**FPSO Mooring Line Fatigue**

For both the situations (FPSO alone and FPSO + offloading tanker connected), the assessment of the fatigue damage of the mooring lines accounts for:

- Low frequency-induced fatigue damage,
- Wave frequency fatigue damage.

The two damages are calculated separately and the summation is performed with the combined spectrum method.

For fatigue calculations, the wave height vs period distribution is needed for each direction. Directional period / wave height scatter diagrams shall be generated by using for each direction the distribution of height specified and assuming that the distribution of periods for each wave height to be the same as the non-directional.

**Assessment of low frequency damage**

In order to estimate the low frequency damage of the mooring lines, the following method shall be followed:

- Time domain, low frequency simulations, for the load cases of the condensed wave scatter diagram,
- Standard deviation and up crossing period of the tension in the lines are extracted from the simulations.

The environments for the analysis can be considered as follows:

- Wave condition as per the condensed scatter diagram,
- 95% non-exceedance wind spectrum in-line with waves,
- 95% non-exceedance current in-line with waves.

In tanker-connected condition and for the calculation of LF damage, the following configurations should be considered:

- Tanker on ballast half of the time – FPSO in maximum load condition,
- Tanker in max-load condition half of the time, with FPSO in ballasted condition.

Mean offsets for each of the sea states of the 8 directions are also extracted. For each of the 8 direction, the maximum mean offset weighted by the occurrence of probability is considered as static offset in the Tension RAO calculation in wave frequency.

**Calculation of wave frequency fatigue damage**

Tension RAOs of the mooring lines shall be computed at the fairlead location from regular wave time domain simulation for each wave heading and a range of periods representative of the whole range of sea-states.

To cope with issues of drag non linearity, the tension RAOs are built using Airy waves of different amplitude. Indeed, for each wave period, the amplitude of the regular wave is calculated as the average height of all the sea state with the same wave period weighted by the probability of occurrence.

In order to consider the incidences of waves in the direction of the mooring line bundles which could lead to higher fatigue results, additional cases of ±15° from each of the 8 prevailing directions shall be included.

For each of the 8 prevailing directions, the tension RAOs of the mooring lines are computed for the base case and the ±15° cases. Only the maximum tension RAOs from the 3 cases for each line is used to calculate the respectively wave frequency damage.

The spectrum of the tension in the mooring lines will then be calculated for each box of the scatter diagrams. From the response spectrum and the individual probability of each sea-state, the fatigue damage is calculated.This process is followed for each sea-state of the scatter diagram, and the total fatigue damage is calculated from each individual sea-state with Palmgren-Miner’s rule.

The offset with tanker connected is calculated with a numerical model including the FPSO, the tanker, the mooring lines and a tug pull.

**Summation of low and wave frequency damage**

Damages due to low and wave frequency motions are combined as recommended by DNV-OS-E301, using a combined spectrum approach.

The combined spectrum method is always conservative and may significantly overestimate the actual fatigue damage.

In a an additional case with the environment condition (Hs, Tp, Dir, FPSO Load condition, Probability Occurrence) leading to the maximum damage in the mooring line with the lowest fatigue life shall be included. A combined LF+WF dynamic calculation is carried out over 10800 seconds simulation with this selected environment condition.

**Sensitivity cases**

Sensitivities study shall be included for the environment condition (Hs, Tp, Dir, FPSO Load condition, Probability Occurrence) leading to the maximum damage in the mooring line with the lowest fatigue life.

- Wave Period sensitivity
- Wind Spectrum sensitivity
- Wave Enhancement factor Gamma Sensitivity

**Wave Period Tp Sensitivity**

Two sensitivity cases (Tp1 and Tp2) shall be carried out for the most damaging sea state where two border Tp values shall be considered for each bin of the block.Upper limit of border Tp and lower limit of border Tp are considered. This is to validate the methodology of selecting the mean Tp value (For instance, Tp=7.5sec for Tp range 7 sec to 8 sec) for each bin in our analysis.

**Wind Spectrum Sensitivity**

A sensitivity study shall be carried out for the most damaging sea state using wind spectrum.

**Gamma Sensitivity**

Two sensitivity cases are carried out for the most damaging sea state by considering one entire gamma value above and below (For instance, gamma=1 and gamma=2 for the sensitivity with the base case gamma=1.30). This is to investigate the effect on the fatigue of the mooring system due to the changes in the Gamma parameter.