as for ideal trimodal processes. Extensive time series have been simulated for different kinds of wide-band processes, including typical marine structural responses induced by waves and wind. It is noted that the narrow-band approximation can be applied to estimate the wide-band fatigue damage if the Vanmarcke’s bandwidth parameter is less than 0.5. The proposed method has been validated with the simulation results and compared with other empirical methods. Although the idea of the proposed method is simple, it seems to be applicable for a wide range of spectral types.

Moreover, previous research work on frequency-domain fatigue analysis has mainly focused on single-slope SN curves. In this thesis, fatigue analysis considering two-slope SN curves has been carried out and especially the methods of bimodal fatigue analysis have been generalized and the accuracy has been verified by time-domain simulations.