Author Contributions
Conceptualization, Z.C. and S.L. (Shewen Liu); methodology, A.Z.; software, A.Z., Z.H. and S.L. (Shiqi Liu); validation, Z.C. and X.C.; formal analysis, S.L. (Shewen Liu); investigation, A.Z.; resources, Z.C.; data curation, A.Z.; writing—original draft preparation, A.Z.; writing—review and editing, Z.C.; visualization, L.H.; supervision, S.L. (Shewen Liu); project administration, Z.C.; funding acquisition, S.L. (Shewen Liu). All authors have read and agreed to the published version of the manuscript.
Figure 1.
Parallel bonding model for spherical elements.
Figure 1.
Parallel bonding model for spherical elements.
Figure 2.
Bonding failure model of particle element. (a) Tensile failure; (b) shear failure.
Figure 2.
Bonding failure model of particle element. (a) Tensile failure; (b) shear failure.
Figure 3.
Fracture criterion with tensile and shear failure.
Figure 3.
Fracture criterion with tensile and shear failure.
Figure 4.
Schematic diagram of broken ice floes area under different conditions: (a) 80% ice concentration, the average area of 20 m2 of ice floes condition; (b) 80% ice concentration, the average area of 100 m2 of ice floes condition.
Figure 4.
Schematic diagram of broken ice floes area under different conditions: (a) 80% ice concentration, the average area of 20 m2 of ice floes condition; (b) 80% ice concentration, the average area of 100 m2 of ice floes condition.
Figure 5.
Simulation of interaction between cylinder structure and level ice. (a) Schematic diagram of finite element method calculation; (b) top view of finite element method calculation; (c) schematic diagram of discrete element method calculation; (d) top view of discrete element method calculation.
Figure 5.
Simulation of interaction between cylinder structure and level ice. (a) Schematic diagram of finite element method calculation; (b) top view of finite element method calculation; (c) schematic diagram of discrete element method calculation; (d) top view of discrete element method calculation.
Figure 6.
Simulation of interaction between cone structure and level ice. (a) Schematic diagram of finite element method calculation; (b) top view of finite element method calculation; (c) schematic diagram of discrete element method calculation; (d) top view of discrete element method calculation.
Figure 6.
Simulation of interaction between cone structure and level ice. (a) Schematic diagram of finite element method calculation; (b) top view of finite element method calculation; (c) schematic diagram of discrete element method calculation; (d) top view of discrete element method calculation.
Figure 7.
Numerical comparison of ice load between finite element method and discrete element method. (a) Cylinder structure at 0.3 m/s ice speed; (b) cylinder structure at 0.4 m/s ice speed; (c) cone structure at 0.2 m/s ice speed; (d) cone structure at 0.4 m/s ice speed.
Figure 7.
Numerical comparison of ice load between finite element method and discrete element method. (a) Cylinder structure at 0.3 m/s ice speed; (b) cylinder structure at 0.4 m/s ice speed; (c) cone structure at 0.2 m/s ice speed; (d) cone structure at 0.4 m/s ice speed.
Figure 8.
Numerical computation model of Kulluk platform. (a) Front view of the model; (b) stereogram of the model.
Figure 8.
Numerical computation model of Kulluk platform. (a) Front view of the model; (b) stereogram of the model.
Figure 9.
The geographical location of the Beaufort Sea [
22].
Figure 9.
The geographical location of the Beaufort Sea [
22].
Figure 10.
Calculation results of hydrodynamic analysis of the Kulluk platform. (a) First-order surge motion transfer function RAO; (b) first-order pitch motion transfer function RAO; (c) first-order surge force; (d) first-order pitch moment; (e) mean drift force in the surge by far-field method; (f) mean drift force in the surge by direct pressure integral method.
Figure 10.
Calculation results of hydrodynamic analysis of the Kulluk platform. (a) First-order surge motion transfer function RAO; (b) first-order pitch motion transfer function RAO; (c) first-order surge force; (d) first-order pitch moment; (e) mean drift force in the surge by far-field method; (f) mean drift force in the surge by direct pressure integral method.
Figure 11.
Numerical simulation of ice load on Kulluk platform. (a) Level ice condition; (b) broken ice floes condition; (c) front view under level ice condition; (d) front view under broken ice floes condition.
Figure 11.
Numerical simulation of ice load on Kulluk platform. (a) Level ice condition; (b) broken ice floes condition; (c) front view under level ice condition; (d) front view under broken ice floes condition.
Figure 12.
Comparison between the numerical simulation results and the field data of the Kulluk platform. (a) Ice thickness as the independent variable; (b) ice concentration as the independent variable.
Figure 12.
Comparison between the numerical simulation results and the field data of the Kulluk platform. (a) Ice thickness as the independent variable; (b) ice concentration as the independent variable.
Figure 13.
Influence of load direction on mooring system. (a) The coupled system for analysis; (b) schematic diagram of different load directions.
Figure 13.
Influence of load direction on mooring system. (a) The coupled system for analysis; (b) schematic diagram of different load directions.
Figure 14.
Tension comparison of four mooring lines under different load directions. (a) Maximum tension of mooring lines under wave loads; (b) mean tension of mooring lines under wave loads; (c) maximum tension of mooring lines under level ice loads; (d) mean tension of mooring lines under level ice loads; (e) maximum tension of mooring lines under broken ice floes loads; (f) mean tension of mooring lines under wave loads.
Figure 14.
Tension comparison of four mooring lines under different load directions. (a) Maximum tension of mooring lines under wave loads; (b) mean tension of mooring lines under wave loads; (c) maximum tension of mooring lines under level ice loads; (d) mean tension of mooring lines under level ice loads; (e) maximum tension of mooring lines under broken ice floes loads; (f) mean tension of mooring lines under wave loads.
Figure 15.
Influence of the number of mooring lines on the mooring system. (a) The coupled system for analysis with four mooring lines; (b) schematic diagram of the design of four mooring lines; (c) the coupled system for analysis with eight mooring lines; (d) schematic diagram of the design of eight mooring lines; (e) the coupled system for analysis with twelve mooring lines; (f) schematic diagram of the design of twelve mooring lines.
Figure 15.
Influence of the number of mooring lines on the mooring system. (a) The coupled system for analysis with four mooring lines; (b) schematic diagram of the design of four mooring lines; (c) the coupled system for analysis with eight mooring lines; (d) schematic diagram of the design of eight mooring lines; (e) the coupled system for analysis with twelve mooring lines; (f) schematic diagram of the design of twelve mooring lines.
Figure 16.
Influence of the number of mooring lines on mooring line tension. (a) Maximum and mean values of mooring system tension under wave loads; (b) maximum and mean values of mooring system tension under level ice loads; (c) maximum and mean values of mooring system tension under broken ice floes loads; (d) the tension of mooring line 1 under wave loads in time-domain analysis; (e) the tension of mooring line 1 under level ice loads in time-domain analysis; (f) the tension of mooring line 1 under broken ice floes loads in time-domain analysis.
Figure 16.
Influence of the number of mooring lines on mooring line tension. (a) Maximum and mean values of mooring system tension under wave loads; (b) maximum and mean values of mooring system tension under level ice loads; (c) maximum and mean values of mooring system tension under broken ice floes loads; (d) the tension of mooring line 1 under wave loads in time-domain analysis; (e) the tension of mooring line 1 under level ice loads in time-domain analysis; (f) the tension of mooring line 1 under broken ice floes loads in time-domain analysis.
Figure 17.
Influence of the number of mooring lines on Kulluk platform motion. (a) Surge motion under wave loads; (b) surge motion under level ice loads; (c) surge motion under broken ice floes loads; (d) pitch motion under wave loads; (e) pitch motion under level ice loads; (f) pitch motion under broken ice floes loads.
Figure 17.
Influence of the number of mooring lines on Kulluk platform motion. (a) Surge motion under wave loads; (b) surge motion under level ice loads; (c) surge motion under broken ice floes loads; (d) pitch motion under wave loads; (e) pitch motion under level ice loads; (f) pitch motion under broken ice floes loads.
Figure 18.
Influence of the number of connection points on the mooring system. (a) The coupled system for analysis with one connection point; (b) schematic diagram of the design of one connection point; (c) the coupled system for analysis with four connection points; (d) schematic diagram of the design of four connection points; (e) the coupled system for analysis with twelve connection points; (f) schematic diagram of the design of twelve connection points.
Figure 18.
Influence of the number of connection points on the mooring system. (a) The coupled system for analysis with one connection point; (b) schematic diagram of the design of one connection point; (c) the coupled system for analysis with four connection points; (d) schematic diagram of the design of four connection points; (e) the coupled system for analysis with twelve connection points; (f) schematic diagram of the design of twelve connection points.
Figure 19.
Influence of the number of connection points on mooring line tension. (a) Mean tension of mooring lines under wave loads; (b) mean tension of mooring lines under level ice loads; (c) mean tension of mooring lines under broken ice floes loads; (d) the tension of mooring line 1 under wave load in time-domain analysis; (e) the tension of mooring line 1 under level ice load in time-domain analysis; (f) the tension of mooring line 1 under broken ice floes load in time-domain analysis.
Figure 19.
Influence of the number of connection points on mooring line tension. (a) Mean tension of mooring lines under wave loads; (b) mean tension of mooring lines under level ice loads; (c) mean tension of mooring lines under broken ice floes loads; (d) the tension of mooring line 1 under wave load in time-domain analysis; (e) the tension of mooring line 1 under level ice load in time-domain analysis; (f) the tension of mooring line 1 under broken ice floes load in time-domain analysis.
Figure 20.
Influence of the number of connection points on Kulluk platform motion. (a) Surge motion under wave loads; (b) surge motion under level ice loads; (c) surge motion under broken ice floes loads; (d) pitch motion under wave loads; (e) pitch motion under level ice loads; (f) pitch motion under broken ice floes loads.
Figure 20.
Influence of the number of connection points on Kulluk platform motion. (a) Surge motion under wave loads; (b) surge motion under level ice loads; (c) surge motion under broken ice floes loads; (d) pitch motion under wave loads; (e) pitch motion under level ice loads; (f) pitch motion under broken ice floes loads.
Figure 21.
Influence of the angle between mooring lines on the mooring system. (a) The coupled system for analysis; (b) schematic diagram of the design of 10° between mooring lines; (c) schematic diagram of the design of 20° between mooring lines; (d) schematic diagram of the design of 30° between mooring lines.
Figure 21.
Influence of the angle between mooring lines on the mooring system. (a) The coupled system for analysis; (b) schematic diagram of the design of 10° between mooring lines; (c) schematic diagram of the design of 20° between mooring lines; (d) schematic diagram of the design of 30° between mooring lines.
Figure 22.
Influence of the angle between mooring lines on mooring line tension. (a) Maximum and mean values of mooring system tension under wave loads; (b) maximum and mean values of mooring system tension under level ice loads; (c) maximum and mean values of mooring system tension under broken ice floes loads; (d) the tension of mooring line 1 under wave load in time-domain analysis; (e) the tension of mooring line 1 under level ice load in time-domain analysis; (f) the tension of mooring line 1 under broken ice floes load in time-domain analysis.
Figure 22.
Influence of the angle between mooring lines on mooring line tension. (a) Maximum and mean values of mooring system tension under wave loads; (b) maximum and mean values of mooring system tension under level ice loads; (c) maximum and mean values of mooring system tension under broken ice floes loads; (d) the tension of mooring line 1 under wave load in time-domain analysis; (e) the tension of mooring line 1 under level ice load in time-domain analysis; (f) the tension of mooring line 1 under broken ice floes load in time-domain analysis.
Figure 23.
Influence of the angle between mooring lines on Kulluk platform motion. (a) Surge motion under wave loads; (b) surge motion under level ice loads; (c) surge motion under broken ice floes loads; (d) pitch motion under wave loads; (e) pitch motion under level ice loads; (f) pitch motion under broken ice floes loads.
Figure 23.
Influence of the angle between mooring lines on Kulluk platform motion. (a) Surge motion under wave loads; (b) surge motion under level ice loads; (c) surge motion under broken ice floes loads; (d) pitch motion under wave loads; (e) pitch motion under level ice loads; (f) pitch motion under broken ice floes loads.
Figure 24.
Comparison of three groups of mooring lines with angles of 5°, 7.5°, and 10°. (a) Surge motion under level ice loads; (b) pitch motion under broken ice floes loads.
Figure 24.
Comparison of three groups of mooring lines with angles of 5°, 7.5°, and 10°. (a) Surge motion under level ice loads; (b) pitch motion under broken ice floes loads.
Table 1.
Main parameters of the structure in finite element calculation.
Table 1.
Main parameters of the structure in finite element calculation.
Mass Density | Young’s Modulus | Poisson’s Ratio |
---|
7850 kg/m3 | 206 Gpa | 0.3 |
Table 2.
Main parameters of level ice in finite element calculation.
Table 2.
Main parameters of level ice in finite element calculation.
Mass Density | Shear Modulus | Yield Stress | Plastic Hardening Modulus | Bulk Modulus | Failure Pressure | Plastic Failure Strain |
---|
900 kg/m3 | 2.2 Gpa | 2.12 Mpa | 4.26 Gpa | 5.26 Gpa | −4 Mpa | 0.35 |
Table 3.
Main parameters of water and air in finite element calculation.
Table 3.
Main parameters of water and air in finite element calculation.
| State Equation | Density | Viscosity Coefficient | Failure Pressure |
---|
Air | *EOS_LINEAR_POLYNOMIAL | 1.25 kg/m3 | 1.74 × 10−5 | −10 Mpa |
Water | *EOS_GRUNEISEN | 1000 kg/m3 | 0.9 × 10−3 | −10 Mpa |
Table 4.
Main parameters of sea ice discrete element calculation.
Table 4.
Main parameters of sea ice discrete element calculation.
Parameter | Symbol | Value | Unit |
---|
Elastic modulus | E | 1.0 | GPa |
The density of water | ρw | 1035.0 | kg/m3 |
The density of ice | ρi | 920.0 | kg/m3 |
The friction coefficient of particle element | μb | 0.25 | — |
The friction coefficient between sea ice and structure | μs | 0.25 | — |
Particle normal bond strength | σbn | 1.57 | — |
Particle tangential bond strength | σbs | 1.57 | — |
Particle compression strength | σc | 2.53 | MPa |
Table 5.
The numerical comparison of different ice load analysis methods.
Table 5.
The numerical comparison of different ice load analysis methods.
| Ice Speed (m/s) | Empirical Formula |
---|
0.1 | 0.2 | 0.3 | 0.4 | 0.5 | Average Value | Standard Deviation |
---|
DEM—cylinder structure | 6007.58 kN | 6983.78 kN | 7717.35 kN | 8386.42 kN | 9063 kN | 7273.78 kN | 1124.58 | 26,343.32 kN |
FEM—cylinder structure | 9043.24 kN | 13,120.88 kN | 18,343.52 kN | 19,272.79 kN | 20,634.68 kN | 16,083.02 kN | 4343.61 |
DEM—cone structure | 4959.72 kN | 5285.41 kN | 5625.54 kN | 5981.75 kN | 6018.99 kN | 5574.28 kN | 406.83 | 6600 kN |
FEM—cone structure | 2869.34 kN | 3451.97 kN | 4971.67 kN | 5863.48 kN | 6226.38 kN | 4676.57 kN | 1316.32 |
Table 6.
Basic parameters of the Kulluk platform.
Table 6.
Basic parameters of the Kulluk platform.
Parameter | Value | Unit |
---|
Top diameter | 81 | m |
Diameter at waterline | 67.5 | m |
Bottom diameter | 60 | m |
Depth | 18.4 | m |
Draft | 11.5 | m |
Displacement | 28,000 | m3 |
Cone angle | 31.4 | ° |