Author Contributions
Conceptualization, Y.C. and P.G.; methodology, B.W. and Z.J.; software, B.H. and W.C.; validation, G.X. and R.S.; formal analysis, X.G. and J.Z.; investigation, Q.M.; resources, P.G.; data curation, Y.C.; writing—original draft preparation, Y.C.; writing—review and editing, P.G. and B.W.; visualization, Z.J.; supervision, Y.C.; project administration, P.G. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Location and specific layout of the Sheyang aquaculture platform.
Figure 1.
Location and specific layout of the Sheyang aquaculture platform.
Figure 2.
Layout of the aquaculture cage and modeling of the suction anchor foundation.
Figure 2.
Layout of the aquaculture cage and modeling of the suction anchor foundation.
Figure 3.
Stresses acting on the liner elements surrounding a node.
Figure 3.
Stresses acting on the liner elements surrounding a node.
Figure 4.
Idealization of interface behavior at a liner node. (a) Shear stress, τ, and incremental relative shear and normal displacements, Δus and Δun, between liner and surface; (b) shear and normal stress update at each time step.
Figure 4.
Idealization of interface behavior at a liner node. (a) Shear stress, τ, and incremental relative shear and normal displacements, Δus and Δun, between liner and surface; (b) shear and normal stress update at each time step.
Figure 5.
3D modeling of foundation and surrounding soils under different scouring and tilt error conditions. (a) Foundation under 0 m scour condition; (b) foundation under 2 m scour condition; (c) foundation with 2 m scour and −5° tilt error; (d) foundation with 2 m scour and +5° tilt error.
Figure 5.
3D modeling of foundation and surrounding soils under different scouring and tilt error conditions. (a) Foundation under 0 m scour condition; (b) foundation under 2 m scour condition; (c) foundation with 2 m scour and −5° tilt error; (d) foundation with 2 m scour and +5° tilt error.
Figure 6.
Deformation of surrounding soils under different conditions based on numerical simulations for 10-year ULS conditions (safety factor 2.0): (a) 0 m scour, causing backward tilting with 5.0 cm pad-eye and 5.67 cm soil displacements, respectively; (b) 2 m scour, amplifying displacements to 7.5 cm (pad-eye) and 8.78 cm (soil); (c) 2 m scour with a −5° tilt error, resulting in displacements of 6.5 cm (pad-eye) and 7.18 cm (soil); (d) 2 m scour with a +5° tilt error, resulting in displacements of 9.1 cm (pad-eye) and 9.94 cm (soil).
Figure 6.
Deformation of surrounding soils under different conditions based on numerical simulations for 10-year ULS conditions (safety factor 2.0): (a) 0 m scour, causing backward tilting with 5.0 cm pad-eye and 5.67 cm soil displacements, respectively; (b) 2 m scour, amplifying displacements to 7.5 cm (pad-eye) and 8.78 cm (soil); (c) 2 m scour with a −5° tilt error, resulting in displacements of 6.5 cm (pad-eye) and 7.18 cm (soil); (d) 2 m scour with a +5° tilt error, resulting in displacements of 9.1 cm (pad-eye) and 9.94 cm (soil).
Figure 7.
Plastic zones in surrounding soils under varying conditions from numerical simulations with 10-year ULS loading (safety factor 2.0), illustrating progressive expansion: (a) foundation under 0 m scour condition; (b) foundation under 2 m scour condition; (c) foundation with 2 m scour and −5° tilt error; (d) foundation with 2 m scour and +5° tilt error.
Figure 7.
Plastic zones in surrounding soils under varying conditions from numerical simulations with 10-year ULS loading (safety factor 2.0), illustrating progressive expansion: (a) foundation under 0 m scour condition; (b) foundation under 2 m scour condition; (c) foundation with 2 m scour and −5° tilt error; (d) foundation with 2 m scour and +5° tilt error.
Figure 8.
Load–displacement curve at pad-eye of suction anchor foundation.
Figure 8.
Load–displacement curve at pad-eye of suction anchor foundation.
Figure 9.
Equivalent stress distributions in the pad-eye under uniform loading (17,089.6 kN tension at a 22.20° initial angle) from solid-element simulations (25 mm mesh, 20,552 elements) with fixed edge constraints: (a) Case 1–1 (0° tilt, 0° directional error); (b) Case 1–2 (0° tilt, 75° directional); (c) Case 2–1 ( +5° tilt, 0° directional); (d) Case 2–2 ( +5° tilt, 7.5° directional); (e) Case 3–1 (−5° tilt, 0° directional); (f) Case 3–2 (−5° tilt, 7.5° directional). All cases show stresses below the 319.5 MPa allowable limit after CCS averaging, confirming compliance with DNV/CCS standards even under installation tolerances.
Figure 9.
Equivalent stress distributions in the pad-eye under uniform loading (17,089.6 kN tension at a 22.20° initial angle) from solid-element simulations (25 mm mesh, 20,552 elements) with fixed edge constraints: (a) Case 1–1 (0° tilt, 0° directional error); (b) Case 1–2 (0° tilt, 75° directional); (c) Case 2–1 ( +5° tilt, 0° directional); (d) Case 2–2 ( +5° tilt, 7.5° directional); (e) Case 3–1 (−5° tilt, 0° directional); (f) Case 3–2 (−5° tilt, 7.5° directional). All cases show stresses below the 319.5 MPa allowable limit after CCS averaging, confirming compliance with DNV/CCS standards even under installation tolerances.
Figure 10.
3D modeling and on-site lifting of the suction anchor foundation: (a) 3D simulation of the process; (b) actual lifting of the suction anchor foundation.
Figure 10.
3D modeling and on-site lifting of the suction anchor foundation: (a) 3D simulation of the process; (b) actual lifting of the suction anchor foundation.
Figure 11.
Equivalent stress distributions in the suction anchor structure under hoisting loads (combined lifting factor 1.7875, fixed constraints at lifting points) from finite element analysis: (a) internal bucket structure (max. 67.89 MPa in stiffeners); (b) top bucket structure (max. 82.05 MPa in cover stiffeners). All components, including the main bucket (46.38 MPa), remain well below the 319.82 MPa allowable limit, confirming compliance with design and regulatory standards.
Figure 11.
Equivalent stress distributions in the suction anchor structure under hoisting loads (combined lifting factor 1.7875, fixed constraints at lifting points) from finite element analysis: (a) internal bucket structure (max. 67.89 MPa in stiffeners); (b) top bucket structure (max. 82.05 MPa in cover stiffeners). All components, including the main bucket (46.38 MPa), remain well below the 319.82 MPa allowable limit, confirming compliance with design and regulatory standards.
Figure 12.
S–N curves for fatigue analysis (DNVGL-RP-C203).
Figure 12.
S–N curves for fatigue analysis (DNVGL-RP-C203).
Figure 13.
Principal stress of the pad-eye structure under fatigue loading conditions: (a) 3D model of pad-eye; (b) fatigue analysis of pad-eye.
Figure 13.
Principal stress of the pad-eye structure under fatigue loading conditions: (a) 3D model of pad-eye; (b) fatigue analysis of pad-eye.
Figure 14.
Principal stress at the welded connection between pad-eye and bucket under fatigue loading conditions: (a) 3D model of the welded connection; (b) fatigue analysis of the welded connection.
Figure 14.
Principal stress at the welded connection between pad-eye and bucket under fatigue loading conditions: (a) 3D model of the welded connection; (b) fatigue analysis of the welded connection.
Table 1.
Recommended design parameters for suction anchor foundations.
Table 1.
Recommended design parameters for suction anchor foundations.
Soil Layers | Compression Modulus (Es1–2, kPa) | Poisson’s Ratio | Undrained Elastic Modulus (E0, kPa) | Unit Weight (γ’, kN/m3) | Internal Friction Angle (φ’, °) | Undrained Shear Strength (cu, kPa) |
---|
Silty Clay with Silt | 2500 | 0.35 | 5000 | 6.8 | / | 5–15 |
Silty Sand with Silt | 9000 | 0.25 | 25,000 | 9.5 | 30 | / |
Silty Clay | 3400 | 0.30 | 12,000 | 7.5 | / | 35 |
Silty Sand with Silty Clay | 8000 | 0.25 | 20,000 | 9.2 | 29 | / |
Silty Clay | 5000 | 0.30 | 25,000 | 8.2 | / | 55 |
Sand | 12,000 | 0.25 | 35,000 | 9.8 | 33 | / |
Table 2.
Material parameters of soil layers.
Table 2.
Material parameters of soil layers.
Soil Type | Poisson’s Ratio | Undrained Elastic Modulus E0 (kPa) | Effective Unit Weight γ’ (kN/m3) | Friction Angle φ’ (°) | Undrained Shear Strength cᵤ (kPa) |
---|
Silty clay | 0.35 | 4000 | 6.8 | - | 8 |
Silty sand with clay | 0.25 | 20,000 | 9.5 | 24.8 | - |
Clayey silt | 0.30 | 9600 | 7.5 | - | 28 |
Sandy silt with clay | 0.25 | 16,000 | 9.2 | 23.9 | - |
Clayey silt | 0.30 | 20,000 | 8.2 | - | 44 |
Table 3.
Suction anchor structural parameters.
Table 3.
Suction anchor structural parameters.
Density (kg/m3) | Elastic Modulus (GPa) | Poisson’s Ratio |
---|
7850 | 210 | 0.3 |
Table 4.
Displacement of different load-bearing cases.
Table 4.
Displacement of different load-bearing cases.
No. | Condition | Max. Pad-Eye Displacement (cm) | Max. Soil Displacement (cm) |
---|
1 | 0 m scour | 5.0 | 5.67 |
2 | 2 m scour | 7.5 | 8.78 |
3 | 2 m scour + −5° tilt (forward) | 6.5 | 7.18 |
4 | 2 m scour + +5° tilt (backward) | 9.1 | 9.94 |
5 | 2 m scour + +5° tilt + 7.5° directional error | 13.2 | 15.1 |
Table 5.
Safety factors of different load-bearing cases.
Table 5.
Safety factors of different load-bearing cases.
No. | Condition | Pad-Eye Tension (kN) | Safety Factor | Compliance Status |
---|
1 | 10-year return period (encircling)—ULS | 8,339.74 | 2.158 > 2.0 | Yes |
2 | 10-year return period (encircling)—ALS | 11,473.29 | 1.569 > 1.5 | Yes |
3 | ULS (Standard maximum limit) | 8,788.63 | 2.048 > 2.0 | Yes |
4 | ALS (Standard maximum limit) | 11,741.6 | 1.533 > 1.5 | Yes |
Table 6.
Stress control criteria for the pad-eye structure of suction anchor foundations.
Table 6.
Stress control criteria for the pad-eye structure of suction anchor foundations.
Parameters | Value |
---|
Chain breaking load factor | 1.1 |
Design load (kN) | 17,089.6 |
Yield strength (MPa) | 355 |
Allowable stress (MPa) | 319.82 |
Table 7.
Summary of design conditions for pad-eye structure.
Table 7.
Summary of design conditions for pad-eye structure.
Tension (kN) | Initial Angle (°) | Tilt Error (°) | Directional Error (°) | Case No. |
---|
17,089.6 | 22.20 | 0 | 0 | 1–1 |
7.5 | 1–2 |
+5 | 0 | 2–1 |
7.5 | 2–2 |
−5 | 0 | 3–1 |
7.5 | 3–2 |
Table 8.
Lifting load factors for suction anchor.
Table 8.
Lifting load factors for suction anchor.
Dynamic Amplification Factor (DAF) | 1.25 |
Self-Weight Factor | 1.1 |
Safety Factor | 1.3 |
Combined Lifting Factor | 1.7875 |
Table 9.
Stress summary under lifting conditions.
Table 9.
Stress summary under lifting conditions.
Component | Allowable Stress (MPa) | Max. Stress (MPa) | Compliance |
---|
Main Structure (Shell + Top Cover) | 319.82 | 46.38 | Yes |
Internal Stiffeners | 319.82 | 67.89 | Yes |
Top Cover Stiffeners | 319.82 | 82.05 | Yes |
Table 10.
Fatigue damage assessment of pad-eye and weld joint zones.
Table 10.
Fatigue damage assessment of pad-eye and weld joint zones.
Fatigue Analysis Zone | Cycles (N) | Stress Range (MPa) | S–N Curve | Calculated Fatigue Damage | Safety Factor | Design Fatigue Damage |
---|
Pad-eye Structure | 1 × 107 | 1.247 | B | 1.04 × 10−11 | 3 | 3.11 × 10−11 |
Weld Zone 1 | 1 × 107 | 0.556 | D | 4.30 × 10−10 | 3 | 1.29 × 10−9 |
Weld Zone 2 | 1 × 107 | 0.458 | D | 1.63 × 10−10 | 3 | 4.89 × 10−10 |