Author Contributions
Conceptualization, J.W.; methodology, J.W., C.H. and J.D.; software, C.H. and K.H.; validation, J.W. and C.H.; formal analysis, J.W., C.H. and J.D.; investigation, K.H.; writing—original draft preparation, C.H.; writing—review and editing, J.W. and D.F.; supervision, J.W. and D.F.; project administration, J.W. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Link failure due to OPB [
3].
Figure 1.
Link failure due to OPB [
3].
Figure 2.
Chain link after fatigue test. (
a) Small secondary crack found on unfailed link; (
b) Secondary crack close to the border of the contact area from the secondary fracture failure [
12].
Figure 2.
Chain link after fatigue test. (
a) Small secondary crack found on unfailed link; (
b) Secondary crack close to the border of the contact area from the secondary fracture failure [
12].
Figure 3.
Research background.
Figure 3.
Research background.
Figure 4.
(a) Mooring line layout; (b) coupled analysis model.
Figure 4.
(a) Mooring line layout; (b) coupled analysis model.
Figure 5.
(a) RAO of surge; (b) LTF of surge; (c) QTF cloud chart; (d) QTF curves at the diagonal and natural frequency.
Figure 5.
(a) RAO of surge; (b) LTF of surge; (c) QTF cloud chart; (d) QTF curves at the diagonal and natural frequency.
Figure 6.
Schematic of FE model.
Figure 6.
Schematic of FE model.
Figure 7.
Results of FE convergence verification. (a) OPB moment between the top 2 links; (b) IPB moment between the top 2 links.
Figure 7.
Results of FE convergence verification. (a) OPB moment between the top 2 links; (b) IPB moment between the top 2 links.
Figure 8.
Flowchart of MeCAP-fatigue.
Figure 8.
Flowchart of MeCAP-fatigue.
Figure 9.
Rod-to-rod connection mode.
Figure 9.
Rod-to-rod connection mode.
Figure 10.
First-order (a) and second-order wave force (b) time course curve (F1~F6 are the wave forces in the direction of surge, sway, heave, roll, pitch, and yaw).
Figure 10.
First-order (a) and second-order wave force (b) time course curve (F1~F6 are the wave forces in the direction of surge, sway, heave, roll, pitch, and yaw).
Figure 11.
Comparison of mooring tension and platform motion response.
Figure 11.
Comparison of mooring tension and platform motion response.
Figure 12.
Calculating the interlink bending stiffness in the theory of the rod.
Figure 12.
Calculating the interlink bending stiffness in the theory of the rod.
Figure 13.
Real-time updating of interlink bending stiffnesses.
Figure 13.
Real-time updating of interlink bending stiffnesses.
Figure 14.
Calculation procedure of OPB combined fatigue.
Figure 14.
Calculation procedure of OPB combined fatigue.
Figure 15.
Comparisons of mooring tensions and OPB/IPB angles.
Figure 15.
Comparisons of mooring tensions and OPB/IPB angles.
Figure 16.
Schematic diagram for the definition of in-plane and out-of-plane angles: (a) Definition of the ML0 and MLv planes; (b) Definition of in-plane and out-of-plane angles.
Figure 16.
Schematic diagram for the definition of in-plane and out-of-plane angles: (a) Definition of the ML0 and MLv planes; (b) Definition of in-plane and out-of-plane angles.
Figure 17.
OPB/IPB angles and moments of Sea State 12: (a) Angles between links in the ML0 plane; (b) Angles between links in the MLv plane; (c) Moments between links in the ML0 plane; (d) Moments between links in the MLv plane.
Figure 17.
OPB/IPB angles and moments of Sea State 12: (a) Angles between links in the ML0 plane; (b) Angles between links in the MLv plane; (c) Moments between links in the ML0 plane; (d) Moments between links in the MLv plane.
Figure 18.
Critical hotspot on chain link for OPB combined fatigue [
22].
Figure 18.
Critical hotspot on chain link for OPB combined fatigue [
22].
Figure 19.
Combined stress and stress range distribution in Case 12.
Figure 19.
Combined stress and stress range distribution in Case 12.
Figure 20.
Difference in the zero and time-varying interlink stiffness with the “taut” (a) and “slack” (b) cases.
Figure 20.
Difference in the zero and time-varying interlink stiffness with the “taut” (a) and “slack” (b) cases.
Figure 21.
“Taut” (a) and “slack” (b) cases of mooring lines.
Figure 21.
“Taut” (a) and “slack” (b) cases of mooring lines.
Figure 22.
Difference in constant and time-varying interlink stiffness with the “taut” (a) and “slack” (b) cases.
Figure 22.
Difference in constant and time-varying interlink stiffness with the “taut” (a) and “slack” (b) cases.
Figure 23.
Fatigue damage of pure TT and different hotspot for mooring #2.
Figure 23.
Fatigue damage of pure TT and different hotspot for mooring #2.
Figure 24.
Tension and combined stresses of mooring line #2 for Case 12 (a) and Case 39 (b).
Figure 24.
Tension and combined stresses of mooring line #2 for Case 12 (a) and Case 39 (b).
Figure 25.
Tension and OPB/IPB angles of mooring line #2 for Case 12 (a) and 39 (b).
Figure 25.
Tension and OPB/IPB angles of mooring line #2 for Case 12 (a) and 39 (b).
Table 1.
Main particulars of the semi-submersible platform.
Table 1.
Main particulars of the semi-submersible platform.
Parameter | Unit | Value |
---|
Overall length | m | 91.5 |
Pontoon | m | 49.5(L) × 21(B) × 9(H) |
Column | m | 21(L) × 21(B) × 59(H) |
Draft | m | 37 |
Displacement | m3 | 105,000 |
Table 2.
Sectional properties of mooring line.
Table 2.
Sectional properties of mooring line.
Item | Unit | Chain | Polyester |
---|
Nominal diameter | mm | 157.0 | 274.0 |
Wet weight | kg/m | 428.6 | 13.0 |
Tensile stiffness | kN | 1.96 × 106 | 5.4 × 108 |
Minimum break load | kN | 2.36 × 104 | 2.16 × 107 |
Drag coefficient | | 2.2 | 1.2 |
Added mass coefficient | | 1.0 | 1.0 |
Table 3.
The geometric and material properties of the chain link.
Table 3.
The geometric and material properties of the chain link.
Parameter | Unit | Value |
---|
Equivalent length | mm | 628 |
Equivalent diameter | mm | 222.03 |
Young’s modulus | MPa | 206, 800 |
Poisson ratio | - | 0.3 |
Density | t/mm3 | 7.85 × 10−9 |
Table 4.
Comparison of the statistical values for the mooring tension and platform motion response.
Table 4.
Comparison of the statistical values for the mooring tension and platform motion response.
| Mooring Tension (kN) | Surge (m) | Sway (m) | Heave (m) |
---|
Mean Value | DeepC | 2411.926 | 1.931 | 1.368 | 0.011 |
MeCAP | 2411.728 | 1.899 | 1.337 | 0.01 |
Difference | −0.01% | −1.62% | −2.27% | −1.85% |
Standard Deviation | DeepC | 62.356 | 1.361 | 1.098 | 0.323 |
MeCAP | 60.907 | 1.392 | 1.134 | 0.312 |
Difference | 2.32% | −2.28% | −3.26% | 3.42% |
Table 5.
Error comparisons by using various time steps (compared to dt = 0.05 s).
Table 5.
Error comparisons by using various time steps (compared to dt = 0.05 s).
dt (s) | Tension | OPB Angle | IPB Angle |
---|
Mean Value | Standard Deviation | Mean Value | Standard Deviation | Mean Value | Standard Deviation |
---|
0.25 | −0.17% | −0.31% | 1.43% | 95.07% | 0.22% | 61.78% |
0.20 | −0.16% | −0.19% | 0.88% | 90.16% | 0.24% | 38.52% |
0.15 | −0.30% | −1.09% | 0.87% | 16.28% | 0.19% | 8.17% |
0.10 | −0.38% | −1.48% | 0.66% | 0.66% | 0.19% | 0.13% |
Table 6.
SCFs at three hotspots.
Table 6.
SCFs at three hotspots.
Loading Mode | Location |
---|
A | B | C |
---|
TT | 4.48 | 2.08 | 1.04 |
OPB | 0.00 | 1.06 | |
IPB | 1.25 | 0.71 | 1.50 |
Table 7.
Parameters of the SN curve.
Table 7.
Parameters of the SN curve.
Environment | | |
---|
Free corrosion in seawater | 12.436 | 3 |
Seawater corrosion under cathodic protection | 14.917 | 4 |
Air | 15.117 | 4 |
Table 8.
The fatigue damage and life of mooring line #2.
Table 8.
The fatigue damage and life of mooring line #2.
Location | TT | Hotspot A | Hotspot B | Hotspot C |
---|
Fatigue damage | 6.85 × 10−4 | 1.71 × 10−3 | 3.69 × 10−3 | 3.88 × 10−3 |
Fatigue life (years) | 146.0 | 58.3 | 27.1 | 25.8 |
Table 9.
Fatigue damage under the wave alone and under the joint action of wave.
Table 9.
Fatigue damage under the wave alone and under the joint action of wave.
| | Case 12 | Case 39 |
---|
Environment | Hs (m) | 5.5 | 5.5 |
Dir (m) | NE | SW |
TT | Wave | 3.22 × 10−3 | 3.42 × 10−3 |
Wave and wind | 4.54 × 10−3 | 3.78 × 10−3 |
Difference | −29.17% | −9.61% |
Hotspot A | Wave | 6.57 × 10−3 | 8.13 × 10−3 |
Wave and wind | 7.85 × 10−3 | 9.73 × 10−3 |
Difference | −16.26% | −16.46% |
Hotspot B | Wave | 1.62 × 10−3 | 1.75 × 10−3 |
Wave and wind | 1.77 × 10−3 | 2.01 × 10−3 |
Difference | −8.45% | −12.96% |
Hotspot C | Wave | 7.15 × 10−4 | 6.97 × 10−4 |
Wave and wind | 7.55 × 10−4 | 7.36 × 10−4 |
Difference | −5.26% | −5.20% |
Table 10.
Statistics of tension and combined stresses for Case 12.
Table 10.
Statistics of tension and combined stresses for Case 12.
| | Wave | Wave and Wind | Difference |
---|
TT | Mean | 3251.18 | 3423.09 | −5.02% |
Standard deviation | 98.35 | 117.29 | −16.15% |
Amplitude | 453.18 | 588.68 | −23.02% |
A | Mean | 406.28 | 427.76 | −5.02% |
Standard deviation | 12.33 | 14.70 | −16.10% |
Amplitude | 57.80 | 73.95 | −21.83% |
B | Mean | 230.24 | 241.95 | −4.84% |
Standard deviation | 6.99 | 8.12 | −13.89% |
Amplitude | 35.79 | 41.31 | −13.36% |
C | Mean | 141.21 | 148.16 | −4.69% |
Standard deviation | 4.49 | 5.05 | −11.15% |
Amplitude | 23.98 | 26.14 | −8.27% |
Table 11.
Statistics of tension and combined stresses for Case 39.
Table 11.
Statistics of tension and combined stresses for Case 39.
| | Wave | Wave and Wind | Difference |
---|
TT | Mean | 3109.75 | 2984.48 | 4.20% |
Standard deviation | 90.47 | 89.17 | 1.46% |
Amplitude | 439.14 | 465.26 | −5.61% |
A | Mean | 388.61 | 372.95 | 4.20% |
Standard deviation | 11.33 | 11.19 | 1.31% |
Amplitude | 55.12 | 58.51 | −5.80% |
B | Mean | 220.45 | 211.89 | 4.04% |
Standard deviation | 6.55 | 6.57 | −0.42% |
Amplitude | 34.60 | 35.95 | −3.75% |
C | Mean | 135.32 | 130.23 | 3.91% |
Standard deviation | 4.27 | 4.35 | −1.96% |
Amplitude | 23.73 | 25.06 | −5.30% |
Table 12.
Fatigue of the mooring chain subjected to wave only and wave and current.
Table 12.
Fatigue of the mooring chain subjected to wave only and wave and current.
| | Case 12 | Case 39 |
---|
Environment | Hs (m) | 5.5 | 5.5 |
Dir | NE | SW |
TT | Wave | 3.22 × 10−3 | 3.42 × 10−3 |
Wave and current | 2.38 × 10−3 | 2.79 × 10−3 |
Difference | 35.28% | 22.51% |
Hotspot A | Wave | 6.57 × 10−3 | 8.13 × 10−3 |
Wave and current | 6.84 × 10−3 | 6.80 × 10−3 |
Difference | −3.89% | 19.49% |
Hotspot B | Wave | 1.62 × 10−3 | 1.75 × 10−3 |
Wave and current | 1.59 × 10−3 | 1.63 × 10−3 |
Difference | 1.77% | 7.80% |
Hotspot C | Wave | 7.15 × 10−4 | 6.97 × 10−4 |
Wave and current | 6.30 × 10−4 | 7.93 × 10−4 |
Difference | 13.46% | −12.06% |
Table 13.
Statistical values of tension and angles.
Table 13.
Statistical values of tension and angles.
Case | Statistic | Name | Wave | Wave and Current | Difference |
---|
12 | Mean value | Tension (kN) | 3251.2 | 3689.3 | −11.88% |
OPB angle | −6.49 × 10−2 | −5.06 × 10−2 | 28.24% |
IPB angle | 5.63 × 10−6 | −3.52 × 10−2 | −100.02% |
Standard deviation | Tension (kN) | 98.4 | 79.5 | 23.67% |
OPB angle | 2.52 × 10−3 | 2.30 × 10−3 | 9.65% |
IPB angle | 3.41 × 10−3 | 3.07 × 10−3 | 11.26% |
39 | Mean value | Tension (kN) | 3109.8 | 2758.5 | 12.73% |
OPB angle | −6.44 × 10−2 | −7.89 × 10−2 | −18.31% |
IPB angle | 3.75 × 10−6 | 4.69 × 10−2 | −99.99% |
Standard deviation | Tension (kN) | 90.5 | 57.5 | 57.25% |
OPB angle | 2.55 × 10−3 | 3.54 × 10−3 | −27.99% |
IPB angle | 3.24 × 10−3 | 4.18 × 10−3 | −22.57% |