## 4 Results and Discussions
### Fairlead Tension  
When the clump masses are added on the mooring lines, the segment of the mooring line from the connection node to the vessel node will be obviously straightened, so the angle between these two segments will become smaller. In the vertical direction, the force provided by the fairlead tension is the sum of the gravity of the clump masses and the vertical force provided by the tension of the mooring line from the connection node to the anchor node. So when the gravity of the clump masses is added, the component force provided by the fairlead tension will be increased several-fold due to the small angle between the upper and lower segments of the mooring lines.  
Figure 13: Frequency domain amplitude at load case 6 for (**a**) surge, (**c**) heave, and (**e**) pitch, and the peak amplitudes for (**b**) surge, (**d**) heave, and (**f**) pitch.  
According to the above calculation and analysis, the motions of the spar platform are very limited, especially the surge. The fairlead tension of the mooring lines of original OC3 model P0 and the OC3 CM models in regular waves are shown in Figures 14-16.  
As shown in the above section, fairlead 2 and fairlead 3 are symmetrically distributed and have an angle of 120 degrees. Therefore, the tension of fairlead 2 is considered to be equal to that of fairlead 3. Taking this into account, only the tension of fairlead 1 and fairlead 2 are presented in the figures. In Figure 14a, Figure 15a, and Figure 16a, the fairlead tension of the same model does not change much in different load cases, which means that changes in wind and wave loads make no significant difference to the fairlead tension. Figure 14a demonstrates that the curve of the original OC3 model P0 is obviously below the curves of the OC3 CM models, whereas the tension of OC3 CM model P1 to P5 is almost the same. At 0 s, there is a significant increase in the fairlead tension of the OC3 CM models, which is brought about by the clump masses. Comparing Figure 14a,b, the trend of the curve can be analyzed. In the figures, it is evident that the tension of fairlead 1 has a dramatic change, eventually getting smaller. However, the tension of fairlead 1 is precisely the opposite, which can be explained by the platform gradually moving to anchor 1. As a result, mooring line 1 becomes slack, making mooring line 2 tense. In case 1, the fairlead 1 tension of the original OC3 model P0 is about 720 kN, while the fairlead 1 tension of the OC3 CM model P5 is 957 kN at stable state. Additionally, the fairlead 2 tension and fairlead 3 tension of original OC3 model P0 are 1060 kN, while that of OC3 CM model P5 is 1320 kN.  
In order to calculate the fatigue load of the mooring line, the slope of the S-N curve is set to 4 and the duration of the wave is set to 365 days. The results are shown in Figure 17. It can be seen that the fatigue loads of the mooring lines undergo obvious changes at different frequencies. The fatigue loads  
Figure 16: Fairlead tension in load case 3 for (**a**) fairlead 1, (**b**) fairlead 2.  
Figure 14: Fairlead tension in load case 1 for (**a**) fairlead 1, (**b**) fairlead 2.  
Figure 15: Fairlead tension in load case 2 for (**a**) fairlead 1, (**b**) fairlead 2.  
of the mooring lines for the OC3 CM models P2 and P5 are found to be relatively small and insensitive to the change in the wave frequencies.  
From the above analysis, it can be concluded that the clump masses will increase fairlead 1 tension by about 30% and fairlead 2 and 3 tension by about 24.5%. However, the position of the clump masses and the changes of wind and wave loads have no significant effect on the fairlead tension. These results verify that the segment of the mooring line from the connection node to the vessel node is obviously straightened by the clump masses, which will increase the tension of the mooring line. Thus, it should limit the motion of the platform in return.