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Composite shallow foundation for subsea structures
T.W. Snel
Delft U
niv
ers
ity o
f Tech
nolo
gy
Composite shallow foundation
for subsea structures
By
T.W. Snel
in partial fulfilment of the requirements for the degree of
Master of Science
in Offshore and Dredging Engineering
at the Delft University of Technology, to be defended publicly on Tuesday, March 22, 2016 at 09:00 AM.
Supervisor: Prof. dr. A. Metrikine TU Delft Thesis committee: Ir. J.S. Hoving TU Delft
Dr. Ir. K.N. van Dalen TU Delft Ir. H.P. Rijneveld Allseas Engineering B.V.
The work in this thesis was supported by Allseas Engineering B.V. Their assistance in development of this thesis is hereby gratefully acknowledged.
Copyright © Offshore and Dredging Engineering (ODE) All rights reserved.
Abstract Large subsea structures on the seabed provide the necessary stability, protection and accommodation for subsea facilities to allow for continuous hydrocarbon exploitation. The current structures are supported by shallow foundations in the form of mud mats to generate sufficient foundation capacity. The large surface area of the foundation limits the installation capabilities of the structure in rough seas. This study describes the design of an alternative for the foundation of such structures, in the form of fiber reinforced polymer (FRP) gratings. These may provide a reduction in vessel waiting time and improve the workability. The low density of this material reduces the weight and the well-ventilated grating configuration allows easier installation through the splash zone. At the seabed, the soil generates friction within the ventilation holes and provides equal bearing capacity to the mud mat foundation for sufficient soil penetration. The study aims to determine the critical design limitations of the new foundation. The harsh subsea environment requires the grating to maintain its properties over the lifetime of the structure. The durability of different fibers and resins are investigated in combination with the fabrication method to determine the most suitable composite material. This resulted in a molded composite grating consisting of E-glass and vinyl-ester resin. The ventilated grating foundation reduces the hydrodynamic forces on the structure during the subsea installation. These reduced loads allow splash zone entry of the structure in less favorable wave conditions. Additionally, the motion behavior of the structure during the lowering operation is assessed. Due to the lower added mass, the eigenperiod of the structure is reduced and resonance may occur for significant lowering depths. Subsequently, the seabed landing of the foundation is compared with the original solution. Assuming the momentum equilibrium, the impact forces on structure are determined for the seabed landing. The less cushioned seabed approach of the grating foundation increases the impact velocity, but the resulting force is lower, due to the reduced dynamic mass of the structure. The required penetration of the grating foundation to obtain sufficient bearing capacity is investigated for both drained and undrained soils. Full plugging of the ventilation holes is not required to obtain sufficient bearing capacity and additional foundation height is only required in undrained soils. The sliding resistance of the foundation shows slight improvement. The deformation of the grating is investigated for the different load cases, from the installation to the in-service loading. Classical plate theory is used to determine the bending and shear stresses within the orthotropic material. These indicate that the slamming loads for the splash zone lift are the critical loads on the foundation during the installation. Accidental loading by dropped objects is shown to exceed the material strength and damage the material. To connect the composite grating to the structure, a new connection method is suggested. Stainless steel clamps are used to connect the gratings to the structure base frame. A cost analysis of the new foundation displays that the new foundation is more expensive, due to the more expensive connection method. If the cost-saving of the improved vessel operability, weighs up against the investment of the new foundation, the grating foundation may be viable alternative to the mud mat foundation.
Table of Contents
Abstract ....................................................................................................................................................................................... I
Table of Contents ...................................................................................................................................................................... III
List of Figures ............................................................................................................................................................................ IX
List of Tables ............................................................................................................................................................................. XI
Nomenclature ......................................................................................................................................................................... XIII
Preface ................................................................................................................................................................................... XVII
1. Introduction ...................................................................................................................................................................... 1
1.1 The oil and gas industry ................................................................................................................................................. 1
1.2 Allseas ........................................................................................................................................................................... 1
1.3 Scope and background................................................................................................................................................... 1
1.4 Research objective ......................................................................................................................................................... 3
1.5 Report structure ............................................................................................................................................................ 3
2. Material selection ............................................................................................................................................................. 5
2.1 Introduction and requirements ...................................................................................................................................... 5
2.2 Fiber reinforced polymer mechanics ............................................................................................................................... 5
2.3 Matrix material ............................................................................................................................................................. 7 2.3.1 Introduction ......................................................................................................................................................... 7 2.3.2 Thermosetting polymers ...................................................................................................................................... 8
2.3.2.1 Polyester matrix .......................................................................................................................................... 8 2.3.2.2 Epoxy matrix ............................................................................................................................................... 9 2.3.2.3 Vinyl ester matrix ........................................................................................................................................ 9 2.3.2.4 Polymerization agents ............................................................................................................................... 10
2.3.3 Thermoplastics ................................................................................................................................................... 10 2.3.4 Filler materials ................................................................................................................................................... 14 2.3.5 Additives ............................................................................................................................................................ 14
2.4 Reinforcing fibers ........................................................................................................................................................ 15 2.4.1 Introduction ....................................................................................................................................................... 15 2.4.2 Glass fibers......................................................................................................................................................... 15 2.4.3 Carbon fibers ..................................................................................................................................................... 16 2.4.4 Aramid fibers ..................................................................................................................................................... 17
2.5 Durability .................................................................................................................................................................... 17 2.5.1 Introduction/design criteria ................................................................................................................................ 17 2.5.2 Hydrolytic ageing ............................................................................................................................................... 17
2.5.2.1 Degradation mechanisms .......................................................................................................................... 17 2.5.2.2 Previous research ...................................................................................................................................... 18 2.5.2.3 Interface degradation ................................................................................................................................ 19 2.5.2.4 Recommendations .................................................................................................................................... 19
2.5.3 Creep ................................................................................................................................................................. 20 2.5.4 Heat and fire resistance ...................................................................................................................................... 21 2.5.5 Fatigue ............................................................................................................................................................... 22 2.5.6 Other properties ................................................................................................................................................ 22
2.5.6.1 Freeze-thaw cycling ................................................................................................................................... 22 2.5.6.2 UV-radiation ............................................................................................................................................. 23
IV Table of Contents
2.5.6.3 Wear ......................................................................................................................................................... 23 2.5.6.4 Residual stresses ....................................................................................................................................... 23 2.5.6.5 Material impact strength ........................................................................................................................... 23 2.5.6.6 Biological degradation ............................................................................................................................... 23
2.6 Discussion ................................................................................................................................................................... 24 2.6.1 Matrix material .................................................................................................................................................. 24 2.6.2 Reinforcing fibers ............................................................................................................................................... 24 2.6.3 Durability ........................................................................................................................................................... 24
2.7 Conclusion ................................................................................................................................................................... 25
3. Manufacturing ................................................................................................................................................................ 27
3.1 Shallow foundation shape............................................................................................................................................ 27
3.2 Manufacturing process ................................................................................................................................................ 27
3.3 Hot molding ................................................................................................................................................................ 28
3.4 Pultrusion .................................................................................................................................................................... 30
3.5 Discussion ................................................................................................................................................................... 31
3.6 Conclusion ................................................................................................................................................................... 31
3.7 Grating dimensions ..................................................................................................................................................... 31
4. Structure transport ......................................................................................................................................................... 33
4.1 Introduction ................................................................................................................................................................ 33
4.2 Sea fastening............................................................................................................................................................... 33
4.3 Possibility of re-hitting ................................................................................................................................................. 33
4.4 Damage during transport ............................................................................................................................................ 33
4.5 Conclusion ................................................................................................................................................................... 33
5. Lifting through the splash zone ....................................................................................................................................... 35
5.1 Introduction ................................................................................................................................................................ 35
5.2 Considerations and assumptions .................................................................................................................................. 35
5.3 Environmental conditions ............................................................................................................................................ 36 5.3.1 Wave spectrum .................................................................................................................................................. 36 5.3.2 Response amplitude operator ............................................................................................................................ 37 5.3.3 Wave particle motion ......................................................................................................................................... 38
5.4 Loads in the splash zone .............................................................................................................................................. 39
5.5 Hydrodynamic forces ................................................................................................................................................... 39 5.5.1 Slamming impact force ....................................................................................................................................... 40 5.5.2 Varying buoyancy force ...................................................................................................................................... 40 5.5.3 Mass force ......................................................................................................................................................... 41 5.5.4 Drag force .......................................................................................................................................................... 41 5.5.5 Snap force .......................................................................................................................................................... 41
5.6 Hydrodynamic coefficients ........................................................................................................................................... 42 5.6.1 Added mass ....................................................................................................................................................... 42 5.6.2 Drag coefficient .................................................................................................................................................. 44 5.6.3 Slamming coefficient .......................................................................................................................................... 46
5.7 Load cases ................................................................................................................................................................... 46
5.8 Operability .................................................................................................................................................................. 48 5.8.1 Dynamic amplification factor .............................................................................................................................. 48 5.8.2 Installation criteria ............................................................................................................................................. 48
5.9 Results ........................................................................................................................................................................ 49
Table of Contents V
5.9.1 Total forces ........................................................................................................................................................ 49 5.9.2 Forces on grating ................................................................................................................................................ 50 5.9.3 Workability scatter ............................................................................................................................................. 50 5.9.4 Operability ......................................................................................................................................................... 51
5.10 Sensitivity analysis .................................................................................................................................................. 52
5.11 Discussion ............................................................................................................................................................... 54
5.12 Conclusion .............................................................................................................................................................. 54
6. Lowering to seabed ......................................................................................................................................................... 55
6.1 Introduction ................................................................................................................................................................ 55
6.2 Resonance period ........................................................................................................................................................ 55
6.3 Results ........................................................................................................................................................................ 55 6.3.1 Motion behavior ................................................................................................................................................ 55 6.3.2 Lowering criteria ................................................................................................................................................ 56 6.3.3 Force on grating ................................................................................................................................................. 57
6.4 Discussion ................................................................................................................................................................... 57
6.5 Conclusion ................................................................................................................................................................... 57
7. Landing on seabed .......................................................................................................................................................... 59
7.1 Introduction ................................................................................................................................................................ 59
7.2 Seabed approach ......................................................................................................................................................... 59 7.2.1 Model ................................................................................................................................................................ 59 7.2.2 Landing phases ................................................................................................................................................... 59 7.2.3 Expectations....................................................................................................................................................... 61
7.3 Forces ......................................................................................................................................................................... 61 7.3.1 High frequency added mass ................................................................................................................................ 61 7.3.2 Drag force .......................................................................................................................................................... 61 7.3.3 Escaping water ................................................................................................................................................... 62 7.3.4 Soil reaction ....................................................................................................................................................... 62 7.3.5 Structure inertia ................................................................................................................................................. 62 7.3.6 Submerged weight ............................................................................................................................................. 63
7.4 Results ........................................................................................................................................................................ 63 7.4.1 Mud mat landing ................................................................................................................................................ 63 7.4.2 Grating landing................................................................................................................................................... 64 7.4.3 Landing impact force on foundation ................................................................................................................... 66
7.5 Sensitivity analysis ....................................................................................................................................................... 67
7.6 Discussion ................................................................................................................................................................... 67
7.7 Conclusion ................................................................................................................................................................... 68
8. Foundation design ........................................................................................................................................................... 69
8.1 Introduction ................................................................................................................................................................ 69
8.2 Design parameters ...................................................................................................................................................... 70 8.2.1 Soil ..................................................................................................................................................................... 70 8.2.2 Friction............................................................................................................................................................... 70 8.2.3 Foundation......................................................................................................................................................... 71 8.2.4 Skirt penetration ................................................................................................................................................ 71
8.3 Drained conditions (sand) ............................................................................................................................................ 71 8.3.1 Vertical bearing capacity .................................................................................................................................... 71
8.3.1.1 Arching ..................................................................................................................................................... 71 8.3.1.2 Interference .............................................................................................................................................. 74 8.3.1.3 Grating foundation .................................................................................................................................... 75 8.3.1.4 Mud mat foundation ................................................................................................................................. 77
VI Table of Contents
8.3.2 Horizontal bearing capacity ................................................................................................................................ 77
8.4 Undrained conditions (clay) ......................................................................................................................................... 79 8.4.1 Vertical bearing capacity .................................................................................................................................... 79
8.4.1.1 Upheaval................................................................................................................................................... 79 8.4.1.2 Remolding ................................................................................................................................................. 80 8.4.1.3 Grating foundation .................................................................................................................................... 80 8.4.1.4 Flat plate ................................................................................................................................................... 81
8.4.2 Horizontal bearing capacity ................................................................................................................................ 81
8.5 Settlement................................................................................................................................................................... 82 8.5.1 Immediate settlement of foundation .................................................................................................................. 82 8.5.2 Consolidation settlement ................................................................................................................................... 83 8.5.3 Objects below the seabed surface ...................................................................................................................... 84
8.6 Results ........................................................................................................................................................................ 84 8.6.1 Assumptions ...................................................................................................................................................... 84 8.6.2 Vertical bearing capacity sand ............................................................................................................................ 85 8.6.3 Vertical bearing capacity in clay .......................................................................................................................... 85 8.6.4 Horizontal bearing capacity ................................................................................................................................ 86 8.6.5 Settlement ......................................................................................................................................................... 86
8.7 Sensitivity analysis ....................................................................................................................................................... 87
8.8 Discussion ................................................................................................................................................................... 89 8.8.1 Bearing capacity ................................................................................................................................................. 89 8.8.2 Horizontal bearing capacity ................................................................................................................................ 93 8.8.3 Settlement ......................................................................................................................................................... 93
8.9 Conclusion ................................................................................................................................................................... 93
9. Grating deformation ....................................................................................................................................................... 95
9.1 Introduction ................................................................................................................................................................ 95 9.1.1 Load cases .......................................................................................................................................................... 95 9.1.2 Plate theory ....................................................................................................................................................... 95
9.2 The Navier solution ...................................................................................................................................................... 95 9.2.1 Plate mechanics ................................................................................................................................................. 95 9.2.2 General solution ................................................................................................................................................. 98
9.3 Elastic foundation ........................................................................................................................................................ 99 9.3.1 Mechanics .......................................................................................................................................................... 99 9.3.2 General solution ............................................................................................................................................... 101
9.4 Orthotropic plate ....................................................................................................................................................... 101 9.4.1 Material properties .......................................................................................................................................... 101
9.4.1.1 Isotropic material .................................................................................................................................... 101 9.4.1.2 Anisotropic material ................................................................................................................................ 101 9.4.1.3 Orthotropic material ............................................................................................................................... 102
9.4.2 General solution ............................................................................................................................................... 102 9.4.3 Grating parameters .......................................................................................................................................... 102
9.5 Membrane stresses ................................................................................................................................................... 104
9.6 Internal forces ........................................................................................................................................................... 105 9.6.1 Section forces................................................................................................................................................... 105 9.6.2 Reaction forces ................................................................................................................................................ 108
9.7 Shear deformation..................................................................................................................................................... 108
9.8 Plate vibration ........................................................................................................................................................... 109
9.9 Results ...................................................................................................................................................................... 110 9.9.1 In-situ loading .................................................................................................................................................. 110
9.9.1.1 Infinitely stiff grating ............................................................................................................................... 110 9.9.1.2 Flexible grating ........................................................................................................................................ 111
9.9.2 Accidental loading ............................................................................................................................................ 115
Table of Contents VII
9.9.2.1 Impact resistance .................................................................................................................................... 115 9.9.2.2 Shear punch resistance ........................................................................................................................... 118 9.9.2.3 Reaction forces ....................................................................................................................................... 119
9.10 Sensitivity analysis ................................................................................................................................................ 119 9.10.1 In-situ loading .............................................................................................................................................. 119 9.10.2 Accidental loading ....................................................................................................................................... 119
9.11 Discussion ............................................................................................................................................................. 122
9.12 Conclusion ............................................................................................................................................................ 123
10. Connection design ......................................................................................................................................................... 125
10.1 Introduction .......................................................................................................................................................... 125
10.2 Adhesive bonding.................................................................................................................................................. 125
10.3 Welding ................................................................................................................................................................ 125
10.4 Interlocking........................................................................................................................................................... 126
10.5 Mechanical fastening ............................................................................................................................................ 126
10.6 Results .................................................................................................................................................................. 128 10.6.1 Connection method ..................................................................................................................................... 128 10.6.2 Connection stresses ..................................................................................................................................... 129
10.7 Discussion ............................................................................................................................................................. 130
10.8 Conclusion ............................................................................................................................................................ 130
11. Cost analysis .................................................................................................................................................................. 131
11.1 Introduction .......................................................................................................................................................... 131
11.2 Cost breakdown .................................................................................................................................................... 131
11.3 Results .................................................................................................................................................................. 132
11.4 Sensitivity analysis ................................................................................................................................................ 133
11.5 Discussion ............................................................................................................................................................. 133
11.6 Conclusion ............................................................................................................................................................ 134
12. Sustainability................................................................................................................................................................. 135
12.1 Introduction .......................................................................................................................................................... 135
12.2 Life cycle assessment ............................................................................................................................................ 135
12.3 Results .................................................................................................................................................................. 136 12.3.1 Emissions ..................................................................................................................................................... 136 12.3.2 Embodied energy ......................................................................................................................................... 137 12.3.3 Waste management .................................................................................................................................... 138
12.4 Discussion ............................................................................................................................................................. 138
12.5 Conclusion ............................................................................................................................................................ 138
13. Results .......................................................................................................................................................................... 141
13.1 Material selection ................................................................................................................................................. 141
13.2 Manufacturing ...................................................................................................................................................... 142
13.3 Structure transport ............................................................................................................................................... 142
13.4 Lifting through the splash zone ............................................................................................................................. 142
13.5 Lowering to seabed ............................................................................................................................................... 142
13.6 Landing on seabed ................................................................................................................................................ 142
VIII Table of Contents
13.7 Foundation design ................................................................................................................................................ 143
13.8 Foundation deformation ....................................................................................................................................... 143
13.9 Connection design ................................................................................................................................................. 143
13.10 Cost analysis ......................................................................................................................................................... 144
13.11 Sustainability ........................................................................................................................................................ 144
14. Discussion ..................................................................................................................................................................... 145
15. Conclusion ..................................................................................................................................................................... 146
Future research and recommendations .................................................................................................................................. 147
Recommendations .............................................................................................................................................................. 147
Developments .................................................................................................................................................................... 148
References ............................................................................................................................................................................. 149
List of Figures Figure 1.1: Global energy consumption by fuel [1] ....................................................................................................................... 1 Figure 1.2: FLET protection structure ........................................................................................................................................... 2 Figure 2.1: Load transfer and stress distribution in a single fiber embedded in matrix material [5] ............................................... 6 Figure 2.2: Unidirectional composite layer [5].............................................................................................................................. 6 Figure 2.3: Arrangement of molecules in (a) amorphous polymers and (b) semi-crystalline polymers [6]...................................... 7 Figure 2.4: Schematic representation of a cross-linked polyester [6] ............................................................................................ 8 Figure 2.5: Schematic representation of a cross-linked solid epoxy [6] ......................................................................................... 9 Figure 2.6: Schematic representation of a cross-linked vinyl ester resin [6] ................................................................................ 10 Figure 2.7: Fiberglass rovings..................................................................................................................................................... 15 Figure 2.8: Typical creep response of material subjected to constant load [26] .......................................................................... 20 Figure 2.9: Schematic representation of TTSP [26] ..................................................................................................................... 21 Figure 3.1: Molded grating [37] ................................................................................................................................................. 27 Figure 3.2: Pultruded grating [37] .............................................................................................................................................. 27 Figure 3.3: Molded grating machine [38] ................................................................................................................................... 28 Figure 3.4: close-up molded grating machine [89] ..................................................................................................................... 28 Figure 3.5: Layout molded grating ............................................................................................................................................. 29 Figure 3.6: Molded grating in platform splash zone [39] ............................................................................................................ 29 Figure 3.7: Pultrusion process [37] ............................................................................................................................................ 30 Figure 3.8: Considered grating dimensions ................................................................................................................................ 31 Figure 5.1: Vessel coordinate system ......................................................................................................................................... 35 Figure 5.2: Diffraction analysis on the Audacia [41].................................................................................................................... 36 Figure 5.3: Crane tip response for incoming wave direction β = 157.5°....................................................................................... 38 Figure 5.4: Definitions reference volume [42] ............................................................................................................................ 42 Figure 5.5: Added mass reduction factor as a result of perforation ratio [42] ............................................................................. 43 Figure 5.6: Definitions reference volume [42] ............................................................................................................................ 44 Figure 5.7: Rectangular plate normal to flow direction............................................................................................................... 44 Figure 5.8: Circular cylinder normal to the flow ......................................................................................................................... 45 Figure 5.9: Flow past sharp plate for high Reynolds number [48] ............................................................................................... 46 Figure 5.10: Load case 1, still water 1 meter beneath foundation .............................................................................................. 47 Figure 5.11: Load case 2, still water 1 meter above top foundation ............................................................................................ 47 Figure 5.12: Load case 3, still water 1 meter beneath top chords ............................................................................................... 48 Figure 5.13: Load case 4, still water 1 meter above top chords .................................................................................................. 48 Figure 5.14: Total forces on structure with mud mat foundation................................................................................................ 49 Figure 5.15: Total forces on structure with grating foundation ................................................................................................... 49 Figure 5.16: Total forces dominant load case ............................................................................................................................. 50 Figure 5.17: Workability structure equipped with mud mat foundation ..................................................................................... 51 Figure 5.18: Workability structure equipped with grating foundation ........................................................................................ 51 Figure 5.19: Sensitivity workability grating projected area ......................................................................................................... 53 Figure 5.20: Sensitivity workability grating wave direction ......................................................................................................... 53 Figure 6.1: Eigenperiod lowering phase grating and mud mat foundation .................................................................................. 56 Figure 6.2: Annual wave spectrum Laggan ................................................................................................................................. 56 Figure 7.1: Landing forces on structure unaffected by seabed .................................................................................................... 60 Figure 7.2: Landing forces on structure close to seabed ............................................................................................................. 60 Figure 7.3: Landing forces on structure for penetrating skirts .................................................................................................... 60 Figure 7.4: Landing forces on structure for foundation touchdown ............................................................................................ 61 Figure 7.5: Structure with mud mat foundation clearance and velocity over time ...................................................................... 63 Figure 7.6: Acting forces on structure with mud mat foundation................................................................................................ 64 Figure 7.7: Combined forces on structure with mud mat foundation ......................................................................................... 64 Figure 7.8: Structure with grating foundation clearance and velocity over time ......................................................................... 65 Figure 7.9: Acting forces on structure with grating foundation ................................................................................................... 65 Figure 7.10: Combined forces on structure with grating foundation ........................................................................................... 66 Figure 7.11: Change in inertia of the mud mat foundation ......................................................................................................... 66 Figure 7.12: Change of inertia of the grating foundation ............................................................................................................ 67 Figure 8.1: Stability envelope undrained soils ............................................................................................................................ 70 Figure 8.2: Stability envelope drained soils ................................................................................................................................ 70
X List of Figures Figure 8.3: Forces acting on soil element [2] .............................................................................................................................. 72 Figure 8.4: Forces acting on a soil element in a grating perforation ............................................................................................ 73 Figure 8.5: Vertical effective stress profile in grating and grillage foundations............................................................................ 74 Figure 8.6: Failure mechanism of a single footing [62] ............................................................................................................... 74 Figure 8.7: Schematic diagram of soil resistance on penetrating bars [3] .................................................................................... 75 Figure 8.8: Mechanics horizontal resistance grating foundation ................................................................................................. 78 Figure 8.9: Correction factor F for rough and smooth footings [71] ............................................................................................ 81 Figure 8.10: Influence factor for settlements of embedded foundations [72] ............................................................................. 82 Figure 8.11: Influence factor for settlement of embedded foundations [72] ............................................................................... 83 Figure 8.12: Vertical bearing capacity in drained soil.................................................................................................................. 85 Figure 8.13: Vertical bearing capacity in undrained soil.............................................................................................................. 86 Figure 8.14: Base contribution to total bearing capacity of foundation ...................................................................................... 89 Figure 8.15: Required penetration depth against spacing ratio .................................................................................................. 90 Figure 8.16: Normalized required penetration depth to spacing ratio ........................................................................................ 90 Figure 8.17: Required grating weight for penetrated depth to spacing ratio ............................................................................... 91 Figure 8.18: Required penetration depth for grillage and grating foundations ............................................................................ 91 Figure 8.19: Side area length against projected area of foundations .......................................................................................... 92 Figure 9.1: Moments and forces acting on an element [74] ........................................................................................................ 96 Figure 9.2: Coordinate system of a plate.................................................................................................................................... 97 Figure 9.3: Dimensions patch load [73] ...................................................................................................................................... 99 Figure 9.4: Schematic representation of plate pressed into soil at the edges [74] ....................................................................... 99 Figure 9.5: Contact pressure and deflection profile flexible footing .......................................................................................... 100 Figure 9.6: Contact pressure and deflection profile rigid footing [76] ....................................................................................... 100 Figure 9.7: Comparison of vertical stress distributions for flexible or rigid slabs [77] ................................................................ 101 Figure 9.8: Grating parameters ................................................................................................................................................ 103 Figure 9.9: Moment distribution between successive nodes .................................................................................................... 106 Figure 9.10: Stress profile over height for bending moments ................................................................................................... 107 Figure 9.11: Stress profile over height for twisting moments ................................................................................................... 107 Figure 9.12: Stress profile over height for shear forces ............................................................................................................ 107 Figure 9.13: Deformation of single grating in clay .................................................................................................................... 111 Figure 9.14: Deformation grating compared with infinitely stiff plate ....................................................................................... 111 Figure 9.15: Bending moment in the x-direction ...................................................................................................................... 112 Figure 9.16: Bending moment in the y-direction ...................................................................................................................... 112 Figure 9.17: Twisting moment acting in the x-direction ............................................................................................................ 113 Figure 9.18: Twisting moment acting in the y-direction ............................................................................................................ 113 Figure 9.19: Shear forces per unit length in the y-direction ...................................................................................................... 114 Figure 9.20: Shear forces per unit length in the x-direction ...................................................................................................... 114 Figure 9.21: Plate reaction for mid plate deflection ................................................................................................................. 116 Figure 9.22: Assumed load profile: half sine pulse.................................................................................................................... 116 Figure 9.23: Work done by grating deflection .......................................................................................................................... 117 Figure 9.24: Mid plate deflection during impact for ti = 2 s ....................................................................................................... 118 Figure 9.25: Sensitivity grating impact deflection ..................................................................................................................... 121 Figure 9.26: Sensitivity grating impact stress ........................................................................................................................... 121 Figure 10.1: Grating M-clip ...................................................................................................................................................... 126 Figure 10.2: Grating C-clip ....................................................................................................................................................... 126 Figure 10.3: Grating E-clip ....................................................................................................................................................... 127 Figure 10.4: Grating Paw-clip ................................................................................................................................................... 127 Figure 10.5: Grating clamp [94] ............................................................................................................................................... 127 Figure 10.6: Clamp layout ........................................................................................................................................................ 127 Figure 10.7: Gratings suspended under bottom flange ............................................................................................................. 128 Figure 10.8: Gratings resting on bottom flange ........................................................................................................................ 128 Figure 12.1: Raw material flow diagram composite [92]........................................................................................................... 136 Figure 12.2: Raw material flow diagram steel .......................................................................................................................... 136 Figure 12.3: Embodied energy diagram pultruded grating [92]................................................................................................. 137
List of Tables Table 1.1: Approximation weight saving composite ..................................................................................................................... 3 Table 2.1: Typical properties thermosetting polymers [7, 10] ..................................................................................................... 10 Table 2.2: Typical properties thermoplastic polymers [12] ......................................................................................................... 14 Table 2.3: Typical properties fibers [7] ....................................................................................................................................... 17 Table 5.1: Specifications of the Audacia [40] .............................................................................................................................. 35 Table 5.2: Coordinates lifting crane [40] [41] ............................................................................................................................. 36 Table 5.3: Annual wave probability scatter for Laggan [%] ......................................................................................................... 51 Table 5.4: Sensitivity grating added mass .................................................................................................................................. 52 Table 5.5: Sensitivity grating maximum load .............................................................................................................................. 52 Table 5.6: Sensitivity local grating pressure load case 1 ............................................................................................................. 54 Table 7.1: Sensitivity landing impact pressure on grating ........................................................................................................... 67 Table 8.1: Soil properties ........................................................................................................................................................... 70 Table 8.2: Structure parameters ................................................................................................................................................ 71 Table 8.3: Horizontal sliding resistance foundations .................................................................................................................. 86 Table 8.4: Soil specific parameters............................................................................................................................................. 87 Table 8.5: Sensitivity vertical bearing capacity in sand at penetration of 0.1 m ........................................................................... 87 Table 8.6: Sensitivity vertical bearing capacity in clay at penetration of 0.1 m ............................................................................ 87 Table 8.7: Sensitivity required penetration depth in sand .......................................................................................................... 88 Table 8.8: Sensitivity required penetration depth in clay............................................................................................................ 88 Table 8.9: Sensitivity immediate settlement in sand .................................................................................................................. 88 Table 8.10: Sensitivity immediate settlement in clay .................................................................................................................. 88 Table 8.11: Sensitivity horizontal bearing capacity in sand ......................................................................................................... 88 Table 8.12: Sensitivity horizontal bearing capacity in clay .......................................................................................................... 88 Table 9.1: Composite properties [82]....................................................................................................................................... 114 Table 9.2: Design impact energy for subsea production structures [83].................................................................................... 115 Table 9.3: Sensitivity grating mid plate deflection in clay ......................................................................................................... 119 Table 9.4: Sensitivity grating reaction forces in clay ................................................................................................................. 119 Table 9.5: Sensitivity grating impact deflection ........................................................................................................................ 120 Table 9.6: Sensitivity grating impact stresses ........................................................................................................................... 120 Table 9.7: Senstivity impact reaction forces on the connections............................................................................................... 120 Table 9.8: Sensitivity shear punch capacity .............................................................................................................................. 121 Table 10.1: Stainless steel hardware properties ....................................................................................................................... 129 Table 11.1: Cost breakdown shallow foundation...................................................................................................................... 133 Table 11.2: Sensitivity grating costs ......................................................................................................................................... 133 Table 12.1: Environmental impact shallow foundations ........................................................................................................... 136 Table 13.1: Composite material properties .............................................................................................................................. 141
Nomenclature Latin symbols
a Single grating length
A33 Heave added mass of structure
aarch Arching effect factor
Ab Total horizontal area of structure
Aboulder Boulder effective area
ac Vertical structure acceleration
Aclamp Clamp connection shear area
aE Type of soil reaction
Aflange Flange connection shear area
Aflow Water escape area
AFRP Grating connection shear area
Ah Horizontal open area of structure
Ahv Embedded vertical cross-sectional area
AM16 Bolt effective cross-sectional area
Ap Structure horizontal projected area
Aperf Perforation flow area
As Skin area per unit height
Aslam Slamming area
asoil Soil adhesion
aw Water particle acceleration
Ãw Mean water line area in the wave surface zone
Aγ Normalizing factor
b Single grating width
BPS Effective width foundation
c Soil cohesion
C Snap velocity correction factor
Ca Added mass coefficient
CD Drag coefficient in oscillatory flow
CD,fr Drag coefficient due to friction
CDS Drag coefficient in steady flow
Cs Slamming coefficient
Cx Torsional rigidity of grating bar in x-direction
d Water depth
D Flexural rigidity
Db Embedded depth
Deff Effective diameter perforations
Dfoundation Equivalent diameter of foundation
Dh Hydraulic diameter
Dosc Characteristic drag dimension
dq,c,γ Embedment depth correction factor
Ds Shear rigidity
Dx Flexural rigidity in x-direction
Dyx Torsional rigidity in x-direction
E Modulus of elasticity
Ef Modulus of the fiber
Ek Impact energy dropped object
Em Modulus of the matrix material
Esoil Modulus of the soil
f Unit skin friction capacity
F Footing roughness correction factor
Fclamp Load on clamp
FD Hydrodynamic drag force
Fescape Force due to escaping water flow
Fhydro Total hydrodynamic force on the structure
Finertia Inertia force of structure motion
FM Hydrodynamic mass force
Fslam Slamming impact force
Fsnap Snap force
Fsoil Force due to skirt and mud mat penetration
Fstatic Static force on the structure
Fstroke Maximum Cranemaster capacity
Ftotal Total structure load
Fρ Varying buoyancy force
G Shear modulus
g Gravitational constant
Gf Shear modulus fiber
Gm Shear modulus matrix material
H Torsional rigidity of grating
h Grating height
hc Structure clearance height
Hs Significant wave height
hskirt Height of the skirt
iq,c,γ Load inclination correction factor
Ixz Second moment of inertia in x-direction
k Subgrade modulus
K Lateral earth pressure coefficient
K0 Neutral earth pressure coefficient
kc Stiffness of Cranemaster
kflow Pressure loss coefficient
Klift Stiffness of hoisting system
Kp Passive lateral earth pressure coefficient
Kr Shear correction factor
Krd Drained horizontal soil reaction factor
Kru Undrained horizontal soil reaction factor
ksu Increase rate undrained shear strength
kwave Wave number
kwire Stiffness of lifting cable
L Cable length
Le Flow development length
LPS Effective length foundation
Lstroke Maximum Cranemaster stroke length
XIV Nomenclature
M Mass structure in air
Marcus moment
m Mass of cable unit length
Mclamp Bending moment due to clamp force
msoil Modulus number of the soil
Msoil Constrained modulus of the soil
Mtotal Total in-service structure weight
Mx Bending moment in x-direction
Myx Twisting moment in x-direction
Nc,q,γ Bearing capacity factors
Nqb Bearing capacity factor by Berezantzev
Nx Membrane stress in x-direction
P Point load
Wetted perimeter
p Perforation ratio
p0 Patch load
psoil Overburden pressure of soil
pw Dynamic water pressure
q Soil pressure
q0 Uniformly distributed load
QA33 Added mass high frequency resistance
Qb End bearing resistance
qb End bearing capacity
qc Lower bound cone resistance
Qd,h Design sliding resistance
Qd,v Design vertical soil resistance
qflow Flow rate of water
Qfoundation Force due to penetrating foundation
Qgrate Grate bearing resistance
Qmesh Added sliding resistance due to perforations
Qplate Plate bearing resistance
qplate Plate bearing capacity
Qs Skin friction resistance
qs Skin friction capacity
Qskirt Force due to penetrating skirts
Qsoil Total force on the soil
qu Ultimate bearing capacity
Qw Force due to water pressure
Qx Shear force per unit length in x-direction
Rd Total horizontal resistance drained soil
Re Reynolds number
Rshear Shear resistance of the structure
Ru Total horizontal resistance undrained soil
Sct Crane tip response spectrum
sgrate Spacing distance of adjacent bars
SJS Spectral density JONSWAP spectrum
SPM Spectral density Pierson-Moskovitz spectrum
sq,c,γ Foundation shape correction factor
su Undrained shear strength
T0 Resonance period of structure
tgrate Thickness grating bars
ti Interaction time impact load
Tp Peak period wave spectrum
Tp-ct Peak period crane tip spectrum
Tz Zero up-crossing period
V Structure displacement volume
vc Structure lowering velocity
vct Vertical crane tip velocity
Vf Fiber volume ratio
vff Freefall velocity
vflow Water escape velocity
Vm Matrix volume ratio
vperf Average water velocity through perforations
vr Vertical relative velocity
Vr Added mass reference volume
vs Slamming velocity
vsnap Snap velocity
vw Water particle velocity
Vx Reaction force at boundary
w Plate deflection
W Submerged weight of the structure
w0 Elastic soil deflection of plate edges
wc Classical theory deflection
Wflange Section modulus flange
ws Shear amplified deflection
xb Longitudinal location crane tip
yb Transverse location crane tip
z Penetration depth
z33 Vessel heave motion
zct Most probable crane tip heave motion
zm Oscillation amplitude
Nomenclature XV
Greek symbols
α Soil roughness factor
β Vessel heading
γ Peak shape parameter
γ' Effective unit weight of soil
γm Soil material coefficient
γr Rate effect factor for rapid loading
δ' Interface friction angle
δav Average settlement of foundation
ΔHclay Lateral resistance in undrained soil
ΔHsand Lateral resistance in drained soil
δsoil Soil displacement
δV Change in volume
εx Plate strain in x-direction
ζa Characteristic wave amplitude
η Vertical motion of lifted object
Vertical velocity of lifted object
Vertical acceleration of lifted object
ηa Most probable heave amplitude of crane tip motion
θ Adjustment factor cable mass and soft springs
θ55 Vessel pitch motion
λ Added mass skirt correction factor
μ Dynamic viscosity
μ0,1 Settlement influence factors
ν Poisson's ratio material
νf Poisson's ratio of fiber
νm Poisson's ratio of the matrix material
νsoil Poisson's ratio of soil
νx Poisson's ratio in x-direction
ξγ Bearing capacity efficiency factor
ρ Density
σ Spectral width parameter
σ’ Soil pressure
σa Reference stress
σbolt Shear stress in bolt
σclamp Shear stress in clamp
σd Design bearing pressure
σflange Flexural stress in flange
σFRP Shear stress in FRP
σ'h Horizontal effective soil stress
σn Normal pressure acting on friction interface
σsc Design soil bearing capacity
σst Shear strength threaded bolt shaft
σsu Shear strength unthreaded bolt shaft
σuts Ultimate tensile strength
σ'v Vertical effective soil stress
σxM Flexural stress in x-direction
σxN Axial stress in x-direction
ση Standard deviation crane tip displacement
τf Shear stress due to soil-foundation interface
τsoil Shear stress due to soil-soil interface
τxz Shear stress along xz-plane
τyx Torsional stress in x-direction
Υ Upheaval factor
φ' Internal friction angle
φ44 Vessel roll motion
ω Angular wave frequency
ωmn Natural frequency plate
ωp Angular spectral peak frequency
ωq Load frequency
Abbreviations
CoG Centre of Gravity
CPT Classical Plate Theory
CFD Computational Fluid Dynamics
DoF Degrees of Freedom
DNV Det Norske Veritas
DAF Dynamic Amplification Factor
FLET Flowline End Terminal
FRP Fiber Reinforced Polymer
FSDT First-order Shear Deformation Theory
JONSWAP Joint North Sea Wave Project
KC Keulegan-Carpenter
ROV Remotely Operated Vehicle
RAO Response Amplitude Operator
TTSP Time Temperature Superposition Principle
Preface This thesis is the conclusion of my master’s study in Offshore and Dredging Engineering at TU Delft. It required me to use all aspects of my bachelors and masters study in the form of soil mechanics, hydrodynamics, structural mechanics and even parts of my minor due to the use of a composite material. I would like to express my gratitude to my parents, for putting up with me throughout the graduation period. And most of all, to my girlfriend, for proofreading and her support during the writing process. Additionally, my thanks go to Patrick and Alireza at Allseas for providing insight and feedback on my report. Finally, I would like to thank Allseas for giving me the opportunity to graduate and the enjoyable time spent there.
1. Introduction
1.1 The oil and gas industry The ever-increasing demand for hydrocarbons has shifted exploitation from onshore production to shallow water production to the deep-water fields. Along with this change, the degree of engineering complexity is increased. Deeper water depth gives rise to more difficult installation of subsea facilities, harsher weather and more challenging well interventions.
Figure 1.1: Global energy consumption by fuel [1]
Until more greener options for energy such as wind farms, tidal energy and solar energy take over this demand, the production and demand of hydrocarbons will not decline. As the oil and gas fields become harder to reach, the oil and gas sector will also inevitably move towards the arctic, where large reserves may still be discovered. The increased amount of engineering required stimulates the use of innovative technologies and materials in the industry.
1.2 Allseas The Swiss-based Allseas Group S.A. is a global leader in the installation of subsea facilities and mainly, offshore pipelines. The company employs over 2,500 people worldwide and operates a fleet of vessels, specialized in pipe laying. The company was founded in 1985 and has gained experience in all kinds of offshore projects. Allseas offers services for project management, engineering and procurement including the installation and commissioning of offshore pipelines and subsea facilities. Recently, Allseas’ latest vessel, the Pioneering Spirit was launched and extends the company’s capabilities to heavy lifts and decommissioning of entire offshore platforms. The company utilizes S-lay mode for all its ships. The motion behavior of these ships in beams waves is therefore weak, with the likely exception of the Pioneering Spirit. The subsea facilities for the project are either installed in-line (welded to the pipeline and lowered over the stinger) or using J-mode (lifted over the side of the ship) if the structure is too large. For a structure installed over the side of the ship, the vessel heading may not be chosen to provide optimal motion behavior of the ship and object. This complicates the installation procedure.
1.3 Scope and background Because of suboptimal vessel heading or unfavorable weather conditions, the vessel and the crane response are amplified and significantly increase the wave forces in the splash zone on the lifted structure. These forces prevent
2 Introduction the structure from being lifted through the splash zone. This may result in rather large periods where the vessel is waiting for favorable weather. This is a costly operation and the effect of circumvention by careful planning and weather forecasting is limited. To avoid this problem a suitable solution is desired. To provide this solution, the considered structure and current practice are first discussed. A reference subsea
structure is selected to attain relevant dimensions and properties. The selected structure is a Flowline End Terminal (FLET) protection structure which Allseas’ vessel Audacia installed in 2012, for the Laggan-Tormore gas fields near the Shetlands. The FLET is the connection between the end of a main pipeline and a rigid spool or flexible jumper connected to other subsea facilities. The protection structure is a large steel frame in which the FLET itself is positioned. The protection structure acts as the foundation and provides protection against fishing activities, which might damage the FLET. The protection structure is a very large structure with a footprint of 35 m × 20 m. It consists of steel tubes and beams and flat steel plates (the mud mat) at the bottom. This provides the bearing capacity for the structure. Additionally, skirts of 0.75 m run along the circumference on the underside and provide extra stability when penetrated in the soil. The mud mats create the large horizontal area, which facilitates the excessive hydrodynamic loads on the structure and complicates the installation of the structure.
Figure 1.2: FLET protection structure
The considered protection structure is too large to be lifted on its side, as this would cause excessive lateral motions. Therefore, the structure had to be lifted through the splash zone upright. This is done by lifting the entire structure off a barge, removing the barge and then lowering it into the water. The structure is left to settle, until the mud mats are submerged, before lowering it further towards the seabed. The structure is subjected to significant slam and inertia forces during this operation. These hydrodynamic forces limit the operation window to install the structure. To reduce the hydrodynamic loads on the structure, Bransby et al. suggested replacing the mud mat plates with a grillage foundation [2, 3]. A grillage foundation is a series of vertical plates, mounted to the underside of the structure at certain spacing. This foundation is more ventilated than the original mud mat plates and the water may flow through the vertical plates. For this foundation, the horizontal area is significantly reduced, thereby reducing the hydrodynamic forces during the lift through the splash zone. This reduction in base area however, coincides with a reduction in the bearing capacity of the structure. The vertical plates penetrate the soil on the seabed and the entire structure is placed on the seabed. To provide sufficient bearing capacity, Bransby suggested increasing the depth of the vertical plates, creating a large enough length for the soil to build up skin resistance and plug between adjacent plates. Once the soil is plugged, the grillage foundation acts as a flat plate and their effective bearing capacities become equal. Bransby experimentally confirmed the effects of soil plugging within grillage foundations due to arching effects in course-grained soils. Koopman attempted to find a similar effect in soft soils experimentally, but a similar result of increased bearing capacity was not established [4]. Bransby additionally determined that the penetration required for a grillage foundation to attain full plugging and have the same bearing capacity as a flat plate was quite large. To obtain the bearing capacity of a flat plate at zero penetration, full plugging was not required and sufficient bearing capacity was reached at a reasonable depth. The weight of the structure is significantly increased by applying the suggested grillage foundations to large structures such as the protection structure. The large increase of steel volume complicates the lifting and lowering operation and therefore a different solution is desired. To reduce the weight, while maintaining the advantages of the grillage foundation, it is suggested to use a composite material. The most suitable composite material is likely a fiber-reinforced polymer (FRP), see table 1.1. This
1.4 Research objective 3
composite has high strength, decent stiffness and good corrosion resistance. Using FRP as a subsea structural material creates its own complications and this will require additional investigation to determine the applicability of this material as a shallow foundation. The material will need to withstand the marine environment and maintain sufficient strength and stiffness after 30 years of service. FRPs are already used in the offshore industry, but its use in the subsea environment is limited to FRP covers, protecting sensitive equipment from dropped objects. This material
is well suited for this application, owing to its high impact strength.
Table 1.1: Approximation weight saving composite
Component Weight in air Submerged weight Unit
Steel mud mat plates 53,000 46,000 kg
Steel grill 132,000 115,000 kg
Composite grating (grill) 34,000 17,000 kg
Composite grating (mesh) 28,000 13,000 kg
Protection structure 306,000 182,000 kg
Protection structure + FLET + Roof panels 465,000 308,000 kg
FRPs lack the stiffness of steels, making the grillage shape a less than ideal solution. By using a mesh-shaped grating, the transverse bars provide lateral support and the low stiffness is resolved. Two kinds of composite gratings are commercially available, which are discussed in chapter 3. An additional benefit of the gratings is the bi-directionality, providing load transfer in two directions. In theory, the composite grating may provide a promising solution to the problems. It is therefore a promising alternative to investigate in more detail. This may determine the benefits and shortcomings of using such a material for the foundation for a large subsea structure.
1.4 Research objective To uncover the pros and cons of a composite shallow foundation for a subsea structure, the following question is posed. When designing a composite shallow foundation for subsea structures, what are the critical design obstacles and
how to overcome them? This results in several sub questions:
What are the most suitable materials in a composite for a structural component? How does the composite material improve the offshore installation procedures? Does the foundation generate enough bearing capacity? How does the grating deform and is the composite material strong enough? How to connect the gratings to the structure? How does the cost compare to the original foundation? What is the impact of the composite foundation on the environment?
1.5 Report structure The report is structured in the procedure of getting the proposed grating built and eventually installed on the seabed. It follows the order of first selecting a suitable material, which satisfies the requirements for the grating integrity and strength after 30 years on the seabed. The matrix material and fibers are separately investigated and the most suitable manufacturing procedure is selected. Next, a comparison between the mud mat plates and the composite gratings is made for the lift through the plash zone. The total dynamic forces and critical load case are determined and the forces on the gratings are analyzed. The structure lowering operation is analyzed for the different foundations. The landing on the seabed is analyzed by checking the clearance and velocity of the structure close to the seabed. The impact on the soil is investigated by examining the forces between the structure and the soil during this operation. As this foundation may be used for different kinds of soil, the required penetration is determined by DNV and API methods and the foundation stability is analyzed. The penetration in sand and clay is different due to the varying bearing mechanics. Furthermore, the horizontal resistance of the foundation is analyzed and the immediate settlement is calculated.
4 Introduction Placing the foundation on the soil deforms the gratings and the magnitude is determined by the classical plate theory. This also allows for the internal forces within the composite to be calculated and the resulting reaction forces on the base frame of the protection structure. The deformation of the grating under dropped object loading is determined and the resulting stresses are checked against the composite strength. Having determined the reaction forces on the
base frame, the connection details are now designed. Two different connection methods are investigated and are dimensioned for the expected load. The cost efficiency of the costs of the new foundation is compared with the original mud mat plates and finally quick environmental impact assessment is done.
2. Material selection
2.1 Introduction and requirements As stated before, fiber reinforced polymers (FRP) provide an interesting option to replace steel in the foundation of a subsea structure. Looking at the design criteria, it becomes obvious why the material is considered, to design a ventilated shallow foundation. Lightweight: The used material may not be too heavy, as the volume required is likely to exceed the volume for
steel mud mats. The increased volume of the foundation in combination with a high-density material would create an undesirable foundation, as lifting off the barge would increase in difficulty.
Manufacturability: The manufacturing process of the material should be malleable enough to create such a relatively complicated shape, without diminishing its physical properties.
Material strength/stiffness: The forces the foundation endures are still very large, despite the ventilated structure reducing the loads during installation through the splash zone. The material is required to maintain strong and stiff enough to mitigate the forces due to installation of the structure and limit the deflection.
Durability: The material is placed in a marine environment, exposed to seawater, for a period of approximately 30 years and under a significant amount of water pressure. The material is required to preserve its physical properties for its intended use over this duration.
An FRP may fulfill all these criteria, but it still needs to be analyzed which type is most suitable for use in the discussed situation. To help determine this, the general mechanics of FRPs are first discussed, providing insight in how the loads act within the material. A composite consists of multiple materials. For an FRP this is generally reinforcing fibers and a polymeric matrix to keep the fibers together. Combining these materials together creates a material that displays a combination of material properties that neither original component can provide. The main components complement each other. The fibers have a very high strength and stiffness, but are also very brittle and vulnerable to environmental degradation. The matrix material solves these problems by keeping the fibers in the desired geometrical arrangement and consequently preventing them from buckling. The matrix material surrounds the fibers and protects degradation by environmental effects. As a result of the matrix material, the loads are able to be redistributed to the reinforcing fibers and allow loads to be transferred between fibers. The last main benefit of FRPs is the low density. Both the fibers and matrix material are significantly lighter than steel resulting in an excellent strength to weight ratio.
2.2 Fiber reinforced polymer mechanics The mechanism of load transfer between the matrix and fibers may be best explained using a single fiber enclosed in a cylinder of matrix material. A tensile load in the composite is transferred between the fiber and the matrix material via shear stress. The shear stress is generated on the outer surface of the fiber, and this stress is decreased from its maximum value at the ends of the fiber to zero moving towards the middle of the element. The tensile stress within the cross-section of the fiber displays the opposite trend, being zero at the ends and maximum towards the middle of the fiber. These two stresses together balance the external force on the material [5].
6 Material selection
Figure 2.1: Load transfer and stress distribution in a single fiber embedded in matrix material [5]
The distance from the ends of the fiber to the point where the shear stresses become zero and the distance to where the tensile stresses become maximum, is the characteristic distance. The stresses caused by a compressive load are of the opposite sign within the characteristic distance. Due to the compression, the fibers tend to buckle, but the
matrix material provides lateral support to prevent this.
Figure 2.2: Unidirectional composite layer [5]
The forces within the fibers and the matrix material must balance. Therefore by taking a representative element of the composite, the stress in the direction of the fibers is (2.1)
Dividing this equation by the strain in the composite results in
(2.2)
This relation is known as the rule of mixtures and predicts the overall stiffness modulus in terms of the composite’s constituents’ moduli and volume fractions. The stiffness in the transverse direction may be determined from the empirical model known as the Halpin-Tsai equation:
(2.3)
The Poisson’s ratio for the composite follows: (2.4)
The shear modulus is
(2.5)
2.3 Matrix material 7
Where and are the shear moduli of the fiber and matrix material respectively:
( )
( ) (2.6)
Where =
= =
= =
=
When comparing the computed properties derived from the composite constituents with the values from manufacturers and literature study, the determined values coincide closely.
2.3 Matrix material
2.3.1 Introduction The definition of a polymer is a long-chain molecule containing one or more repeating atoms, bonded together by strong covalent bonds. A polymeric material, better known as a plastic, is a collection of these large chains of similar chemical structure. In a solid form these molecules may be fixed, either randomly, as an amorphous polymer, or as a mixture of ordered and randomly distributed chains, as semi crystalline polymers, see figure 2.3.
Figure 2.3: Arrangement of molecules in (a) amorphous polymers and (b) semi-crystalline polymers [6] Polymers for the use in structural applications are divided in two broad categories: thermoplastic and thermosetting polymers. The chains in a thermosetting polymer (called resins) are chemically joined together by strong cross-links formed during a polymerization process (the curing reaction). The material is polymerized by the reaction between the resin and a hardener. The molecules connect together to form a rigid three-dimensional network. This process is irreversible. The formed cross-links do not soften under application of heat and thus thermosetting resins may not be reshaped. Common thermosetting polymers are polyesters, vinyl esters and epoxies. Traditionally, thermosetting polymers are the commonly used matrix material in FRPs. The precursor materials used in the curing process of thermosetting polymers are usually of low molecular weight and with very low viscosity. Fibers are infused with this material prior to the start of the polymerization process. The low viscosity of the resin provides easy wetting of the fibers, leading to a good wet-out without the requisite of pressure or high temperatures. A good wetting between the fiber and the surrounding resin is vital in achieving a good mechanical performance of the composite. Advantages of thermosetting polymers in favor of thermoplastics are the thermal stability and chemical resistance. A thermosetting polymer will typically have a higher maximum operating temperature and usually improved strength and stiffness over thermoplastic polymers. Downsides of thermosets are the limited storage life of the resin before it
8 Material selection is used in the manufacturing process and the slow curing time. The relative low impact strength results from their low strain to failure. In thermoplastic polymers, the molecular chains do not share a chemical bond nor undergo any chemical transformation during processing. Instead, weak secondary bonds and intermolecular forces hold them together.
These bonds may be broken by application of heat, which allows the chains to flow to a new configuration, and upon cooling, the secondary bonds are repaired. Once these bonds are restored, the polymer is fixed in its new shape. This softening, melting and reshaping is the main characteristic of thermoplastic polymers. Common thermoplastic polymers are polyamides (PA), polypropylenes (PP) and polycarbonates (PC). Thermoplastics display high impact strength and fracture resistance. In combination with the long shelf life and short manufacturing time, make this re-shapeable polymer an interesting option. Furthermore, thermoplastics are easily handled, joined together and reprocessed or recycled. In spite of these practical properties, reinforced thermoplastics are not yet regularly applied, due to higher creep and low thermal stability. Continued development of thermoplastics is ongoing and its use is expected to eventually rise. Other disadvantages of thermoplastics are that they show significantly worse properties of fiber impregnation and the thermoplastic polymers are difficult to process due to their higher viscosity. Heat or pressure is required which increase the manufacturing costs.
2.3.2 Thermosetting polymers To be able to select a suitable matrix material, the polymeric are investigated in more detail. The common thermosetting polymers are first examined.
2.3.2.1 Polyester matrix Polyester is the most widely used polymeric resin in FRP products. It is estimated that 75 % of the polymer composites employ this material. This high amount is due to the excellent balance of properties that polyesters provide. The resin demonstrates good mechanical, chemical and electrical properties. The resin is dimensionally stable and the low viscosity enables easy processing and a reasonable pot life. But the most attractive characteristic of polyesters is likely its low material cost. A downside of polyesters is the high shrinkage of the resin after polymerization. [7]
Thermosetting polyester starts as an unsaturated polyester resin that contains multiple carbon double bonds. This polyester is dissolved into a reactive polymerizable diluent, usually styrene, also containing C=C bonds. This reduces its viscosity and makes it easier to handle. The styrene helps form the cross-links in the matrix once the polymerization agent initiates the curing process. Once heat is applied, the polymerization agents decompose into free radicals, which predominantly react with the styrene and breaks the C=C bonds. The styrene now joins with the polyester molecules at the unsaturated points and forms new cross-links. This results in the solid polyester. [6]
Figure 2.4: Schematic representation of a cross-linked polyester [6]
Isophthalic polyester is the highest grade of polyester with specifically developed protection against corrosion and harsh chemicals. This resin sees use in both the molded and pultrusion manufacturing processes, which are discussed in chapter 3.
2.3 Matrix material 9
2.3.2.2 Epoxy matrix Epoxy resins have the best mechanical properties of the thermosetting polymers. Therefore, they are the preferred material when high mechanical properties are required. The temperature range in which they retain their strength and durability is particularly higher than the other thermosetting resins. They are widely used as adhesives and can be used in combination with a large amount of different fillers and reinforcing fibers. Epoxies however have higher viscosity, reducing the processing capabilities and impregnation of the fibers. As the curing time is longer than the poly- and vinyl esters, epoxy matrices show a considerable reduction in shrinkage of the material. This feature leads to the excellent adhesive capabilities and resistance to harmful substances. Epoxy resins are considerably more expensive than polyesters. Epoxy resins are shown to perform equally or better than other resins in a dry state, but also behave more sensitive to water ingress resulting in property degradation [8]. The base material for epoxy is diglycidyl ether of bisphenol A (DGEBA), which contains two epoxide groups at the end of the molecule. Diluents and flexibilizers can also be mixed with the starting material. The curing process is initiated by adding small amounts of polymerization agent (amine) to the mix, before adding the fibers. Hydrogen atoms in the amine group react with the epoxide groups and form cross-links with each other. This reaction continues and eventually a solid epoxy polymer is created.
Figure 2.5: Schematic representation of a cross-linked solid epoxy [6]
The properties of a cured epoxy essentially depend on the cross-linking density. By increasing this cross-linking density, the tensile modulus, glass transition temperature, thermal stability and chemical resistance may be improved.
Downsides of increasing the cross-linking are reduction of strain to failure and fracture toughness. The high viscosity of epoxies complicates the manufacturing of composites. Epoxy resins are not regularly used to create composite grating. Especially the pultrusion process has strict requirements, which may limit the use of epoxies.
2.3.2.3 Vinyl ester matrix Vinyl esters show intermediary properties and costs with respect to polyester and epoxy resins. They retain the low viscosity of polyester resins and thus fast curing and show thixotropic characteristics, while providing a higher environmental performance. Vinyl esters also exhibit the good properties of epoxies, such as good chemical resistance and high tensile strength. This marks vinyl ester resins as an interesting option. Vinyl esters are applied when increased corrosion resistance and durability are required. These resins show excellent wetting with a variety of fibers and low degradation of mechanical properties due to hydrolysis. The processing of vinyl esters is very similar to that of polyesters. An unsaturated vinyl ester is the base material. The carbon double bonds in a vinyl ester exist at the ends of the molecule chains and this limits the cross-linking to only occur at the ends. A unique characteristic of vinyl esters is that they also contain hydroxyl groups, which may form hydrogen bonds with similar groups on glass fibers. This results in excellent wet out and good adhesion with glass fibers. The vinyl ester resins are dissolved in styrene, reducing its viscosity. Styrene is used in its monomeric form, in quantities of 20 % to 60 %. A benefit of using a high volume of styrene is that it improves the hydrophobicity, the resins’ resistance to water. A high amount of styrene however, also causes higher shrinkage of the matrix, increasing the possibility for micro cracking. During the curing process, the styrene reacts with the vinyl ester resin, creating the cross-links between the unsaturated ends and eventually the resin solidifies [6].
10 Material selection Vinyl ester provides excellent corrosion resistance and fire protection. It is developed to withstand frequent and direct contact to the harshest of chemical environments. It is used in acidic and caustic environments such as chemical plants, wastewater treatment and as plating material for small vessels. Vinyl ester resins can be used in both the molding and the pultrusion processes. Generally speaking, carbon fibers do not have a surface finish compatible with
vinyl ester, which causes a concern for the durability of the fiber-matrix bond [9].
Figure 2.6: Schematic representation of a cross-linked vinyl ester resin [6]
The properties of the thermosetting polymers are shown in table 2.1. Other thermosetting resins (high performance) are not discussed even though they show very good properties; their costs are many times that of the standard thermosetting polymers.
Table 2.1: Typical properties thermosetting polymers [7, 10]
Property Polyester Epoxy Vinyl ester Unit
Tensile strength 20-70 60-80 68-82 MPa
Young's modulus 2.0-3.0 2.0-4.0 3.5 GPa
Maximum strain 1.0-5.0 1.0-8.0 3.0-4.0 %
Density 1200-1300 1200-1300 1120-1160 kg/m3
Glass transition temperature 70-120 100-270 102-150 °C Costs 1.80 3.90 1.80 $/kg
2.3.2.4 Polymerization agents Thermosetting polymers do not polymerize by themselves. Therefore, so called polymerization agents are included to start the reaction. The agents react with the resin, activating the curing of the composite material. Epoxy resins utilize amine hardeners that are added at ratios of 25 % to 50 % of the resin mass. The curing process of polyesters and vinyl esters is quite different as organic peroxides are included at only 0.25 % to 1.5 % of the resin mass [7].
2.3.3 Thermoplastics The second type of matrix materials is thermoplastic polymers. This material is formed a step before being molded into its final shape. To diffuse the resins into the reinforcement, the material is heated to above its melting temperature allowing the resin to seep into the fibers and then recrystallizes when cooling down, hardening the matrix. A thermoplastic material has a very high viscosity in its melted state, which complicates the fabrication.
Reinforced thermoplastic polymers will typically have higher toughness and impact resistance than thermosetting polymers. The remolding property of thermoplastics allows the material to be recycled. The important benefits of thermoplastics are the cost effectiveness and the reduced creep tendency [11]. The five most common thermoplastics (PP, PE, PVC, PET, and PS) comprise 75% of the total thermoplastics production. These five polymers, together with select other promising thermoplastics, are discussed and investigated for their applicability in a composite shallow foundation.
2.3 Matrix material 11
Polyethylene (PE)
The polymerization process mainly determines the properties of the polyethylene. The one most likely applied for engineering purposes is the Ziegler-Natta polymerization, which is used to create high-density polyethylene (HDPE). This subfamily of PE is most often used for structural applications. The general advantages of PE are its low price, low density and easy processing. Furthermore, the polymer has good impact resistance, low absorption of water and good resistance of hydrolysis. HDPE in particular is more rigid than its low-density counterpart and displays better thermal and creep behavior. Disadvantages are the sensitivity to heat, UV-light, stress cracking. The mechanical properties are generally good, with high elongation at breaking, but more limited strains at yielding. The stiffness of PE is rather low, but the impact strength is very good. The dimensional stability of the polymer is less favorable, displaying high shrinkage, coefficient of thermal expansion and creep. Polyethylene has very low water absorption and additionally does not contain any hydrolysable chemical bonds. Therefore, these polymers show very good aging behavior in water. Hot water and oxidation however, do negatively affect the polymer [12]. Polypropylene (PP)
( ) From the polymerization of polypropylene (PP) two structures may be obtained. An atactic structure with the methyl groups ( ) randomly located on either side of the polymer chain or an isotactic structure where the methyl groups are all located on the same side. This latter structure is the one used for engineering purposes. The properties of PP are quite similar to polyethylene. PP is quite cheap and easily processed and has a very low
density. Furthermore, the material is chemically inert and the absorption of water is low, combined with good hydrolysis resistance. Disadvantages are the sensitivity to heat, low temperatures and UV-light. Additionally low rigidity, creep and the significant shrinkage of the polymer matrix present difficulties. The mechanical properties of PP are decent with very high elongation at break, but the strain at yielding is much lower. The moduli and hardness are improved over polyethylene, but still rather weak. The impact strength of the polymer is intermediate. The dimensional stability of polypropylene is mediocre, as the coefficient of thermal
expansion and the creep are quite high, depending on the crystallinity of the polymer. Polypropylene has the same aging properties in water as polyethylene due to the lack of hydrolysable chemical bonds. The properties of glass reinforced PP submerged in water show an initial reduction in values, but after this reduction, no additional change in time is observed. When confronted with hot water, PP may be rapidly oxidized [13]. Polyvinyl chloride (PVC)
( )
Polyvinyl chloride is the linear homopolymer of vinyl chloride. PVC may be polymerized with a co-monomer, usually vinyl acetate. Simple polymerized PVC does not have great properties. However, PVC lends itself to add a wide of variety additives, fillers, plasticizers and stabilizers, allowing large customization of the polymer. This ability to accept many additives is a big advantage of PVC. The rigid type of PVC provides decent rigidity at low costs. It has good chemical resistance to most solvents and is dimensionally stable. Drawbacks are its sensitivity to UV. Softening and creep occur due to temperature increases. The density is quite high and impact resistance is low. The material produces dangerous fumes in the event of fire. The mechanical properties of PVC show a rather high modulus and high tensile strength, but this coincides with low elongation at break and weak impact strength. The rigid type of PVC is an amorphous polymer with a low amount of shrinkage and a decent thermal expansion coefficient for a polymer. It has low creep at room temperature and water absorption is low. Polyethylene terephthalate (PET)
( ) ( )
12 Material selection Thermoplastic polyesters are created from the copolymerization of a di-acid and a di-alcohol leading to a linear macromolecule. For the creation of PET, the di-acid is terephthalic acid and the di-alcohol is ethylenediol or ethylene glycol. The advantages of PET are good rigidity, creep behavior and resistance to fatigue. Additionally it shows good
moisture resistance. The costs of PET for engineering purposes are slightly higher than the earlier discussed thermoplastics. Drawbacks of the polymer are its sensitivity to water above temperatures of 60 °C and the low protection against UV light. It only has limited chemical resistance and PET crystallizes slowly, which decreases the production rate. The mechanical properties of PET are good, with high elongations at break, but more limited strains when yielding. The moduli and hardness of the polymer are high and impact strength is intermediate. The shrinkage and coefficient of thermal expansion depend on the crystallinity of the polymer, and creep resistance is good, with improved values for increasing glass fiber content. Polystyrene (PS)
( ) Polystyrene may be polymerized alone (homopolymer), creating rigid and brittle polymers, or in conjunction with co-monomers (copolymer), such as acrylonitrile to improve its mechanical or chemical performance. The main polymerization techniques for PS are a continuous bulk process and a discontinuous suspension method. Advantages of PS are its low cost coupled with good mechanical properties and rigidity at room temperature. The polymer also shows decent dimensional stability and easy processing. It has good chemical resistance against certain chemical and low absorption of water and good density. Polystyrene may be processed by different manufacturing methods. Disadvantages of PS are the innate sensitivity to heat, low temperature and UV light. PS shows weak impact resistance, low flexibility and creep for increased temperatures. The polymer is easily combusted leading to health issues. The mechanical properties of PS are generally good with low strain at breaking and the polymer displays brittle behavior at room temperature. The moduli and hardness are higher than PE and PP. PS is an amorphous polymer and displays low shrinkage of the matrix.
Polyamide (PA)
( ) Polyamides, also better known as nylons, are homo-polymers of an amino acid or copolymers of a di-amine and di-acid. Polyamides differ in length of the units between amide groups and the arrangement thereof. PA-66 and PA-6 are the most commonly used polyamides. Polyamides have good mechanical properties, good heat and fatigue resistances. PA has excellent toughness and impact resistances and resists common solvents as oils, greases and hydrocarbons. Disadvantages of polyamides are brittleness when dry and the polymer is quite sensitive to water and oxidation, which reduces its mechanical properties. Nylon has high water absorption due to its polarity. Furthermore, it is more expensive than the more common thermoplastics discussed above [13]. The mechanical properties of PA show high elongation at break and more limited strain at yield. The moduli and hardness are decent, according to the moisture content in the polymer. Shrinkage, coefficient of thermal expansion, moisture uptake and the resulting swelling are high. Polycarbonate (PC)
Polycarbonates are created from the poly condensation of carbonic anhydride and a bisphenol.
2.3 Matrix material 13
Polycarbonates are mainly used for their transparency. They have excellent mechanical properties and impact resistance. They show good rigidity and creep behavior, in addition to good fatigue resistance and low moisture uptake at ambient temperature. Even though water uptake is small, hydrolytic degradation is large. Polycarbonates are sensitive to UV-light. Furthermore, they are susceptible to environmental stress cracking and show degradation when exposed to bases, oils, chlorinated solvents and ketones. Their costs are higher than the commonly used
polymers. Additionally, water uptake increases for higher temperatures. The mechanical properties of polycarbonate include the high elongation at break, but more limited strains at yield. They have medium moduli and hardness, coupled with excellent impact strength. Its dimensional stability is also good. The shrinkage and coefficient of thermal expansion are low and creep resistance is good, with further improvement for increasing glass fiber content. Polyacetal (POM)
Polyacetal or Polyoxymethylene exists as the homopolymer of oxymethylene, or a copolymer of oxymethylene combined with another co-monomer. Acetals show good mechanical properties, are elastic and have good chemical resistance against water, oils, greases and solvents. Polyacetals are very sensitive to UV-light. The polymer shows good strength retention in water. The polymer is flammable and strong acids may cause degradation. The cost and density are higher than the general thermoplastics. Acetals show fair rigidity for lower temperatures. Impact resistance is generally low. Water absorption is low, but shrinkage and the coefficient of thermal expansion are high. Creep behavior is good at ambient temperature. Polyphenylether (PPE)
Polyphenylether is similar to polyacetals, but an aromatic unit replaces the methylene group. PPEs are used for their good cost/performance ratio. Creep behavior is good, in addition to low moisture uptake and resistance to hot water. Additionally the material shows good dimensional stability. Disadvantages are the sensitivity to fire and the low chemical resistance. UV-light causes light degradation of the plastic. The mechanical properties are generally good, with decent stiffness and impact resistance. Creep resistance is good at room temperature and the thermal expansion coefficient is low. Polysulfone (PSU)
Polysulfone is considered a better version of polycarbonates and is created by the reaction of a diphenol and bis(4-chlorophenyl)sulfone. PSU displays good mechanical properties, good rigidity, low creep and fair shrinkage. Moisture uptake in polysulfone is low. Disadvantages are the sensitivity to UV-light; the material is sensitive to environmental stress cracking and attacks by chemicals. The excellent mechanical properties correspond to a high relative cost of the polymer.
The elongation at break is medium to low and strains at yield are even lower. Which means impact resistance is bad. Tensile strength and moduli of this polymer are high. The material shows fair resistance against moisture. The shrinkage and coefficient of thermal expansion are low, with the creep resistance improving as the glass fiber content increases. Annealing of this polymer causes reduction of the elongation capability and consequently its ductility, but this provides a small increase in tensile strength.
14 Material selection Concluding, it may be seen that PE and PP have a rather high shrinkage of the material upon curing, but still reasonable in comparison to thermosetting polymers. The density of these two polymers is quite low, but elongation at break is very high. PA and PC are very susceptible to hydrolysis, which is a severe downside if the polymer is to be placed in a marine environment. PET also shows water susceptibility for higher temperatures. Some mechanical properties of PVC are not suited for the intended purpose, such as the low impact resistance and relative high density
of the polymer. PS shows sensitivity to low temperatures and has weak impact resistance. Additionally PS is quite brittle at room temperature. POM has very good mechanical properties, but its impact strength is limited and the polymer shows high shrinkage and high density. PPE shows excellent resistance against water ingress, even for boiling water. Its mechanical properties are decent, but low chemical resistance and high flammability are drawbacks. Considering higher performance thermoplastics, i.e. PSU, it becomes apparent that improved mechanical properties coincide with increased costs. The properties of thermoplastic polymers are shown in table 2.2. In general, using the high performance thermoplastics easily provide sufficient strength and stiffness for creating suitable FRPs. However, using these materials would significantly increase the cost of the foundation. Commonly used high-end thermoplastics include: Polyether-imide (PEI), Polyamide-imide (PAI), Polyimide (PI) and Polyetheretherketone (PEEK)
Table 2.2: Typical properties thermoplastic polymers [12]
Property PE PP PVC PET PS PA PC POM PPE PSU Unit
Density 960 910 1380 1350 1050 1140 1200 1420 1080 1270 kg/m3
Shrinkage 2.8 3.00 0.40 1.60 0.40 1.90 0.60 2.00 0.65 0.65 %
Absorption of water 0.01 0.06 0.22 0.15 0.03 2.00 0.15 0.32 0.09 0.65 %
Elongation at break 600 380 30 50 3 175 125 45 53 70 %
Tensile strength 35 30 53 58 48 75 66 67 53 81 MPa
Flexural modulus 1.1 1.4 3.0 3.2 3.0 2.3 2.3 2.8 2.5 2.6 GPa
Continuous use temperature 100 125 60 110 73 115 108 95 95 150 °C
Cost /kg 1.8 1.8 1.7 2.0 1.9 3.5 3.6 2.2 3.1 9.5 $
The use of thermoplastics is seeing a large increase in use due to the application of 3D printing. Even the first printers utilizing carbon fibers within the resins are being produced. This might spur the development of low cost reinforced thermoplastics. Aside from the base material in the form of thermosetting or thermoplastic polymers, the matrix material in a composite often also contains fillers and additives. These may be included to reduce the production costs, speed up the curing process and improve specific properties of the final product. [12]
2.3.4 Filler materials Apart from fibers and resins, fillers are often used for two reasons. The fillers reduce the cost of the composite and are used to modify the material to exhibit certain properties not possible with only the fibers and resin. Fillers may be added to reduce the shrinkage of the material, lowering the possibility of residual stresses and cracking. Similarly, hardness, creep performance and environmental degradation resistance may be improved. Common fillers are calcium carbonate, aluminum silicate, alumina trihydrate and calcium sulphate. The last two mentioned fillers are used to improve fire resistance and reduce smoke production. As a structural FRP is desired, the fraction of fillers will be low, but in non-structural products, the filler grade can go as high as 65 % of resin weight. Addition of fillers may improve certain attributes and lower the cost, but this will usually be at the expense of other mechanical properties. Aluminum
hydroxide is a filler material used in molded gratings to provide for extra flame and smoke resistance [7].
2.3.5 Additives Additives are included in the polymeric resin to improve the material processing and enhance the performance of the final product. They may be included to improve a variety of properties required for the design of a suitable FRP. The difference between fillers and additives is that additives are included in much smaller amounts, generally less than
1 % of the resin mass. Common characteristics that additives may change include reduction of flammability, reduction of shrinkage, reduction of void contents, increasing the toughness, prevention of UV-degradation, coloring and facilitating removal from the mold. Even though they are only included in small quantities, they can have considerable effects on the properties of the FRP. The bonding capability of the different resins with the reinforcing fibers, in combination with the durability over its lifetime and the strength performance will determine the preferable matrix material. The next section discusses the
reinforcing fibers within the composite.
2.4 Reinforcing fibers 15
2.4 Reinforcing fibers
2.4.1 Introduction The polymers themselves are not strong enough to take up the entire load. Therefore, fibers are included as reinforcement to bear the loads and improve the general mechanical properties of the composite. The reinforcing fibers alone are very susceptible to bending, but as the polymer keeps the fibers in their geometric arrangement, the fibers are able to effectively transfer the forces in the material among each other. The fibers can be included in various forms to design for a certain purpose. The fibers may be produced as a mat in a random pattern, woven into a fabric to provide directional strengthening or filament wound around a cylinder or pipe to provide radial strength. Sizing is used to cover fibers and provide protection against damage during processing, from contact with one another or contact with processing equipment. Sizing is made up of lubricants for protecting from wear between the fibers, anti-statics, reducing the friction between fibers. Additionally sizing may include binder material to promote the bonding of the fibers and the resin matrix. Sizing may also consist of ingredients that improve corrosion resistance. Furthermore, it is adjustable for different types of matrix materials to yield optimal interface strength. For glass fibers, sizing also protects the fiber from moisture uptake during the composite service life. Water uptake may lead to degradation of the glass fibers, creating a porous surface. The pores become defects and reduce the strength of the fibers [14].
Rovings are unidirectional filaments of strands of fibers, see figure 2.7. These are applied in all grating products and can be seen as the rebar of FRP in gratings. The rovings provide tensile and flexural strength and contribute to the overall stiffness of the grating. The three most common reinforcing fiber materials, glass, carbon and aramid fibers, will be discussed in more detail. Other fibers exist, but not deemed suitable for this purpose due to their cost or mechanical properties.
2.4.2 Glass fibers Glass is the most common reinforcing fabric in composites. Its low cost makes it a popular material in various applications. The fibers do not melt, but soften progressively up to 2000 °C. These high temperatures are required to produce glass fibers from its base material, silica. Despite these high temperatures, silica is a valuable material for engineering. Different types of glass fibers are available: A-glass or alkali-glass used to be the most common base material for glass fibers. E-glass or electrical grade glass has replaced these fibers. C-glass is a special chemical resistant glass and R-glass and S-glass are high strength glasses mostly used in aerospace applications. Advantages of glass fibers are the low cost, high tensile strength, its high chemical resistance and excellent insulating properties. Disadvantages are relatively low tensile modulus and relatively high density, sensitivity to abrasion, relatively low fatigue resistance and high hardness. The two most commonly used types are E-glass and S-glass. E-glass is the cheapest reinforcing fiber and S-glass is the fiber with highest tensile strength, at a higher cost. Glass reinforcement has an additional benefit for marine environments, as it reduces rate of moisture absorption. Glass is more impact resistant than carbon [13]. Glass fibers are created from various ingredients. They are dry-mixed and melted together at around 1370 . The molten glass is then drawn into fine fibers, known as ‘filaments’, of approximately 10 μm. These are then coated with sizing for protection, gathered into a strand, and wound on a spool. The internal structure of glass fibers is a three-
Figure 2.7: Fiberglass rovings
16 Material selection dimensional, long network of silicon, oxygen and other atoms arranged randomly. Therefore, glass is considered amorphous (non-crystalline) and isotropic. The strands consist of approximately 200 filaments or more. Binding many untwisted parallel strands together creates a roving, or yarn for twisted strands. The rovings are woven on a spool. These are used in the various manufacturing
processes. By impregnating the rovings with a small layer of resin, prepregs (from pre-impregnated) are created. After hardening, these can be cut to shape and allow for easier processing, in for example hand lay-up. These fibers of prepregs are pre-impregnated, improving the bonding capability of the fibers with the resin. Chopped strands may be produced by cutting continuous strands into short lengths. Short chopped strands (3 mm to 13 mm) are used in injection molding techniques, whereas longer strands (up to 50 mm) are mixed with a resin to create chopped strand mats. In these two-dimensional mats, the fibers are randomly distributed. These mats are nearly isotropic in the plane, and are used for hand lay-up moldings. Glass rovings and yarns may also be woven to create woven roving and woven cloth respectively. Different weaving techniques may be applied to create various configurations of woving to improve fabric drapability and other properties, but in general, the fabrics provide excellent bi-directional properties [6].
2.4.3 Carbon fibers Carbon fibers are commercially available with highly varying properties. The tensile modulus may range from 200 GPa to approximately 1000 GPa. Generally, the relatively low-modulus fibers have a lower density, lower cost and higher tensile and compressive strengths than the high-modulus fibers. Carbon fibers are the most expensive material of the commonly used fibers. However, carbon fibers show excellent mechanical properties and have a low density, which make the material indispensable to FRPs. These fibers are therefore mostly used for applications where cost is of secondary importance. Carbon fibers are characterized by a high tensile modulus compared with other fibers. Especially the high strength/density ratio and exceptionally high modulus/density ratios make carbon a very important material in the composite market. Disadvantages include low strain to failure, low impacts resistance and high electrical conductivity. The process to create carbon fibers involves controlled oxidation and carbonization in temperatures up to 2600 °C. Carbon fibers may be produced from either textile or pitch precursors. The most used textile precursor is polyacrylonitrile (PAN) from which filaments are wet spun and stretched at elevated temperature. The stretched filaments are oxidized and kept at 200 °C to 300 °C for several hours to stabilize the molecule structure. After which the PAN filaments are carbonized at 1000 °C to 2000 °C, removing the oxygen and nitrogen atoms. To further geometrically order the carbon atoms, the filaments are now heat treated at 2000 °C or higher. The filaments are now graphitized and attain high strength if stretching is applied and a high modulus is attained if no stretching is applied. Pitch is a lower cost precursor then PAN precursors. Pitch is a by-product of the petroleum refinement process. The pitch is heated to a temperature of 300 °C to join the molecules together. From this highly viscous stage, the heated pitch is spun to align the filaments. By cooling the filaments, the orientation of molecules is fixed in a direction and by reheating and oxidizing between 200 °C to 300 °C the filaments are stabilized and become infusible, preventing the filaments from fusing together. At this step the manufacturing process is similar to the PAN precursors: carbonizing the filaments at 2000 °C and subsequently graphitizing at 3000 °C [6]. The difference between the two carbon filaments created from different precursors is that PAN precursors produce a higher quality carbon fiber than pitch precursors. Carbon fibers created from PAN show higher compressive strengths. Additionally, PAN carbon fibers show lower thermal conductivity and electrical conductivity. Carbon fibers may now be produced into three different forms. The fibers may be kept in a continuous tow, consisting of an untwisted bundle of 1,000 to 160,000 parallel filaments. This is mainly used for high performance applications. Additionally, the carbon fibers may also be chopped into smaller shapes (6 mm to 50 mm) or milled (30 μm to 3000 μm) into even smaller parts. Higher filament counts in the tow are desirable for continuous production processes as filament winding and pultrusion, as it improves the productivity. The downside of having more filaments in a tow is that it becomes increasingly difficult to wet the fibers. If the fibers are not wetted sufficiently with polymer resin, the fibers are not able to transfer their stresses and strains amongst each other, resulting in a reduction of the mechanical performance [15].
2.5 Durability 17
2.4.4 Aramid fibers Polyaramid is one the most important synthetic organic fibers developed. Due to its very distinct combination of properties, it is used for a wide variety of applications. Aramid is better known by its commonly used brand product, Kevlar-49. Aramid fibers provide high tensile strength at much lower density than glass fibers ( %). Additionally, this synthetic organic material also fractures in a ductile manner, in contrast to the other fibers, which provide excellent resistance to impact damage. It has excellent thermal and dimensional stability and wear resistance, but a rather low compressive strength. Combining aramid fibers with other fibers, may allow mitigation of the low compressive strength. This creates a possibility to take advantage of aramids excellent tensile strength/density ratio. A major drawback of aramids is its difficulty cut or machine composites created from the fibers. The material is highly abrasive. Aramid fibers are created by extruding an acidic solution of a precursor from a spinneret. This precursor is created as the product of the polycondensation of terephthaloyol chloride and p-phenylene diamine. During the filament drawing the molecules become highly one directional. Adjacent molecule chains are held together in the transverse direction by weak hydrogen bonds. The created filament is highly anisotropic and shows significantly better properties in the longitudinal direction. If polyaramides are subjected to bending, the compression side shows initial yielding. This failure mode is not observed in the other fibers and explains the superior damage tolerance against impact or dynamic loading. This explains why the material is popular for use in body armor and other protective gear [15]. The discussed fibers, polymer matrices and possible additives may now be combined into a composite. This may be done by a variety of different manufacturing processes.
Table 2.3: Typical properties fibers [7]
Property E-glass Carbon Aramid Unit
Tensile strength 2350-4600 2600-3600 2800-4100 MPa Tensile modulus 73-88 200-400 70-190 GPa Maximum strain 2.5-4.5 0.6-1.5 2.0-4.0 % Density 2600 1700-1900 1400 Kg/m3
Thermal expansion coefficient 5.0-6.0 LW: -1.3 to -0.1
CW: 18 -3.5 10-6 /°K
Fiber diameter 3-13 6-7 12 μm Costs 1.55 20 22 $/kg
2.5 Durability
2.5.1 Introduction/design criteria Durability of composites may be defined as: the ability of the materials to resist damage for a specified period of time, subjected to the appropriate load, in the specified environment. The damage in FRP may occur as cracking, oxidation, chemical degradation, and delamination, wear or impact damage. The performance of a composite for a structural application is evaluated by its properties and behavior by static or dynamic loading in different environments. The information of how the material behaves in these conditions helps decide on the correct choice for the required constituents. The effects of the environmental conditions on the physical and mechanical properties of the composite are discussed. The influence on the composites is investigated by literature study and is analyzed for the long-term effects identified to be important for durability of the composite, for this specific design.
2.5.2 Hydrolytic ageing
2.5.2.1 Degradation mechanisms The performance of composites in water relies on the amount of water the composite absorbs and the effect this has on the mechanical properties. Resistance of the composite to water and other solvents requires that the polymer does not dissolve, swell or crack in marine environments. The degradation of the polymer due to water uptake generally follows one of three mechanisms:
18 Material selection Direct diffusion of water molecules into the matrix material or the fibers. Capillary flow of water molecules along the fiber/matrix interface, followed by diffusion into the resin. This
generally occurs due to poor bonding between the fiber and resin. Diffusion through micro-cracks, pores and defects in the material [16].
For a composite material, this may have several detrimental effects: Dimensional changes (swelling) Appearance changes (color, gloss, crazing, blistering, etc.) Reduction in glass transition temperature of the resin
Reduction in mechanical and physical properties (stiffness, strength and hardness) The reduction in mechanical properties is caused by the hydrolytic breakdown of the fiber-matrix interface, which results in a decrease in efficiency of load transfer between the matrix and the fiber reinforcement. Despite that, the process of water absorption is almost immediate; the diffusion into the bulk material is a slow process. It may take months before a significant amount of water is absorbed by the composite, and even several years for saturation. This process of water uptake is accelerated by higher temperatures. [17]
2.5.2.2 Previous research Several studies have investigated the influence of water immersion of the properties of composites. Bedford Reinforced Plastics, a company manufacturing composite gratings amongst others, performed immersion tests on their pultruded glass-vinyl ester composites. The results indicated a tensile and flexural strength reduction in the order of ~20 % for samples immersed for one year. The influence of water on the tensile and flexural moduli was small, not indicating any stiffness decrease [18]. Immersion of carbon-epoxy composites strained in bending, displayed similar results. The tensile strength displayed a small decrease after 20 weeks of immersion. The tensile modulus displayed no significant change. Additionally, these tests were performed in seawater. The tensile modulus remarkably showed a significant increase after 20 weeks of immersion in seawater. This was attributed to the successive hardening of the matrix after complete curing [19]. It is interesting to see that an increase of strain due to compressive stresses in polymers show signs of reduced water uptake. This might be caused by a reduction in free volume, limiting the penetration of water molecules into the resin. For tensile stresses the opposite effect occurs, the free volume increases. This is coupled with formation of micro cracks and debonding of the fiber-matrix interface, increasing the amount of moisture being absorbed. This same effect was observed in samples strained by bending. The samples with a higher amount of bending strain show a reduced water uptake. The reduction in free volume limits the penetration of water molecules into the resin. A distinct difference in water absorption is observed in samples strained by bending. The strained samples showed a much lower diffusion of water [19, 20]. Pultrusion creates thermal stresses within the composite. When the composite material is cured at a high temperature, the resin polymerizes and subsequently shrinks when cooling down. The fibers on the other hand hardly shrink and create residual stresses in the composite. These stresses are highly dependent on the curing temperature and cure cycle. A large decrease of tensile strength was observed during the first two weeks of water immersion, which may be accredited to these residual stresses. Following these two weeks, an increase in tensile strength was observed, possibly due to relaxation of these stresses due to the water absorption, which accelerate the post curing of the resin [19]. Bradley and Grant examined the influence of pressure in combination with seawater on composites [20]. The resulting moisture absorption and transverse strength were determined at several periods. The samples were exposed to a pressure of roughly 20.7 MPa, simulating a depth of 1500 m. In the carbon/epoxy composites, a beneficial effect was observed due to seawater over distilled water as lower moisture absorption was found. It was suggested that if the resin acts as a semi-permeable membrane, the dissolved salts hinders water diffusion by osmosis, thus reducing the total water absorbed. Hydrostatic pressure may have two possible opposing effects. On one hand the pressure might reduce the free volume in the resin, reducing the water diffusion and on the other hand, the pressure may create a greater driving force for water absorption. The absolute effect of pressure on the transverse strength and moisture absorption was rather small. The same minimal pressure effects were observed in other thermosetting composites. The composites composed of carbon or glass in combination with vinyl ester indicated that the carbon composites had higher moisture absorption. This was attributed to the weaker interface bond of carbon/vinyl ester in contrast to glass/vinyl ester. The addition of pressure induced a further increase in moisture uptake of the carbon composites, whereas the glass composites remained relatively unchanged.
2.5 Durability 19
Investigation of the seawater durability of carbon and glass in combination with polyester and vinyl ester resins by Kootsookos and Mouritz, showed that polyester-based composites are less chemically stable in seawater than vinyl ester-based composites [21]. This was assumed to be the result of hydrolysis reaction with the unsaturated groups of the polyester resin. The chemical degradation of vinyl ester composites was shown to be much lower. The saturation of glass/vinyl ester composites immersed in seawater displayed good agreement with Fick’s second law of diffusion,
reaching a limit after approximately 6 months. The agreement of carbon/vinyl ester was poor, but a limit was still observed after 2 years, near the expected mass change due to water absorption. This observed behavior of vinyl esters is quite different from polyester resins, which experienced a decrease in mass after saturation. This is the result of the less chemically stable polyester. Despite the better chemical stability, the flexural properties of vinyl ester composites were degraded to a similar extent as polyester composites: a reduction of 20 % to 40 % in flexural modulus and a reduction of 10 % to 20 % in flexural strength. It was also observed that glass-reinforced composites absorb more moisture than carbon-reinforced composites, but this was attributed to the different sizing used on the fibers.
2.5.2.3 Interface degradation The effect of moisture on the interface between fiber and resin may be ascribed to two processes. In the first place, moisture reduces the bond strength between the fibers and the matrix, by reacting with the sizing. The other process is matrix swelling, which promotes the water absorption and ultimately reduces the interface strength. The absorbed moisture in polyester can act as a plasticizer, which increases the molecular mobility and accommodates molecules occupying positions between large polymer chains. This increases the intermolecular distance and decreases the cohesive forces of the molecules. For long exposure to water, the polyester undergoes chemically ageing through hydrolysis. This causes a chemical attack on the ester linkages of the resin, decomposing the polyester or vinyl ester, causing visual damage. Chemical aging due to moisture ingress can also occur in the form of post-curing, either increasing or decreasing the mechanical integrity of the matrix, dependent on the exposure temperature. The difference between ‘absorption’ and ‘adsorption’ is important to distinguish, in order to prevent confusion, as they are two different phenomena. Absorption encompasses the capillary moisture uptake of the material through pores, voids or defects in the polymer. Absorption therefore does not affect plasticity of the composite. This mobile water may be easily desorbed and the process reversed. Adsorption however, is the process in which a solution is formed through physical interactions between the polar water molecules and polar groups in the polymer. The concentration of water permeating into the resin depends on the free energy of the mixing of the polymer and solvent. This process is more difficult to reverse as the molecules are physically connected. The generated heat and swelling in this process is much larger than with absorption [22]. Glass fibers are very sensitive to corrosion due to water. When the glass is exposed, the water first wets the surface, before diffusing into the glass network. The water reacts with the glass and several chemical reactions may occur. Aramid fibers are also known to be affected by moisture and alkaline environments. In contrast, carbon fibers are inert for normal temperatures. They are considered insensitive to moisture and only a little affected by alkaline environments [23]. Osmosis is the process in which different solution strengths are leveled by crossing of the solvent through a semi-permeable membrane. In composites the polymer matrix may function as this membrane. As water diffuses at the interface of the polymer, the soluble molecules dissolve and this forms a solution. This causes a gradient in concentrations on either side of the membrane and additional water will dissolve until the gradient is reduced. This additional water increases the solution volume behind the membrane and increases the pressure on the surrounding material. This causes delamination and creates blisters on the material surface. The blisters generate propagating cracks within the material along the surface. This process is called osmotic cracking and may be prevented by using the correct polymer material [24].
2.5.2.4 Recommendations Both resins and fibers display a vulnerability to water, leading to some form of deterioration. The durability of the materials may be significantly improved by careful selection of materials, quality control during the manufacturing processes and using the appropriate coatings. Karbhari made several recommendations regarding the use of FRP in aqueous environments [25]:
20 Material selection The polymeric resin plays an important role in protecting the fiber and slowing the diffusion process. Therefore,
preference should be given to use of appropriate epoxies and vinyl esters. The possibility of moisture and chemicals in solution moving through the bulk resin and towards the fiber must be
reduced. This may be achieved by selecting a composite with an appropriate thickness of the resin-rich surface, providing a resin layer, which remains uncracked during its intended use. This may be further improved by using gel coatings.
Recognizing the impact of an uncured resin on the moisture absorption allows a better design of the product. Before placing the composite in the aqueous environment, a full cure of the composite is recommended, as this greatly improves the hydrolytic behavior.
It is emphasized that by extrapolating the results of tests performed over a short period may lead to inaccurate results. This is particularly true for composites cured at ambient temperatures.
The effect of moisture on the glass transitioning temperature requires the composites to be cured in a way that a is achieved which is significantly higher than the maximum service temperature.
Taking in consideration the effects of degradation and damage tolerance requirements, it is recommended that the composites are loaded to less than 25 % of design strength for glass fiber composites, 30 % for aramid fiber composites and 40 % for carbon fiber composites. These high safety factors may be reduced if validated data is available.
The use of these recommendations, in combination with the design requirements of the composite, allows a better
selection of material for the design of the grating. The property of difficult extrapolation of results makes it difficult to design composites for the desired period of 30 years.
2.5.3 Creep Creep is the time dependent and permanent deformation due to external loading over extended periods. Creep is usually undesired and affects the durability of the material. As a composite consists of multiple materials and different creep responses, the overall creep compliance of the composite is a complex mechanism. Many polymers display high creep strain at room temperature and low stress levels. At higher temperatures and stresses, this becomes more critical. Generally, the creep vulnerability is dependent on the amount of cross-linking in the polymer. A higher amount of cross-linking in the polymer results in lower creep. Creep in a composite is highly dependent on the fiber orientation in the material. A load off-axis to the fiber direction generates the largest amount of creep strain, whereas loading in the fiber direction minimizes this. Compression loading shows more exponential creep compliance compared to tension loading, which produces a more predictable compliance. For long-term deflections, the viscoelastic nature of the material has to be taken into account, as this may result in a significant increase in deflection [26, 27]. The idealized creep strain curve shows three distinct areas. After the initial elastic strain, the primary state is the area where the creep strain rate quickly decreases. In secondary creep, the material acts linearly in time and in tertiary creep the strain rapidly increases until fracture or rupture of the material.
Figure 2.8: Typical creep response of material subjected to constant load [26]
2.5 Durability 21
Several factors are known to influence the creep rate. An increase of environmental temperature increases the creep compliance, due to softening of the matrix. Additionally, moisture augments the creep strain due to degradation effects such as plasticization and hydrolysis. Moisture ingress significantly reduces the creep rupture strength in composites. Fatigue damage in combination with creep damage is shown to be additive, as they both increase the rate of deterioration caused by the other. On the other hand, increased physical aging is shown to decrease the creep
in a polymer. However this is coupled with increased brittleness, and reduced stress relaxation, which in turn decreases the materials overall durability. Long-term creep behavior of composites may be analyzed using Findley’s power law, the Boltzmann superposition principle (BSP) or the time temperature superposition principle (TTSP). Findley’s power law provides a curve fit procedure to extend creep data to long term. It has been shown to be accurate for primary creep and should not exceed 33% of the ultimate strength. The Boltzmann superposition principle additionally takes into account the stress history over its service life. The advantage of this model is that an approximation of the displacement may be obtained [26]. Another useful method to determine the long term creep behavior of viscoelastic materials is to use the time-temperature superposition principle (TTSP). This is based on the observation that the short term behavior of viscoelastic materials at higher temperatures is similar to long-term behavior at a lower temperature. The principle assumes that increasing the temperature is equal to shifting the creep response over a logarithmic time period. Using this, the creep response at a certain temperature may be determined over its entire lifetime. This is done by measuring the creep strain at various temperatures over a short time, and superimposing these short curves to the chosen temperature, obtaining one master curve for the reference temperature [28].
Figure 2.9: Schematic representation of TTSP [26] This procedure may be used with short-term experimental predictions using Findley’s power to determine the long-term creep response of a composite. The accelerating effect of temperature, stress and moisture may be included by using shift factors, but the accuracy is limited due to the subjective aspect of the shifting technique. Shao investigated the creep response of a pultruded FRP water retaining wall. The FRP specimens were subjected to a four-point bending configuration at 25 % and 50 % of the maximum load for the duration of one year. The resulting creep deflection after one year ranged from 13 % to 19 % of the initial static deflection. By predicting the deflection by Timoshenko beam theory and Findley’s power law, the creep deflection was estimated to exceed 70 % of the static deflection at 30 years. This is a significant deflection and needs to be further investigated for the design of a composite shallow foundation [29].
2.5.4 Heat and fire resistance Polymers are generally quite reactive to fire, therefore, its resistance against heat and fire is investigated. Especially during installation of the composite and to a lesser extent during transport this will be an important safety aspect.
22 Material selection Possible welding activities during fabrication of the steel frame may introduce heat to the composites and harm the integrity of the composite. Therefore, it is suggested to postpone installation of the gratings in the steel frame to the last fabrication step. However if the selected connection technique requires welding of clamps or profiles to attach the grating with, it is
unavoidable that heat will be generated. Therefore caution is needed to protect the composite during such activities to prevent damage and fire hazards. Heat also reduces the integrity of the polymer, but if the added heat remains below a certain threshold, damage is not to be expected. In service on the seabed, with the pipeline connected and all the equipment in place, heat can still be a factor. The produced hydrocarbons heat up the subsea facilities quite significantly and convection through the surrounding water or conduction through the steel frame, heat may be transferred. Therefore, this is to be prevented, as prolonged exposure to this heat would cause detrimental effects. A possible solution is to ensure sufficient distance between the heated piping and the gratings.
2.5.5 Fatigue Composites can be damaged by fatigue due to repeated dynamic processes. These consist of cyclic mechanical loading, cycling of the temperature or moisture or repeated attack of chemicals. The performance of the reinforced polymer is highly dependent on the fibers, the orientation of the fibers and the manufacturing process. The mechanical properties of fiber tend to determine the eventual fatigue performance. Typically, fibers with higher modulus have better fatigue performance. Research supports the premise that the fatigue damage mechanism is fiber dominated. Unlike other structural materials, in which the fatigue process consists of crack initiation and propagation, FRPs behavior shows initiation followed by multiplication of cracks. Fatigue behavior in pultruded samples is worse than in vacuum assisted resin transfer molding (VARTM), which in turn is slightly worse than filament winding. This is due to fiber waviness within the composite, showing significantly lower S-N curves [30, 31]. The loading sequence is shown to be of great influence on the fatigue performance of the composite. Post investigated the effect of loading sequence on the fatigue strength of E-glass-vinyl ester composites created by VARTM. The results indicated that random loading is far more detrimental than ordered loading sequences [32]. Fatigue effects are expected to be limited as the major loads are only applied for a short time. When the subsea structure is in place, vibrations from the system will likely be damped as the composite is situated in the soil. In case fatigue damage does occur, it is not expected to cause a significant negative effect for the bearing capacity of the structure, as the entire structure is supported by the soil. Fatigue cracking in combination with hydrolysis may promote material degradation. The cracks expose additional resin and fibers, increasing the possibility of debonding, fiber breakage, corrosion and matrix diffusion.
2.5.6 Other properties
2.5.6.1 Freeze-thaw cycling The possibility exists that the composite will be used for the same purpose, or in a different capacity, in an arctic environment. The material may be exposed to single or multiple freeze-thaw cycles. It is therefore interesting to know the durability of the material in such an environment. Difference in thermal expansion coefficients of the composite materials create residual stresses after thermal cycling. The thermal expansion coefficient of resins is at least an order of magnitude larger than glass fibers. Under repeated cycles this may cause stresses which have detrimental effects to the composite. For carbon fibers this is even more significant as they are anisotropic, having a positive thermal expansion coefficient in the transverse direction, but negative in the longitudinal direction. This often results in debonding of the fibers from the matrix and micro-cracking in the matrix material [33]. Continuous exposure to sub-zero conditions is shown to minimally increase strength and modulus, while increasing matrix brittleness and transitioning to a more dangerous failure mechanism. This effect becomes more pronounced with moisture absorption and consequent matrix hydrolysis and plasticization. This causes irreversible damage to the composite. The hydrolysis of the resin matrix under freeze thaw conditions is not fully understood due to the combination of these effects in addition to possible mass dissolving. A combination of long-term environmental exposure and thermal cycling may therefore not be adequately modelled by linear expansion of the short-term behavior. Hydrolysis, plasticization of the resin and subsequent debonding may lead to large mass loss and macro cracking along the fiber matrix interface [9].
2.5 Durability 23
2.5.6.2 UV-radiation Degradation by UV radiation is a significant hazard for polymeric systems. A series of photochemical reactions occur when UV radiation is absorbed in the presence of oxygen. This leads to chemical changes, creating functional groups containing oxygen molecules. This in addition to possible chain scissions, cross-linking and rearranging process causes physical damage to the composite. Some damage characteristics include discoloration, chalking, micro cracking, blistering, loss of resin and ultimately delamination. The performance of a polymer with regard to its durability, strength and stiffness and rate of degradation highly depend on the material composition and environmental conditions. In general, the influence of the variability in weathering conditions, due to temperature changes, humidity and UV-radiation is not fully understood. The photochemical reactions are accelerated for elevated temperatures and mechanical stress in the materials. The light spectrum scatters in the rough seawater and a large range of wavelengths is absorbed, UV light largely passes through. The most harmful wavelength group (to polymers) is UV-B radiation (280 nm to 315 nm). Jerlov studied the UV penetration in seawater and discovered that UV does not penetrate to large depths. He predicted penetration depths between 20 m and 40 m [34]. Another study on the UV-B radiation in waters off the coast of Iceland indicated a depth of only 10 meters. The penetration of UV-light was assumed highly dependent on the clarity. The composite will likely be installed in far greater depths, thus removing the dangers of UV-degradation [35].
2.5.6.3 Wear Wear is usually not an issue for civil structures constructed from steel or concrete, due to their good wear resistance. However, composites do not share this fortune. Composites are much more susceptible to wear (10 to 100 times) and therefore, this should be considered in the design. The commonly occurring types of wear are gouging, abrasion and erosion. Gouging is the scraping of a large object against the composite, removing a considerable amount of material. Abrasion is the sliding of small grit particles over the surface removing a small amount of material every time and
erosion is the process of hard grit particles hitting the surface at a high speed, thereby removing material. Other degradation effects such as moisture absorption and thermal ageing can enhance the rate at which material is removed. When considering the wear resistance of composites it should be ideally considered to its end-of-life condition in its foreseen service environment. This is because the laboratory results can vary significantly from the composites’ in-service performance. The abrasive wear resistance is dependent on the fiber content of the composite. However, the relation between wear rate and fiber content is very different for every fiber-polymer composite. This means it is not possible to describe a general relationship. The wear rate is also dependent on the fiber orientation, being different for abrasion parallel, anti-parallel and normal to the fibers. If the composite is applied at a seabed with a substantial current, wear resistance certainly is an important aspect to design for, but for deeper waters, with lower current velocities this may be disregarded [36].
2.5.6.4 Residual stresses As a result of the curing process, the polymers tend to shrink. This shrinking is apparent to a smaller extent in epoxy resins, but up to 10 % in polyesters and vinyl esters. The fibers however barely shrink at all, because of their low coefficient of thermal expansion. The shrinkage in these polymers has the effect that residual stresses are formed within the matrix. Inhomogeneous curing, due to improper mixing also causes residual stresses. Certain areas cure faster than others creating a stress variation between the two parts. These stresses may cause cracking of the matrix. The interaction between fibers and resins also play a part in this.
2.5.6.5 Material impact strength E-glass fiber composites are shown to have improved impact energy, due to the high strain to failure of glass fibers. Carbon fibers have a much lower strain to failure, which leads to composites including carbon having lower impact energy. Impact energy is also influenced by the fiber-matrix interfacial shear strength. If the fibers and the matrix display very good adhesion, the failure mode is brittle, and thus, less energy is absorbed. At very low adhesion, the energy absorption is high, but the composite may fail undesirably. Intermediate adhesion produces progressive delamination, thus optimizing the energy absorption resulting in high impact energy. Additionally the impact energy is improved for increasing fiber content.
2.5.6.6 Biological degradation Biological degradation is not a common form of degradation of composites, as most polymers are resistant to microbiological attacks by fungi or bacteria. Polymers with good water and weathering resistance generally have
24 Material selection excellent resistance against microbial attack. The chemical additives and pigments in a composite however, may be susceptible to microbial attack. There is little reason to suggest that this also leads to negative structural changes in the composite. If microbial growth is promoted due to environmental conditions and the composite structure is affected, it is likely that the removal is more harmful to the composite, than the biological action of the marine organisms [17].
2.6 Discussion
2.6.1 Matrix material Most manufacturing processes may be used for both thermosetting and thermoplastic composites. Due to their differences in physical and thermal properties, some differences can be observed. One of the differences is in the
prepregs. The thermoplastic prepregs are, in contrast to thermosetting prepregs, not sticky. This problem is overcome by spot-welding the layers in place along the outside edges. This keeps the layers in place before the curing procedure. Additionally, the required processing temperatures for thermoplastic composites are much higher. Contrasting the thermosetting composites, no chemical reaction occurs in the processing of thermoplastic composites. A benefit of using thermoplastics is that these may be reshaped by applying heat and pressure. This makes them suitable for post-processing techniques, similar to metals. These techniques are highly efficient processing to create various shapes from flat plates and may be used to improve production rates.
Another advantage of thermoplastics is the reduced need of hazardous hardeners. Thermoplastics are cured by application of heat and pressure, improving the safety of the manufacturing process. This may also eventually lead to the use of welding thermoplastics in structural applications, when a suitable technique is developed. Especially for the oil and gas industry and then in particular the subsea environment the reinforced thermoplastics may surpass the reinforced thermosets. The danger of melting due to heat is largely eliminated due to its subsea application. When the material is retrieved at the end of service life, it will be able to be melted and possibly be reused in a different shape, significantly reducing its impact on the environment. Despite these benefits of thermoplastics, the improved knowledge of thermosetting polymers with regard to its durability and its expertise of using these materials in the oil and gas industry is decisive. The predictable behavior of thermosetting polymers lowers the uncertainty of the use of FRP in such a remote and harsh area. Therefore, the thermosets are preferred. Polyester is not considered a suitable matrix material for high performance fibers such as carbon, as it would not be able to fully exploit its strength. Vinyl ester may do this job with better mechanical properties and improved water resistance. Polyester is shown to be less chemically stable in seawater than vinyl ester composites. The polyester resin is susceptible to hydrolysis. Epoxies may provide a viable alternative at a higher cost for better mechanical properties, but with reduced hydrolytic stability.
2.6.2 Reinforcing fibers The reinforcing fibers provide the mechanical properties of the shallow foundation. Glass fibers are by far the cheapest of the conventional reinforcement materials. They show decent mechanical properties in addition to a higher maximum strain. Carbon fibers have a high modulus, but have a low maximum strain. Aramid fibers show the highest tensile strength and improved impact properties. The durability of the composite may be improved by the selection of fibers, provided they display a good bonding capability with the polymer. If required, a combination of fibers may be used to improve certain properties of the foundation. E.g., carbon fibers may be included to improve the modulus of the composite and including aramid fibers significantly improve the impact resistance.
2.6.3 Durability The lifespan of the composites is ideally equal to the design life of the structure. Due to the extreme conditions of the desired application, this may be hard to match. Additionally, the traditional methods of predicting the durability by
accelerated ageing may not comply to composites. Therefore, the properties at the end of life may be difficult to predict and additional material factors should be taken into account to mitigate this. The most critical property of using FRP as a shallow foundation for a subsea application, is its resistance against hydrolytic ageing. To maintain the properties of the composite for the entire lifetime, the selected material will have to show excellent resistance against water. Using thermosetting polymers, the composite requires a high amount of curing time. A fully cured composite has considerable improved properties and this is therefore desired for the composite gratings.
2.7 Conclusion 25
2.7 Conclusion The use of polymeric composites for structural components in a subsea environment exhibits potential. The application of the composite is predominantly critical for its resistance against environmental effects; therefore vinyl ester resin is selected as the matrix material for its excellent environmental stability. Due to the good bonding capability of E-glass fibers with vinyl esters, these are selected as the reinforcing fibers. The performance of thermoplastics is still difficult to affirm for the expected service life of the structure. Several thermoplastic polymers do show sufficient properties, but at a higher cost than the accustomed thermosetting polymers. Current composites are used in many different compositions. To establish certainty in the composite materials for the offshore industry, the material should be standardized, to provide reliable data on the durability.
3. Manufacturing
3.1 Shallow foundation shape It may be quickly determined that applying the composite material to the grillage solution by Bransby and Koopman, results in several problems. For one, the reduced stiffness moduli of the composite requires the individual grills to be significantly higher to obtain a similar deflection of the foundation. This reduces the stability against buckling and reduces the overall sturdiness of the structure. Additionally, the connection to the steel base frame of the protection structure becomes increasingly difficult, as the material cannot be welded to the frame. It is suggested to use a grating solution, which comprises of multiple bars in both directions. The mesh-like configuration provides lateral support to the bars in both directions. This structural configuration is currently already utilized in combination with FRPs for the application of walkways or protective measures. Two different types of FRP gratings exist, each manufactured in its own way, with distinct benefits as a result. The different gratings are shown in figure 3.1 and figure 3.2.
Figure 3.1: Molded grating [37] Figure 3.2: Pultruded grating [37]
3.2 Manufacturing process The process of creating a composite from its constituents varies widely, but the main procedures remain similar between all processes. The general process to produce a composite starts with the mixing of the resin with a hardener (for thermosetting polymers). This activates the chemical reaction of the resin and takes the resin from its low viscosity to the cured state. The uncured polymer is positioned in the mold, which determines its eventual geometric shape. The next procedure is the application of heat, allowing the resin to cure, harden and obtain the final shape of the mold. The addition of reinforcing fibers adds two additional procedures. The first is the positioning of the reinforcing fibers. This is a vital procedure, as the reinforcement should not be exposed, but protected by the surrounding resin. Careful placement of the fibers allows good load transfer and protection against environmental weathering effects. The introduction of reinforcing fibers also adds the procedure to impregnate the fibers with resin, either beforehand, or during the process to ensure the fibers are protected and may optimally transfer the forces amongst each other. These five procedures are essential in creating a composite material. The different methods to perform these procedures result in many different manufacturing processes. Each of these processes has their own benefits and drawbacks. They can be categorized in three main types: Open mold processes: these processes usually are lower strength composites, but require lower tooling costs.
This includes hand lay-up, spray-up, filament winding and centrifugal casting. Closed mold processes: these processes usually apply pressure to produce stronger composites, at a higher
capital investment. Examples are vacuum and pressure bag molding, cold and hot press molding and resin injection processes.
Continuous processes: these processes are highly productive and capital intensive, but limited to flat sheets and simple profiles. This includes continuous laminating, pultrusion and continuous filament winding [15].
28 Manufacturing Composite gratings may be fabricated by two distinct processes. Both manufacturing processes are used extensively to create a composite grating, each with their separate characteristics. These are the pultrusion process and the hot molding process. Both processes have their advantages and limitations and produce quite different gratings. The hot molding process produces gratings with higher resin content, which lead to a greater corrosion resistance. The more fiber-rich pultruded gratings on the contrary, display improved stiffness and strength. Additionally, the pultrusion
process leads to gratings with unidirectional properties, whereas the molded gratings are bi-directional. The less stiff molded grating has improved impact resistance and easier installation.
3.3 Hot molding Molded grating is created in a large open heated mold, bearing resemblance to a waffle iron. The grating mold consists of a faceplate, mold blocks and a side close. The flatness and surface finish of the faceplate may decide the quality of the grating. The mold blocks dimensions and individual distance determines the grating dimensions. The side closes are the edges of the mold and determine the eventual size of the plate.
Figure 3.3: Molded grating machine [38]
Continuous fiber rovings is fed from bobbins into the mold, and are manually woven in the two directions to produce the desired thickness and panel dimensions. The rovings are thoroughly wetted to prevent the fibers from being exposed. The continuous fibers in two directions yield an excellent bi-directional strength.
Figure 3.4: close-up molded grating machine [89]
3.3 Hot molding 29
Figure 3.5: Layout molded grating
When the rovings are in place, the mold is immersed in the premixed resin, filling the mold and connecting the individual rovings. The high percentage of resin (approximately 65 %) in molded fiberglass provides good corrosion resistance and optimal impact resistance. The grating is created in one piece, providing extra safety against environmental damage, as no point of entry is created by possible finishing methods. Additionally, a resin press may be used to guarantee the roving fully absorbed the resin. The next step is curing the resin by applying heat to the mold. By heating the resin at a predetermined temperature for an extended period, the optimal strength within the grating is achieved. An electric heating tube beneath the molding table provides the heat. The electric heating tube is connected to a heater and thermostat controller and a pump and valve system to provide an even distribution of temperature throughout the mold. When the grating has reaches a sufficient cure, the cooling process may start. This is done by pumping water through a series of piping, close to the mold. This takes the heat away from the system.
Figure 3.6: Molded grating in platform splash zone [39]
When fully hardened, the grating is removed from the mold using ejector pins to eject it without damaging the grating. The excess material is removed and the surface is polished to remove any irregularities. Afterwards, the gratings are prepared for transport.
30 Manufacturing Other than the size of the molded grating machine and transport limitations, there exist no maximum dimensions of gratings. A minimum bar thickness to bar height ratio can be used to prevent local buckling to occur within the grating. Several surface finishes of the gratings are available. A concave surface is the standard finish, as a concave on the
grating surface is formed during the curing process, when the top surface shrinks to create the concave effect. A smooth surface finish is formed by sanding the grating after curing. This finish is not desired, as this may induce defects and a non-smooth surface has beneficial effects for the design. The final possible surface finish is a gritted finish in which a silicon oxide is included in the top surface during the manufacturing process. This creates the highest roughness and is the preferred finish for the gratings. If it is possible to produce a gritted inner surface on the gratings, this would greatly improve the bearing capacity of the gratings as the friction is greatly improved. This enhances the arching mechanism, discussed in section 8.3.1.1, and increases the bearing capacity generation.
3.4 Pultrusion
Figure 3.7: Pultrusion process [37]
Pultruded grating is formed from bars fabricated by the continuous pultrusion process. It is a continuous process which produces pultruded profiles which are mechanically connected together to form a grating. This manufacturing process consists of several stages, see figure 3.7.
At the start of the process, the rovings are pulled together and joined by continuous filament mats and woven fabrics. The mats and fabrics act as additional protection and improve the transverse strength of the profiles. These materials are aligned and the materials are fed through a resin bath to impregnate the fibers and subsequently joined by an outer veil. This veil protects the composite by enhancing its surface characteristics. It improves the corrosion protection, provides UV protection, can include pigment and protect the fibers from being exposed. The bundle is guided in the right direction in preparation for the curing phase
The aligned rovings, mats and fabrics are held under tension and now enter a heated die. This has the cross-section of the desired shape. Here the materials cure under pressure and eventually exit the die in a cured state, in the profile shape. Due to tensioning, the produced material obtains very high and consistent mechanical properties in the longitudinal direction. The cured profiles are held in tension by pullers to keep tension in the fibers, which still have to enter the heated die. After the profiles pass the pulling rolls, they are cut to the desired length by a circular saw.
The pultruded grating may now be constructed by connecting multiple profiles parallel to each other. This is done by drilling holes in the profiles and inserting pultruded rods as crossbars. The crossbars are either glued or mechanically interlocked to form a single structure. Partly due to its continuous process, pultrusion offers the highest productivity to cost ratio of the manufacturing techniques. Fillers may also be included in the composite material and the heated die may be adjusted to allow specific geometrical arrangements. The pultrusion process allows a large degree of flexibility in matrix and reinforcing fiber choice, which makes it a desirable process for composites. To allow for a proper pultrusion, the materials should fulfill four requirements. The resin viscosity is should be relatively low (500 cP to 2000 cP). Long pot life ensures that the process stays continues for a significant time. High reactivity of the resin with heat is desired as this allows the resin to cure within a short time and lastly a good wetting capacity allows the process to produce profiles with high mechanical properties. The maximum dimensions to be produced by this process may have a width up to 1.5 m and a maximum height of 35 cm. Wall thicknesses may range from 1.2 mm up to 60 mm.
3.5 Discussion 31
3.5 Discussion Significantly different processes, produce the two kinds of composite gratings, each with distinct properties. An additional factor to take into account is the straightforward geometry of the molded grating. During installation through the wave zone, the wave direction is not expected to have much influence on the forces on the structure. In contrast, the pultruded grating has quite a different cross section when turned 90°. This may influence the installation phase, as water entering the pultruded grating will generate varying loads on the structure for changing wave directions. Additionally, the lower flexural modulus of the molded gratings, reduce the achievable span for a certain deflection of the grating. This may lead to additional steel stiffeners to provide support for the molded grating. It is expected that the molded gratings, providing better chemical resistance, are the better option for the design of a composite shallow foundation. This is due to the high uncertainty in the ageing of the physical properties of the material. It is reasoned that to provide the best protection of the integrity of the grating, it is critical to ensure the highest chemical protection. Molded gratings provide better protection against environmental damage, due to the higher resin content. In contrast to the pultruded gratings, the molded gratings are formed as a single shape, inherently providing better chemical protection. The more flexural molded gratings are expected to provide better protection against damage during the transport and installation of the grating, due to their higher impact resistance.
3.6 Conclusion Even though the pultrusion process exhibits better mechanical properties in comparison to the molded grating, it is expected that the chemical resistance is the deciding factor for choosing the appropriate manufacturing process. The molded grating contains more resin on the exterior of the composite, providing better protection for the reinforcing fiber. Additionally the molded grating is fabricated in a single piece, whereas the pultruded bars are connected using crossbars, which require machining of the pultruded bars. This initiates additional stresses and provides additional
points of entry for water ingress. Therefore, the molded gratings are preferred and investigated further. If the stability of molded gratings is proven in the subsea environment over an extended time, pultruded gratings become a viable alternative.
3.7 Grating dimensions In the following sections, the loads on foundation are assessed for different load cases, which it endures from load-
out until the in-service loading. To be able to make a comparison with the original mud mat solution, the initial grating dimensions are first assumed. This is done in line with the expected loads. These grating dimensions are kept constant throughout the report, to determine the critical areas and to see whether the assumed dimensions are reasonable or if adjustments are required.
Figure 3.8: Considered grating dimensions
It is assumed that the current mud mat plates are replaced by grating panels of similar dimensions. The dimensions of a single grating panel are given in figure 3.8. These dimensions are based upon the commercially available gratings. These give a good indication of what dimensions are manufacturable and mechanically strong enough to be
32 Manufacturing used as end-product. The commercially available gratings are quite flexible for the intended use. It is therefore suggested to use gratings with a height of , instead of the more commonly used high gratings. In the next section, the consequence of replacing the mud mat plates with gratings, relating to the transport of the structure, is briefly discussed.
4. Structure transport
4.1 Introduction The transport of the new foundation is not very different from the original operation. The few factors that do differ will be discussed in this chapter. The transport is assumed to cover the displacement of the structure from the fabrication yard to the barge and the eventual lifting location.
4.2 Sea fastening The transport of the structure with the grating foundation is not expected to alter the sea fastening requirements. The created weight-save will improve the stability of the transport barge carrying the subsea structure. Alterations to the sea fastening are therefore not required.
4.3 Possibility of re-hitting Due to the different heave motions of the barge and the lifting vessel, the lifted structure may hit the barge right
after liftoff. The probability of the structure re-hitting the barge is not expected to change for the different foundations. As a guidance, DNV prescribes that the re-hitting probability should be less than 1 %. The only factor for which may influence the probability is the relative motion between the barge and the lifting vessel during loading. The structure equipped with the composite foundation is less heavy, resulting in lower pitch during unloading and the relative heave motion of the structure is reduced. This provides a small reduction in the probability of re-hitting. As this effect provides a benefit, the re-hitting probability is not further investigated.
4.4 Damage during transport The composite material is more prone to damage and therefore, the structure should be handled more carefully. This may prevent unnecessary damage to the gratings. It is not desirable to let the structure rest on the gratings during fabrication transit and load out. This would put additional stress on the materials and the connections. Therefore, the structure should be placed on pedestals, as in current practice, skipping the load transfer of the steel frame to the gratings. This ensures the gratings are only loaded by their own weight during transport to the installation site.
As the structure is prepared for the lifting operation, the gratings are also vulnerable to impact by dropped objects. The dynamic load due to a dropped object is assumed to occur during the lifting phase, between hooking up the structure to the vessel crane and the entry in the splash zone. This timeframe has the highest probability for shackles or other equipment to fall on the grating. The gratings are subjected to an impact load specified by Norsok U-001 and allowed to freely deform laterally. The deformations of the gratings for this load case are discussed in section 9.9.2.
4.5 Conclusion One benefit of the composite gratings is that it is possible replace damaged gratings prior to installation through the splash zone. It is a relatively easy process, which may be performed at the target location, providing favorable weather conditions. As will be shown in chapter 10 the best option to attach the gratings to the structure is mechanical fastening, which allows easy replacement of the individual parts.
The following chapter deals with lifting the structure equipped with the grating foundation, through the splash zone.
5. Lifting through the splash zone
5.1 Introduction The installation of a subsea structure is a difficult procedure. A subsea lifting operation may be divided into three main phases: Lifting through the splash zone Deepwater lowering operation
Landing on the seabed The new foundation affects all these operations and alters the loads and stresses on the structure. In this section, the lift of the structure through the splash zone is investigated. As a result of the environmental conditions and the vessel- and crane-motions, the resulting forces are an important element of the structural integrity. First, the crane tip response spectrum is determined from the vessel RAOs and the wave spectrum. Next, the forces on the structure during the lift are examined and eventually the total hydrodynamic force and operability of the installation are determined. The DNV standard is used as a guidance to provide a conservative approach of the hydrodynamic loads on the structure.
5.2 Considerations and assumptions The Audacia installed the reference protection structure and this vessel is therefore the basis of comparison for the two foundations. This will provide some additional reference and assurance regarding the forces and motion behavior. The Audacia is one of Allseas’ dynamic positioning pipelaying vessels and is also used to install subsea structures on the seabed. The specifications of the Audacia are shown in table 5.1.
Table 5.1: Specifications of the Audacia [40]
Property Value Unit
Length 217 m
Breadth 32.26 m
Draught 8.50 m
Displacement 50,448,000 kg
The vessel operates an A-frame and a suspension frame to lower the structure to the seabed. The A&R cables (Abandonment and Recovery) are connected to a sheave block frame to provide a steady frame to distribute the forces from the structure to the crane. The A-frame and suspension frame are designed to carry a maximum static load of 700 t and a maximum dynamic load of 1100 t. The coordinate system of the vessel is shown in figure 5.1 and the crane coordinates are stated in Table 5.2: Coordinates lifting crane table 5.2.
Figure 5.1: Vessel coordinate system
36 Lifting through the splash zone
Table 5.2: Coordinates lifting crane [40] [41]
Coordinates
Description X Y Z Unit
Center of Gravity Audacia 115.52 0 12.19 m
A-frame tip location 143.84 -26.79 44.00 m
Suspension frame 143.84 -37.22 45.56 m
The A- and suspension frame are located on the starboard side of the ship. Therefore, considering that the frames are slightly more towards the bow from midships, the most optimal wave direction will be a wave heading of 157°. From diffraction analysis in AQWA by modelling the Audacia, it may be assumed that the incoming wave energy from high frequency waves are damped by approximately 90% and longer waves are damped by 50 %, see figure 5.2.
This difference in damping is caused by the low frequency waves being less affected by the obstruction of the ship in their propagating direction.
Figure 5.2: Diffraction analysis on the Audacia [41]
The structure lifting operation can be assumed to be a light lift. This criterion holds as the mass of the subsea structure is well below 1 % to 2 % of the displacement of the vessel. This means that vessel motions may be considered unaffected by the lift of the structure. In reality, the vessel heels up to 1.5° during the structure installation phases. To mitigate this, the ballast system of the vessel is used reduce these motions. The redistribution of ballast requires time between the installation phases to readjust the heeling angle and prepare for the next phase. The vertical forces on the structure clearly dominate the loads of the system. Therefore, it is assumed that the horizontal forces on the structure may be neglected. Furthermore, the horizontal motions will be limited due to tugs holding the structure in place. The load cases are assumed to be dominated by the vertical relative motion between the object and water. It is assumed that the structure length is small compared to the wave length. This allows the forces to be considered uniform over the entire structure. For deep water this is a reasonable assumption [42]. Furthermore, it is assumed that the stiffness of the lifting cable plays a minor role in the method of determining the forces on the structure during the splash zone entry. Therefore, the vertical motion of the object will follow the crane tip motion. It is expected that the loads resulting from the wave action dominate the hydrodynamic forces during lifting through the splash zone. Therefore, the wind and current forces are not considered.
5.3 Environmental conditions
5.3.1 Wave spectrum Different wave spectra have been published over time describing the energy density spectrum of the vertical surface displacement of an irregular sea. The most common ones are JONSWAP, Pierson-Moskovitz (PM), Ochi-Hubble and Torsethaugen. The PM-spectrum is used for fully developed seas and the JONSWAP spectrum was developed to include fetch limited seas. The Ochi-Hubble and Torsethaugen are two-peak spectra. These may be applied for combined wind sea and swell [43].
5.3 Environmental conditions 37
The PM spectrum is given by:
( )
(
(
)
) (5.1)
Where = =
The JONSWAP spectrum may be written as an adaptation of the PM-spectrum for a developing sea states:
( ) ( ) ( (
) ) (5.2)
Where is a normalizing factor [42] and
{
is the spectral width parameter. (5.3)
The non-dimensional parameter γ describes the peakedness of the spectrum and may be determined by:
{
√ ⁄
√
√ ⁄
(5.4)
Taking reduces the JONSWAP spectrum to the Pierson-Moskovitz spectrum. The wave angular frequency is defined as: (5.5) The zero up-crossing period may be related to the peak period by the following relation:
(5.6)
5.3.2 Response amplitude operator By means of Response Amplitude Operators (RAO) the wave energy of an irregular sea is transferred to vessel motions, and subsequently the crane tip motions. RAOs are the transfer functions which describe the amplitude and phase lag in the CoG for all 6 degrees of freedom (DoF) as a result of an incoming wave amplitude and frequency. The RAOs differ per vessel and for the Audacia they are determined by the software package AQWA [40].
The heave RAO of the crane tip can be calculated from the heave, roll and pitch RAOs from the vessel. The heave RAO of the crane tip follows from:
( )
( )
( )
( ) (5.7)
(5.8)
38 Lifting through the splash zone
Figure 5.3: Crane tip response for incoming wave direction β = 157.5°
Using this transfer function for all frequencies the crane tip RAOs can be formed. This is plotted in figure 5.3. The response spectrum of the crane tip then follows from:
( ) |
( )|
( ) (5.9)
The standard deviation can then be determined from this response spectrum by:
√ √∫ ( )
(5.10)
The most probable largest vertical single amplitude crane tip motion , for the wave period follows from:
{
(5.11)
Now that the most probable heave motions of the crane are determined, the vertical motion, velocity and acceleration of the lifted object can also be determined from the heave amplitude. These are related to heave motion by the circular frequency of the crane tip motion response spectrum: ( ) (5.12)
( ) (5.13)
( ) (5.14)
Where = = = = ⁄
5.3.3 Wave particle motion To determine the forces on the lifted object, the characteristic wave particle velocity and acceleration of the waves are required. These follow from the airy wave theory for deep water: ( ) (5.15)
0.0
0.5
1.0
1.5
2.0
2.5
2 6 10 14 18 22
Cra
ne
tip
hea
ve R
AO
[m
/m]
Peak period [s]
Crane tip motion spectrum β = 157.5°
5.4 Loads in the splash zone 39
( ) (5.16) Where =
The characteristic wave amplitude is related to the significant wave height and depends on the duration of the lifting operation:
{
(5.17)
The wave number is given by:
( ) (5.18)
Which simplifies for deep water to:
(5.19)
5.4 Loads in the splash zone A structure being lowered through the splash zone is exposed to a number of different loads. The problem is non-linear and difficult to predict the forces and the effect this has on installability of the structure. The structure is therefore simplified, and the loads are estimated conservatively by DNV [42]. By accurately predicting the design loads on the structure, one can wait for suitable weather for easier installation. This may provide cost saving, as the predicted loads are less conservative. Additionally, other vessels may prove capable of installing the structure. The safety of the operation improves as the expected loads are better defined. The loads on the structure are a combination of the static loads, in the form of the object’s weight and the hydrodynamic loads. The sum of these loads determines the stress on the hoisting lines and pad eyes connected to the structure. (5.20)
The static force is equivalent to the buoyant weight of the lifted object. This definition depends on the volume of displaced water relative to the still water level, given for each load case. ( ) (5.21) Where = ( ) =
5.5 Hydrodynamic forces The hydrodynamic force is a combination of several contributions. The individual forces are described in the following sections. The zero up-crossing period is used for the analysis of hydrodynamic forces. The period range to cover is determined by √ (5.22)
This period range uses increments of . The subsea lift is analyzed for wave directions at least ± 15° off the vessel heading. As the protection structure has a very complex arrangement, it is easier to analyze the forces on the separate parts of the structure. These separate forces are later combined to find the total force on the structure. The structure is
40 Lifting through the splash zone therefore divided into three distinct parts: the bottom part with the mud mats or gratings, the middle section with the diagonal braces and the top section with the 2 top chords. The hydrodynamic force is a combination of the different load components. The different forces on the structure are not in-phase. The total hydrodynamic force follows from:
√( ) ( ) (5.23)
Where = = = =
The drag and the hydrodynamic mass forces are analyzed for their separate sections. When the forces on each section have been determined, the sum of the parts are combined; ∑
(5.24)
∑
(5.25)
5.5.1 Slamming impact force The slam force on objects that penetrate the water surface is calculated by:
(5.26) Where
= - 5.6.3 = Damsgaard et al. performed testing on a grating to determine the resulting force from a water flow. It was determined that the variable with the most influence on the force is the porosity of the grating. The other factors investigated in this study were the size and shape of the holes and the angle of attack on the walls. An open area of 70 % to 87 % gave a reduction of the load by a minimum of 70 % as compared to a closed wall. The angle of attack had little to no change in load (45° to 90°). This test was performed using a molded grating with a height of 40 mm.
These results corresponds to the reduction in slam forces based the additional open area in on the bottom grating [44]. The slamming velocity is determined from: √
(5.27)
Where = = = .1 )
5.5.2 Varying buoyancy force The static weight of the structure is dependent on the still water level. The varying buoyancy, due to the wave
excitation may be approximated by: (5.28)
Additional elements of the structure are submerged as a wave passes by, leading to an increase in buoyancy and an additional upward force acting on the structure. The change in volume when a structure part is submerged by the wave, is estimated by:
5.5 Hydrodynamic forces 41
√ (5.29)
Where
= = ( )
5.5.3 Mass force The mass force is a combination of the inertia force, the Froude-Krylov forces and the diffraction forces. They are dependent on the wave particle accelerations and the accelerations of the crane tip motion. The characteristic hydrodynamic mass force on a structure part is equal to:
√(( ) ) (( ) )
(5.30)
Where = = = = .1 )
5.5.4 Drag force The viscous drag force on a structure part may be estimated by:
(5.31)
Where = =
The relative velocity between the water particles and the lifted object, is equivalent in magnitude to the slam velocity determined in equation (5.27). For the gratings, the drag generated by the skin friction drag is added to the pressure drag of the projected base area. This additional drag force is determined by a separate drag coefficient for the friction and the total skin area. The force may then be calculated by:
(5.32)
Where =
=
5.5.5 Snap force The snap force is the force resulting from the wire becoming slack after a large upward force on the structure. This may occur when the criterion for preventing snap, is not fulfilled. The snap load may be determined by:
√ ( ) (5.33)
Where =
= = The stiffness of the hoisting system is equal to the stiffness of the hoisting wire used for determining the natural
period of the hoisting system.
42 Lifting through the splash zone
(5.34)
Where the stiffness contributions are:
(5.35)
Where = = = =
The characteristic snap velocity follows from: (5.36)
Where the freefall velocity is determined by
√
(5.37)
The correction factor accounts for the difference between the free fall velocity and the relative vertical velocity .
{
( (
))
(5.38)
5.6 Hydrodynamic coefficients The equations above describe the major loads on the protection structure. They depend on the specific hydrodynamic coefficients, which stem from the dimensions and geometries of the structure. The evaluation of these factors may be determined theoretically, empirically or by model testing.
5.6.1 Added mass The added mass of an object is the mass of the extra volume a body displaces when it moves through a medium. The added mass of a protection structure is difficult to model as it is a complex structure. The foundation below the protection structure has the greatest projected area in the movement direction and provides the largest contribution to the added mass. The added mass of perforated mud mat plates may be determined from a non-perforated mud mat and using a factor to include the perforation ratio. The skirts below the structure, providing extra stability when penetrated in the soil, provide additional added mass by trapping water underneath the structure. The heave added mass of a 2-dimensional flat plate equal to the horizontal projected area of the mud mat is defined in DNV [42]. (5.39)
Figure 5.4: Definitions reference volume [42]
Where
= [-]
=
5.6 Hydrodynamic coefficients 43
The additional heave added mass, due to the skirts may be determined by:
( √
( )) (5.40)
Where
√
√
(5.41)
Where = =
As the perforation of the mud mat on the original protection structure is less than 5 %, the reduction of the added mass may be neglected. The total added mass of the mud mat is therefore equal the flat plate added mass multiplied by the factor for the trapped water
Since the suggested grating as a shallow foundation has an open area of 70 %, the perforation falls outside the range specified in DNV. Additionally, as this ratio is larger than 50 %, interaction effects may be neglected as they will likely be relatively small for large perforations.
Figure 5.5: Added mass reduction factor as a result of perforation ratio [42]
There are no methods specified to determine the added mass of a grating foundation, therefore the DNV method for a perforation range of 34 % to 50 % is taken. These values are already conservative for the specified range. The
added mass for the newly designed foundation is therefore estimated by:
(5.42)
This relation is plotted in figure 5.5. Here, is the perforation of the object. For the assumed grating dimension, the perforation is equal to 70 %, resulting in an added mass factor of:
(5.43)
This reduction in added mass agrees with studies by Molin on the effects of circular perforations on the added mass. The added mass was determined for different sizes circular hollows by potential theory. This resulted in a factor of
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 20 40 60 80 100
Ad
ded
mas
s re
du
ctio
n fa
cto
r
Perforation ratio [%]
Effect of perforation on added mass
DNV method
exp(-p/28)
44 Lifting through the splash zone approximately 0.09 at 70 % perforation for holes of 2.4 m in diameter. Orifices of lesser diameter generally showed a further reduction in added mass, but these were not investigated up to 70 % perforation [45, 46]. The remainder of the protection structure consists of mainly long circular members and the added mass is determined in similar manner to equation (5.39).
The coefficients for a circular member may be estimated by
Figure 5.6: Definitions reference volume [42]
=
=
5.6.2 Drag coefficient The general drag coefficient for an object in oscillating flow depends on the oscillation amplitude. This oscillation amplitude is expressed in the Keulegan-Carpenter (KC) number, which relates it to the considered member dimension. The number is defined as:
(5.44)
Where = =
For cylinders, this dimension is equal to the diameter of the tubular. The drag coefficient for objects in oscillating flow , is different than the drag coefficient in steady flow. The oscillating flow coefficient may be determined by taking
two to three times the steady flow coefficient [42]. This simplification also holds for the flat plate on the bottom of the protection structure. Øritsland discovered this relation between steady flow and oscillating flow drag coefficients. In his study, the hydrodynamic coefficients of subsea structures were determined by the performed experiments. The resulting from the linear and quadratic drag coefficient from his experiments, coincides closely with three times the steady flow drag coefficient for a flat plate [47].
The steady flow drag coefficient may be estimated for by
Figure 5.7: Rectangular plate normal to flow
direction
B/H 1.16 1 1.20 5 1.50 10 1.90
5.6 Hydrodynamic coefficients 45
The drag coefficient for the tubular on the structure may be determined in similar way.
Figure 5.8: Circular cylinder normal to the flow
L/D 0.80 2
0.80 5 0.82 10 0.90 20 0.98 40 0.99 50 1.00 100
The drag of the protection structure cannot be described by a single coefficient, due to the complexity of the object. To accurately determine the drag, the structure is partitioned in three sections, and the parts’ separate coefficients are determined. For the two different foundations, only the drag force of the bottom section is altered. The middle and top section are the same for both structures. The bottom section is modelled as a flat plate and the middle and top section are modelled by the sum of its multiple cylinders. The drag on the grating is calculated by using the 2-dimensional cross-section of a single bar of the grating [48]. It is then multiplied by the total length of bar within the grating. This does neglect the interaction effects, but a safety factor of 3.0 is used on the drag coefficient, which is expected to be sufficient, as the chosen drag coefficient is already quite conservative due to the geometry. Frictional drag The frictional drag is a result of the flow through the vents. It is first investigated if the flow can be assumed an internal flow. From the entrance length, one can determine if interaction effects occur between the flow layers, generating additional drag. The Reynolds number for the flow through the vents of the grating follows from:
(5.45)
Where = =
= The hydraulic diameter for cross-sections may be determined by:
(5.46)
Where is the wetted perimeter of the perforation and is the flow area. The effective hydraulic diameter for
laminar flow through a square perforation hole is [48]:
(5.47)
This results in a Reynolds number of approximately 105, which is sufficiently higher than the transition number of 2300, making it reasonable to assume that the flow is turbulent. Once the fluid enters the square perforation hole, it will require some distance for the velocity profile to become full developed. The distance for this to occur in turbulent flow is:
⁄
(5.48)
Where is the entrance length where the flow becomes fully developed. The determined Reynolds corresponds to an entry length of 28 times the effective diameter. This entrance length is far greater than the height of the grating.
46 Lifting through the splash zone The flow is therefore still in the developing region, resulting in low interaction between the flow layers. The frictional drag may be calculated for an external flow. For the external flow, a local Reynolds number is required, where is the distance along the grating bar height, see figure 5.9.
(5.49)
The flow layer thickness is formulated by:
{
⁄
(5.50)
The resulting drag coefficient for the grating inner area now results from:
{
(5.51)
Analyzing the flow through the grating as an external flow, the Reynolds number is still below 106 and thus the frictional drag coefficient can be calculated for laminar flows.
Figure 5.9: Flow past sharp plate for high Reynolds number [48]
5.6.3 Slamming coefficient The slamming coefficient is specified by DNV [43]. For circular cylinders the slamming coefficient . For non-circular shapes the slamming coefficient . Faltinsen specified the total force on a body as the rate of change in added mass over its submergence multiplied by the slam velocity squared, but this method is based on slender circular members [49]. The slamming coefficient is therefore assumed similar to the drag coefficient. This drag coefficient , fulfilling the criteria stated by DNV. The installation analysis of the considered protection structure quantified the slamming coefficient equal to the drag coefficient for the plate, leading to a conservative value of .
5.7 Load cases The lowering of a protection structure through the splash zone can be modelled by determining the loads on the structure during several stages. By calculating the total hydrodynamic loads on the structure during each typical load
case, the governing load case for certain sea state may be computed. When the critical loads in the design of the structure are known, this may be accounted for, allowing safe installation. The hydrodynamic loads are investigated for different phases, where the expected loads may be the largest. Each phase represents a different submergence of the structure into the splash zone. The submergence levels are given with respect to the bottom of the skirts.
Load case 1: -0.25 m
5.7 Load cases 47
For the first load case, the object is hanging in air, with the mud mats or grating foundation located 1 m above the still water level, see figure 5.10. At this location the slam forces are maximum, due to the wave crests hitting the mud mats or gratings. The mass and drag force are negligible assuming the horizontal projected area of the skirts is small. The varying buoyancy also generates a small force, but this is negligible with respect to the slam force.
Figure 5.10: Load case 1, still water 1 meter beneath foundation
Load case 2: 2.25 m The second load case assumes that the bottom section of the structure is now submerged and the still water is 1 m above the top of the bottom section, see figure 5.11 The dominating forces are now the drag force , mass force and varying buoyancy force . The vertical relative velocity and acceleration are related to the CoG of the submerged
part of the structure. Slamming impact forces are expected to be low, as the middle section only has vertical or inclined tubular.
Figure 5.11: Load case 2, still water 1 meter above top foundation
Load case 3: 4.69 m For the third load case the still water level is just below the top chords, see figure 5.12. Slam forces on these members are therefore substantial and are to be taken into account. The varying buoyancy force is calculated around the still water level. The mass forces are determined separately for the bottom section of the structure and for the middle section. The characteristic velocity and acceleration are determined with respect to the CoG of the sections individually. The total mass force is then the summation of the components. Drag forces are also determined for each section separately, and subsequently combined.
48 Lifting through the splash zone
Figure 5.12: Load case 3, still water 1 meter beneath top chords
Load case 4: 7.19 m The fourth load case is when the entire structure is beneath the still water level. The top of the structure is then located 1 meter below the surface, see figure 5.13. Slamming forces are negligible. When the structure is fully submerged, the varying buoyancy forces are also zero. The mass forces are determined for the bottom section, middle section and the top chords with respect to the distance from their individual CoGs to the still water level. The drag forces for the three sections are calculated separately.
Figure 5.13: Load case 4, still water 1 meter above top chords
5.8 Operability
5.8.1 Dynamic amplification factor A dynamic amplification factor (DAF) may be determined as an indication of the magnitude of the dynamic load. If this factor is above a certain limit, the motion response may become significant and the operation may become less safe. The DAF is calculated by:
(5.52)
Where
= {
[N]
5.8.2 Installation criteria The dynamic amplification factors for the wave spectrums are determined and using the specified criteria, an workability diagram can be created. Several criteria are to be fulfilled to ensure safe installation:
smaller than allowable static force on crane (700 t) smaller than the allowable dynamic force on crane (1100 t) smaller than 0.9, which is equal to a DAF of 1.9
5.9 Results 49
5.9 Results
5.9.1 Total forces As the structure is shielded by the vessel, the incident waves lose a significant amount of their wave energy. The high frequency waves are shielded more than the low frequency waves. The static and hydrodynamic forces are determined for the occurring wave periods. By determining the loads on the structure for every load case, the dominant load case may be determined. Figure 5.14 shows the combined contribution of the static and the dynamic loads acting on the mud mat foundation during splash zone entry for a significant wave height of 1.5 m. This shows that the load on the structure with the mud mat foundation is dominant for the second load case, where the foundation is located 1 meter below the still water level. The combined action of the mass and drag forces are larger than the hydrodynamic slam forces in load case 1.
Figure 5.14: Total forces on structure with mud mat foundation
For the structure equipped with a grating foundation, the critical load is determined in load case 1, see figure 5.15. Due to the highly ventilated structure, the hydrodynamic forces are lower, but the mass and drag contributions are reduced more than the slam forces of load case 1. This results in the critical loads for the grating foundation to occur in load case 1.
Figure 5.15: Total forces on structure with grating foundation
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
4 6 8 10 12 14 16 18
Tota
l lo
ad [
kN]
Period [s]
Total load on mud mat foundation for Hs = 1.5 m
Load case 1
Load case 2
Load case 3
Load case 4
0
500
1000
1500
2000
2500
3000
3500
4000
4 6 8 10 12 14 16 18
Tota
l lo
ad [
kN]
Period [s]
Total load on grating foundation for Hs = 1.5 m
Load case 1
Load case 2
Load case 3
Load case 4
50 Lifting through the splash zone Comparing the two foundations for their dominant load cases, gives an indication on the reduction in maximum load on the structure, figure 5.16. This displays a large reduction of total load on the structure for a significant wave height of 1.5 m. The static load for grating is higher, as the structure is still in air for load case 1, whereas the mud mats are already submerged in load case 2.
Figure 5.16: Total forces dominant load case
5.9.2 Forces on grating The replacement of the mud mat plates with composite gratings additionally results in different local forces on the foundation and its connection. To check if the new foundation may resist the forces caused by the lifting through the splash zone, the strength of the material is checked against the sum of the hydrodynamic forces acting on the bottom of the structure for each load case.
As expected, the force acting on the underside of the structure is maximum for load case 1. This is when the slamming forces are maximum. The exerted loads on the structure for a significant wave height of 1.5 meters are only slightly larger than the soil pressure caused by the structure weight on the seabed. The material stresses therefore remain limited and damage is prevented. Higher wave heights increase the risk of losing multiple gratings, but this is limited by the maximum acceptable wave conditions for the lift through the splash zone.
5.9.3 Workability scatter Figure 5.17 and figure 5.18 show significant improved for the lifting through the splash zone for the structure equipped with the grating foundation. The higher ventilated grating has a lower added mass, effectively reducing the dynamic loads on the structure. The diagrams are established using the installation criteria and consider the worst load case for each foundation.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
4 6 8 10 12 14 16 18
Tota
l lo
ad [
kN]
Period [s]
Total load on structure for critical load cases for Hs = 1.5 m
Total load mud mat
Static load mud mat
Total load grating
Static load grating
5.9 Results 51
Figure 5.17: Workability structure equipped with mud mat foundation
Figure 5.18: Workability structure equipped with grating foundation
5.9.4 Operability From the dynamic amplification factors, the acceptable wave conditions for safe installation are determined. These may be compared with the workability diagram of the original mud mat foundation. The difference indicates the improvement in installation capability. If there is a high probability that the grating application improves the workability of the vessel during the installation period, the costs of waiting for weather may be saved. If these retained costs weigh up against the investment of the grating foundation, this foundation may provide an
advantageous solution. Considering the annual wave scatter diagram for Laggan, see table 5.3 an approximation can be made for the improved installation window. This does not consider the wave directions, but provides an initial indication of the achievable improvement for the grating foundation. This shows that even an increase in allowable wave height of may provide an increase in operability of 25 %. The grating foundation provides an increase in installability for the significant wave heights that occur most for this location.
Table 5.3: Annual wave probability scatter for Laggan [%]
Tp [s]
5 6 7 8 9 10 11 12 13 14 15
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
Operable seastate
Non-operable seastate
Tp [s]H
s [m
]
5 6 7 8 9 10 11 12 13 14 15
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
Operable seastate
Non-operable seastate
Tp [s]
Hs
[m]
52 Lifting through the splash zone
3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total
Hs [m
]
0.5 0.1 0.4 0.6 0.4 0.7 0.6 0.6 0.3 0.2 0.1 4.0 %
1.5
0.8 1.7 4.1 5.4 4.7 2.7 1.4 0.6 0.1 0.1
21.6 %
2.5
0.2 2.1 4.7 7.7 6.3 3.8 2.2 0.6 0.2
27.8 %
3.5
1.4 2.7 5.4 5.4 3.8 1.4 0.5 0.1 21.0 %
4.5
0.7 1.4 3.1 4.2 2.1 0.9 0.3 12.8 %
5.5
0.4 0.8 2.0 2.1 1.0 0.4 6.8 %
6.5
0.3 0.5 0.9 1.1 0.5 0.1 3.4 %
7.5
0.2 0.3 0.5 0.4 0.1 1.5 %
8.5
0.1 0.1 0.2 0.1 0.6 %
9.5 0.1 0.1 0.1 0.3 %
5.10 Sensitivity analysis In order to estimate the sensitivity of the results, some parameters can be varied in order to determine their quantitative effect on the lift through the splash zone. The changed parameters are the projected area of the grating, to improve bearing capacity or strength of the foundation; the grating weight, by using more fibers or increased density of the composite, to improve the material properties; and the vessel heading, to adjust the motion response of the structure. Changing these factors has an effect on the size of the added mass, the hydrodynamic forces acting on the structure and the workability of the lifting operation. The added mass of the grating foundation varies mainly for the area perpendicular to the direction of movement. This corresponds to the open area or perforations in the foundation. The effect of changing the projected area by 10 % with respect to the original considered area of 158 m2 is displayed in table 5.4.
Table 5.4: Sensitivity grating added mass
Sensitivity grating added mass
Description Parameter -10 % +10 %
Projected area Ap -7.6 % +8.3 %
This indirectly also affects the hydrodynamic forces on the structure. However, the grating weight and the vessel heading also affect these forces. To show the sensitivity of these parameters, the effect on the maximum load (hydrodynamic + static) acting on the structure is determined for a significant wave height of 1.5 m. The vessel heading is changed by turning the vessel 22.5° and 45° away from the incoming waves, see table 5.5.
Table 5.5: Sensitivity grating maximum load
Sensitivity structure maximum load for Hs = 1.5 m
Description Parameter -10 % +10 %
Projected area Ap -3.6 % +3.6 %
Grating weight kg -0.8 % +0.8 %
Description Parameter -45° -22.5°
Vessel heading β +18.7 % +9.5 %
This shows that the grating parameters have little influence on the actual force on the structure. However, turning the vessel away from the waves, subjects the vessel to beam waves and the influence of the roll motion is increased, subjecting the structure to a greater load. The projected area and the incoming wave direction also affect the workability. The influence of these factors is shown in figure 5.19 and figure 5.20.
5.10 Sensitivity analysis 53
Figure 5.19: Sensitivity workability grating projected area
Figure 5.20: Sensitivity workability grating wave direction
This indicates that the best motion behavior of the ship for the lifting through the splash zone phase is achieved by choosing the heading with the optimal shielding. If the vessel turns more into the waves, the shielding effect is reduced and the structure is no longer protected from the higher frequency waves. If the vessel turns away from the waves, the beam waves cause additional structure motion due to the increased roll action. The increase in workability for the optimal vessel heading, may amount to quite a substantial increase in workability. This is due to the sea states, which are now deemed acceptable, have a high chance of occurrence. If detailed wave data at a location is available, this allows the calculation of the effective increase in workability. The local pressure on the grating during the splash zone lowering phase, varies according to the grating dimensions, the wave height and the direction. The loads in the critical load case have been determined and are presented in table 5.6.
5 6 7 8 9 10 11 12 13 14 15
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
Operable seastate
Non-operable seastate projected area -10%
Non-operable seastate considered grating
Non-operable seastate projected area +10%
Tp [s]H
s [m
]
5 6 7 8 9 10 11 12 13 14 15
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
Operable seastate
Non-operable seastate 22.5° off beam waves
Non-operable seastate 45° off beam waves
Non-operable seastate vessel heading 157.5°
Tp [s]
Hs
[m]
54 Lifting through the splash zone
Table 5.6: Sensitivity local grating pressure load case 1
Sensitivity local grating pressure for LC1
Description Parameter -10 % +10 %
Projected area Ap +0.5 % -0.4 %
Wave height Hs -13.6 % +14.6 %
Description Parameter -45° -22.5°
Vessel heading β +25.7 % +6.1 %
The low sensitivity of the grating properties may be explained by the projected area; as the projected area increases, the slam forces become larger due to larger added mass, but this is also distributed over a larger grating footprint.
5.11 Discussion The suggested grating foundation displays large improvement in the installability through the splash zone. The allowable significant wave height in which the structure may be safely installed is increased by approximately 1.5 meters for the entire wave spectrum. This improvement in installability is predominantly caused by the reduction of horizontal projected area of the shallow foundation. This reduces the added mass in the heave direction of the structure, thereby lowering the hydrodynamic loads.
This changes the dominant load case during splash zone entry. For the mud mat foundation, the dynamic amplification factor is maximum for load case 2, with the shallow foundation just below still water level. The grating foundation has the highest loads for load case 1, due to the slamming loads, with the foundation just above still water level. This may not be a desirable development, as the slam forces are more unpredictable in comparison with the dominant mass- and drag forces for the mud mat solution. Further improvement may be achieved by using even more perforated foundation, but the influence on the maximum load reduces and this affects the grating’s stability
and seabed performance. As the hydrodynamic behavior of the structure is determined using DNV’s simplified approach, the values are conservative and only give a rough estimate of the actual forces during the lift through the splash zone. Numerical simulations may give less conservative forces on the lifted structure. Computational fluid dynamics (CFD) and experiments may be used to further improve the hydrodynamic coefficients of the lifted structure.
5.12 Conclusion The behavior of lifting the protection structure equipped with the two different foundations through the splash zone is analyzed using the simplified method specified by DNV. This showed considerable improvement in installability, for a DAF of 1.9, allowing the structure to be lifted through the splash zone in much rougher wave conditions. The more ventilated foundation has reduced added mass, resulting in lower hydrodynamic forces to resist the vertical motions of the structure. The saved costs due the improved workability, which reduces the vessel waiting for weather time, should be compared with the increased investment of the new foundation.
6. Lowering to seabed
6.1 Introduction The operation of lowering the structure to the seabed is dependent on the added mass of the structure. Thus changing the mud mat foundation for a grating will alter the natural period of the pendulum system. The vertical motion of the structure is discussed in this chapter.
6.2 Resonance period Resonance amplification may occur when lowering objects to deep water as the resonance period of the hoisting system increases for increasing depth of the hoisting line. Resonance with the crane tip period or the wave period may occur and cause unwanted motions of the structure. Therefore, it is imperative to investigate the resonance of the mass spring system over the entire lowering range. The resonance period of the subsea lift may be estimated by:
√
(6.1)
Where = = = = = The stiffness of the hoisting system is dominated by the softest springs, see equation (5.34). For this system
these are the Cranemasters. Cranemasters are used to decouple the movement of the crane tip from the movement
of the lifted object. The adjustment factor to account for the cable mass follows from:
( ⁄ ) (6.2)
Where
(6.3)
6.3 Results
6.3.1 Motion behavior The resonance period of the subsea lift of both foundations as described in equation (6.1) is shown in figure 6.1. The period of the hoisting system, increases for longer cable length. Both the foundations are susceptible to resonance amplification if the crane tip oscillation period or the wave period is close to the resonance period of the hoisting system. The crane tip motion spectrum for a vessel heading is given in figure 5.3.
56 Lowering to seabed
Figure 6.1: Eigenperiod lowering phase grating and mud mat foundation
The resonance of the crane tip is located at the peak period of the motion spectrum, . The wave peak
period may be determined from the annual wave spectrum, see figure 6.2.
Figure 6.2: Annual wave spectrum Laggan
6.3.2 Lowering criteria The annual wave spectrum describes the occurrence of waves for a certain location over the entire year. This may be used to determine the most common wave period. The peak period .
According to DNV, resonance amplification may be neglected if the peak period of the response spectrum of the crane tip, is larger than the resonance of the hoisting system: (6.4)
Likewise, the wave induced resonance amplification of the structure in the splash zone may be disregarded if the peak wave period is larger than the resonance period of the hoisting system: (6.5)
0
5
10
15
20
25
30
35
40
0 500 1000 1500 2000 2500 3000
Per
iod
[s]
Cable length [m]
Eigenperiod of structure in lowering phase
Mud mat foundation
Grating foundation
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Occ
ura
nce
[%]
Wave period [s]
Annual wave spectrum Laggan
6.4 Discussion 57
6.3.3 Force on grating The force on the grating is not expected to be of significant value, as the drag force during structure descent will result in a low local pressure on the grating. Additionally the reduced horizontal projected area of the gratings reduces the force on the foundation. The drag force on the grating for a lowering velocity of 2 m/s is approximately 925 kN, see equation (5.31), which is well below the force on the gratings caused by the splash zone entry.
6.4 Discussion The protection structure with a mud mat foundation stays well outside the range of occurring wave periods, but is within the range of crane tip oscillation. As the structure is lowered further, past the crane tip oscillation period, the structure period moves outside the resonance period and the structure will not experience excessive movement as the structure is placed on the seabed.
In contrast, the oscillation periods of the structure with the grating foundation is well within the range of wave periods, but not at the peak period. The lowering operation is therefore considered safe for reference installation depth of 600 m. The lowering criteria from DNV state that resonance amplification for this installation depth may be neglected. Even though the period of the grating foundation not quite reaches the crane tip oscillation period, it is still in a
dangerous period range for the lift through the splash zone, due the wave periods. For deeper installations depths this will reach the crane tip oscillation period and resonance amplification may occur. To mitigate this, the Cranemasters stiffness and damping may be adjusted to compensate this. Additionally, the vessel may turned in a different heading to lower or increase the typical crane tip peak period, reducing the possibility of resonance. By replacing the steel wire with a fiber rope, one may decrease the total stiffness of the system and the period range over the depth will increase. This solution has a limited effect, due to relative high weight of the structure with
respect to the weight of the wire over its entire depth. Using stiffer steel wires will also have little effect, as the softer springs of the Cranemasters dominate the stiffness of the system. The lower weight and reduced dynamic motion of the structure, due to the new foundation may allow use of fewer Cranemasters. However, this may negatively affect the structure landing, due to an increase in motion response of the structure. The stiffness of the hoisting system at short wire lengths is mainly dependent on characteristics of the Cranemasters. These relatively soft springs provide more damping than the steel cables. For increasing wire length, the stiffness of
the steel cables decreases and its influence becomes more significant. At a wire length of 700 meters the stiffness of the steel cables is equal to the damping of the Cranemasters, and both provide a similar contribution to the stiffness of the system. Due to the prominence of the Cranemasters, the natural period of the hoisting system increases mostly linear over the first 700 meters of cable length. The stiffness of the cranemasters is less than the stiffness of the cable length and therefore the cables have little effect on the resonance period. To avoid the structure lift turning into a pendulum perpendicular to the vessel, winches are used to limit the movement of the structure. Therefore, horizontal movement of the structure is expected to be negligible. Possible currents are assumed constant and therefore assumed to not affect the vertical motions of the structure.
6.5 Conclusion The lowering installation phase is significantly affected by the interchanging of foundations. The lower added mass and resulting lower dynamic mass of the grating foundation increases the resonance frequency of the hoisting
system. For the reference structure this resulted in approaching the peak wave period for the lift through the splash zone and for deep water the crane tip period. To avoid resonance amplification within the system, it is suggested to change the stiffness of the passive heave system or change the vessel heading. This may allow avoiding the critical oscillation periods. Additionally, knowing the installation depth and the structure properties, the period range of the structure may be accurately predicted and the lowering operation may be planned to avoid undesirable motions.
7. Landing on seabed
7.1 Introduction When the structure approaches the seabed, the water body between the structure and the soil is pushed aside. As the clearance to the seabed further decreases, the water evacuation area reduces and the hydrodynamic pressure increases further. The increased pressure generates a load on the structure and the soil, effectively decreasing the momentum of the structure. This generated pressure depends on the interaction with the soil and the amount of water, which may escape through the perforations in the foundations and the clearance below the structure. The total contribution of the hydrodynamic forces slow down the structure and as the skirts and foundation penetrate, these take over the bearing capacity. The structure equipped with the grating foundation is compared with the original mud mat foundation for the seabed landing.
7.2 Seabed approach
7.2.1 Model Assuming that the water is incompressible, the escape of the water body from under the foundation may be determined. The clearance of the structure from the seabed is assumed 2 m at the start of the model and the initial lowering velocity is assumed to be 0.5 m/s. It is assumed that the maximum heave velocity is included in this value. This represents the worst phasing of the heave motions, as this is unlikely to be controllable. The Cranemasters attached to the crane take up the largest heave motions of the structure. The escape of water is determined by the penetrations in the foundation and the height of the structure above the seabed. As the structure lowers, the original volume becomes smaller and the superfluous water is pushed out. The velocity at which this is occurs is determined by the change in momentum of the structure and the escape area. To determine the worst-case scenario, it is assumed that structure is in freefall, when the structure velocity is reduced below the crane lowering velocity. The force in the cable is then neglected for the momentum equilibrium.
The hydrodynamic forces acting on the structure balance the submerged weight and inertia of the structure. By balancing the momentum of the structure for every clearance height, the velocity and acceleration may be determined. From this, the structure clearance over time can be determined. The momentum balance of the forces acting on the structure during landing consists of:
(7.1)
Where
= = =
= = =
7.2.2 Landing phases The analysis of the landing operation may be divided in four different phases. A momentum equilibrium may then be established for each phase. From this balance, the vertical structure velocity and the forces are determined. The first phase considers the structure unaffected by the seabed boundary. The structure is lowered at the cable lowering velocity. The forces acting on the structure consist of the viscous drag force, the submerged weight of the structure and the resistance caused by the outflowing water. The forces are schematically displayed in figure 7.1.
60 Landing on seabed
Figure 7.1: Landing forces on structure unaffected by seabed
For the second phase, the structure is closer to the seabed, but the skirts have not yet penetrated the soil, see figure 7.2. The structure motion is now affected by the seabed. The smaller escape area for the water volume increases the escape flow, resulting in a large force on the structure. Additionally, seabed proximity increases the added mass of the structure, leading to an upward ‘slamming’ force. The resulting deceleration of the structure provides a downward inertia force. Drag is reduced due to the lower velocity.
Figure 7.2: Landing forces on structure close to seabed
As the skirts penetrate, this takes up a part of the load and reduces the structure velocity further. The escape area is now limited to the perforations in the foundation and the increase in added mass force reaches a maximum. The acting forces on the structure are displayed in figure 7.3.
Figure 7.3: Landing forces on structure for penetrating skirts
In the final phase, as the foundation hits the seabed, the hydrodynamic forces are reduced to zero. The acting forces
are now the soil reaction consisting of the skirts and the foundation, and the submerged weight of the structure. See figure 7.4.
7.3 Forces 61
Figure 7.4: Landing forces on structure for foundation touchdown
7.2.3 Expectations The protection structure with the grating underneath is expected to have a larger impact force on the seabed. The projected area of the grating is considerably smaller, compared with the flat plate, leading to a lower hydrodynamic pressure during lowering. The cushioning effect is reduced as the water between the skirts may now easier escape through the large open area of the grating. This means that full skirt penetration is easier achieved, but the resulting higher velocity may cause damage to the foundation and lower its integrity. The increased impact may produce an over penetration of the gratings in the soil, which may provide a positive effect on the sliding capacity [50].
The maximum impact velocity and impact force during landing are determined for the upper bound undrained soil strength. Assurance of full skirt penetration and sufficient vertical bearing capacity of the foundation are determined by the lower bound undrained soil strength. The lower bound undrained shear strength is used to determine the resistance of the skirts and the foundation.
7.3 Forces The forces acting on the structure are now explained for their physical meaning.
7.3.1 High frequency added mass For the vertical motion of the closed mud mat plate very close to the surface, the added mass increases logarithmically. This added mass may be calculated by the high frequency limit, which for a circular plate close to the seabed is specified as [51]:
[
]
(7.2)
Where = =
The resulting upward force now follows by the rate of change of the added mass,
(
) (7.3)
Where =
This high frequency added mass term is a lot lower for the landing approach of the grating foundation. The grating foundation only has a horizontal projected area of 25 % of the mud mat foundation leading to an added mass of roughly 10 %. Molin investigated the slamming loads on perforated disks, which are considered similar to the added mass load near the seabed [46]. This displays significant reduction factors due to the perforations. Similar investigations on an inclined perforated wedge displayed a reduction factor of 0.14 for a porosity of the body of 20 % [52].
7.3.2 Drag force The viscous drag force caused by the vertical motion of the mud mat foundation provides quadratic damping on the system. This value may be determined using equation (5.13). As the velocity of the structure reduces, this force goes
62 Landing on seabed to zero. For the grating foundation, the same equation may be used. However, the grating drag coefficient for this motion is determined in section 5.6.2.
7.3.3 Escaping water As the structure lowers, more water is pushed out of the volume underneath the structure. The flow velocity of this outflowing water increases the dynamic water pressure. This dynamic pressure may be determined from Bernoulli’s equation. The static pressure is not included in the analysis, as this does not affect the movement of the structure. As the water flows through the perforations in both the mud mat and the grating foundation, energy is lost. This is included in the pressure loss coefficient .
(7.4)
Where
= {
The velocity of water out of the volume may be determined by:
(7.5)
Where = =
( )
= Where is the equivalent diameter of the foundation and the clearance height between the foundation
skirt tip and the soil. Assuming incompressible water, the water flow that escapes at any time from within the volume between the structure and soil is equal to: (7.6)
Where =
The escaping water results in a force on the structure: (7.7)
7.3.4 Soil reaction The reaction by the skirts and the mud mat and gratings as they penetrate the soil is given by: (7.8)
This reaction is dependent on the penetrated depth of the foundation. This contribution is zero when the foundation has not yet penetrated the soil. The reaction caused by the penetrated skirt is calculated using equation (8.3). As the actual foundation penetrates the seabed, the structure motion is slowed down further and eventually stops. The reaction force resulting from the flat mud mat plate is determined using equation (8.44). This bearing resistance increases very fast for any significant penetration of the foundation, leading to an abrupt stop of the structure. The reaction by the grating foundation as it hits the soil is calculated by equation (8.39). This generation of vertical bearing resistance is slower, as the soil penetrates the mesh of the gratings. When the grating penetration has generated sufficient bearing resistance, the structure comes to a stop.
7.3.5 Structure inertia The above-mentioned forces balance the inertia and the submerged weight of the structure. The inertia of the structure resisting the deceleration of the structure is calculated by:
7.4 Results 63
( ) (7.9) Where = This added mass for the inertia of the structure is assumed not to be affected by the seabed proximity. Predominantly, the water body above the mud mats provides the added mass contribution to the inertia. This part of the added mass section is not changed or increased close to the seabed boundary. The calculation method for the added mass is given in section 5.6.1. This results in different values for the structure equipped with the grating and the mud mat foundation.
7.3.6 Submerged weight The submerged weight is the weight in air of the structure reduced by the weight of the displaced volume. This is analogous to equation (5.21) for a fully submerged structure. (7.10) Providing these forces balance each other, the structure velocity may now be iteratively determined. This is used to
determine the deceleration of the structure and the kinetic energy of the system. During the seabed landing, the soil is compressed as a result of the combined action of the increase in water pressure. This compression of the soil provides additional cushioning of the structure motion. For softer soils this effect is greater.
7.4 Results
7.4.1 Mud mat landing Assuming the approach to the seabed of the structure starts with a crane lowering velocity of 0.5 m/s, the lowering velocity will slowly lower. This is the result of the water body below the structure that is to be displaced in order for the structure to move in its place. The resulting pressure on the structure and the soil is determined by the area by which the water body may escape. The escape area reduces when the structure lowers, resulting in an increase in
pressure and a reduction of the structure lowering velocity. The skirts eventually penetrate the soil, causing further reduction of structure velocity. During skirt penetration the water may only escape through the ventilation holes of the mud mat foundation. However, the structure motion is dominated by the increase in pressure caused by the seabed proximity. When the skirts are fully penetrated, the mud mat plates hit the soil and the foundation quickly takes up the entire load. The remaining water loads reduce to zero. The structure velocity lowers to zero and the structure comes to a stop. The structure clearance and velocity over time are shown in figure 7.5. The acting forces on the structure during the landing operation are shown in figure 7.6.
Figure 7.5: Structure with mud mat foundation clearance and velocity over time
0
0.1
0.2
0.3
0.4
0.5
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 4 8 12 16 20 24
Stru
ctu
re v
elo
city
[m/s
]
Stru
ctu
re c
lear
ance
[m]
Time [s]
Landing of structure with mud mat foundation
Structureclearance
Structurevelocity
64 Landing on seabed
Figure 7.6: Acting forces on structure with mud mat foundation
The contributions of the hydrodynamic forces have been combined for clarification in figure 7.7.
Figure 7.7: Combined forces on structure with mud mat foundation
7.4.2 Grating landing The structure equipped with the grating foundation is more ventilated than the original solution. This results in significantly lower hydrodynamic forces, leading to a less cushioned seabed landing. The structure motion is only affected by the increase in added mass (slamming) very close to the seabed. The structure velocity is only reduced as the skirts already penetrate the soil. The structure velocity is therefore higher than the structure with mud mats, as the foundation hits the soil. The structure position over time is displayed in figure 7.8 and the acting forces on the structure in figure 7.9.
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 4 8 12 16 20 24
Forc
es o
n s
tru
ctu
re [k
N]
Time [s]
Forces on structure with mud mat foundation
Inertia force
Slamming
Drag force
Submerged weight
Escaping water
Skirts
Mud mat
Skirt penetration
Mud mat penetration
0
200
400
600
800
1000
1200
1400
1600
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0 4 8 12 16 20 24
Forc
es o
n s
tru
ctu
re [k
N]
Time [s]
Forces on structure with mud mat foundation
Total force
Hydrodynamic forces
Skirts
Mud mat
Skirt penetration
Mud mat penetration
7.4 Results 65
Figure 7.8: Structure with grating foundation clearance and velocity over time
Figure 7.9: Acting forces on structure with grating foundation
The maximum force on the grating occurs as the skirts are already penetrated, due to of the increased added mass (slamming) of the foundation. By combining the hydrodynamic forces acting on the structure, the figure becomes more straightforward, see figure 7.10. Before the skirts penetrate, the cable forces take up the majority of the weight.
0
0.1
0.2
0.3
0.4
0.5
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6 7 8 9
Stru
ctu
re v
elo
city
[m/s
]
Stru
ctu
re c
lear
ance
[m]
Time [s]
Landing of structure with grating foundation
Structureclearance
Structurevelocity
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1 2 3 4 5 6 7 8 9
Forc
e o
n g
rati
ng
[kN
]
Time [s]
Forces on structure with grating foundation
Inertia force
Slamming force
Drag force
Submerged weight
Escaping water
Skirts
Grating
Skirt penetration
Grating penetration
66 Landing on seabed
Figure 7.10: Combined forces on structure with grating foundation
7.4.3 Landing impact force on foundation The landing operation may cause excessive local forces on the grating, due to the large change in momentum of the structure. The local force on the foundations is determined from the change in kinetic energy of the structure. By determining the change in kinetic energy of the structure between two heights, the exerted force on structure may be estimated. This force is not entirely taken up by the foundations, but by assuming this, a conservative approximation is achieved. The kinetic energy and the local force on the structure equipped with a mud mat foundation is displayed in figure 7.11. This shows a maximum force at . This is where the deceleration of the structure is maximum, due to the combined action of the escaping water, the increased added mass and the drag force. A secondary peak may be
observed at , just before the mud mats hit the soil. This is caused by the high increase of added mass. The maximum force on the mud mat is , but this distributed over the entire foundation area.
Figure 7.11: Change in inertia of the mud mat foundation
The kinetic energy and the local force on the gratings are shown in figure 7.12. This shows that the hydrodynamic forces do not reduce the kinetic energy of the structure. Only the skirts and eventually the gratings penetration slow down the structure motion. The largest force on the gratings occurs at , at a value of . This value is lower than the mud mat solution, due to the lower initial kinetic energy of the structure. The added mass of the ventilated grating foundation is lower, leading to a lower dynamic mass. This results in the reduced kinetic energy and
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1 2 3 4 5 6 7 8 9
Forc
es o
n s
tru
ctu
re [k
N]
Time [s]
Forces on structure with grating foundation
Total force
Hydrodynamic forces
Skirts
Grating
Skirt penetration
Grating penetration
0
100
200
300
400
500
600
700
0
200
400
600
800
1000
1200
1400
0 4 8 12 16 20 24
Forc
e o
n s
tru
ctu
re [k
N]
Kin
etic
en
ergy
[kN
m]
Time [s]
Force on mud mat during landing operation
Kineticenergy
Force onstructure
Skirtpenetration
Mud matpenetration
7.5 Sensitivity analysis 67
makes it easier to reduce the motion of the structure. This maximum force is distributed over a smaller area, resulting in higher material stresses.
Figure 7.12: Change of inertia of the grating foundation
7.5 Sensitivity analysis The sensitivity of the local pressure on the grating during the landing impact may be determined by varying the grating properties and crane lowering velocity.
Table 7.1: Sensitivity landing impact pressure on grating
Sensitivity landing impact pressure
Description Parameter -10 % +10 %
Projected area Ap +0.2 % -0.4 %
Crane lowering velocity vc -15.8 % 12.0 %
For a reduction in horizontal projected area, the force is distributed over a smaller area, resulting in a higher local stress on the material. The effect is only small, as the reduced projected area also results in a smaller kinetic energy of the structure, reducing the force on the grating. Reducing the initial lowering velocity reduces the initial kinetic energy of the structure and less force is required to reduce the motion of the structure. For a higher initial lower velocity, the force required to stop the structure is higher and this results in higher stresses in the material.
7.6 Discussion The seabed landing of the structure is analyzed using the conservation of momentum. The acting forces on the system are balanced for each clearance height. The added mass load is significantly lower for the grating foundation, causing a large difference between the foundations. The seabed proximity increase of the added mass is lower for the largely open foundation. The lower hydrodynamic forces do not cushion the motion of the structure and the skirts penetrate the soil at the crane lowering velocity. The results show that grating foundation barely slows down as the skirts penetrate, only reducing the velocity as the gratings penetrate the soil. This results in a relative quick landing of the structure. This is further promoted by the reduced kinetic energy of the system. The reduced dynamic mass of the grating foundation allows the structure velocity to be reduced more easily. The reduction in set-down period may improve installability, as the operation becomes less dependent of unexpected wave motions. The maximum force on the grating foundation during the landing is lower than the force on the original mud mat foundation. This is caused by the reduced dynamic mass of the grating foundation. However, the local pressure on the grating is still higher, due to the reduced horizontal projected area. Coupled with the lower material strength, this results in an increased possibility of damage. This should be mitigated by monitoring the structure clearance height and adjusting the lifting velocity accordingly. The foundations penetrate less in softer soils. The softer soil is easier compacted, before the foundation hits the soil. This consequently causes more cushioning on the structure and the relative velocity between the foundation and the
0
100
200
300
400
500
600
700
0
20
40
60
80
100
120
140
160
180
0 1 2 3 4 5 6 7 8 9
Forc
e o
n s
tru
ctu
re [k
N]
Kin
etic
en
ergy
[kN
m]
Time [s]
Force on grating during landing operation
Kineticenergy
Force onstructure
Skirtpenetration
Gratingpenetration
68 Landing on seabed soil is less. For the stiffer soils, the required pressure for the soil to yield is much higher and thus the pre-settlement is less than for softer soils. This increases impact velocity for the foundation and results in a higher penetration into the soil. It is expected that the skirts take up more force for the structure with the grating foundation. This may be
contributed to the larger penetration of the skirts in the soil. The higher penetration, results in a higher bearing resistance of the skirts. The structure with the mud mat foundation penetrates less, leading to lower bearing resistance generated by the skirts. The longer settling time of the grating foundation is caused by the clay filling up the holes of the grating.
7.7 Conclusion The seabed landing duration is considerably smaller for the grating foundation, due to the lower hydrodynamic cushioning of the water. The higher ventilated grating foundation allows water to evacuate at a much higher pace, effectively reducing the effect of cushioning. This result is also seen when examining the expected loads on the structure during the landing operation. The hydrodynamic water pressure on the original foundation provides a large load on the structure even before the skirts and plate foundations touch the seabed. This hydrodynamic water pressure is not fully generated for the grating foundation. The results indicate that the grating foundation may provide some benefit over the mud mat foundation. Because of the lower dynamic mass of the lifted structure, the kinetic energy is reduced. Therefore, the maximum force on the foundation is lower than for the mud mat foundation. However, this maximum force is distributed over a smaller area, resulting in higher material stresses. To keep the material stresses within limits, the lowering velocity and clearance of the structure to the seabed will have to be monitored, adjusting the velocity according to the structure’s position. This may reduce the loads on the structure sufficiently to avoid the possibility of damage to the grating and the steel structure.
8. Foundation design
8.1 Introduction The allowable load on the suggested grating foundation is difficult to estimate from the conventional formulations for bearing capacity. Due to the complex shape, different interaction mechanisms may occur, providing additional foundation capacity beyond the bearing capacity generated by the projected area of the foundation. In this section, the occurring mechanisms are discussed and a method of predicting the bearing capacity of the grating foundation in drained and undrained soils is suggested. Additionally, the horizontal sliding resistance and the immediate settlement of the foundations are investigated. Once the structure has landed on the seabed, the loads will be transferred to the soil. If this resulting bearing stress exceeds the bearing capacity of the soil underneath the structure, the settlement will increase further until a new equilibrium is found. To provide a comparison between the original mud mat plates and the grating foundation, the foundation stabilities of both foundations are investigated. This is determined for both sand and clay. The formula for bearing capacity of a strip foundation may be described by the equation of Brinch-Hansen:
(8.1)
Where = = = = =
=
The equation may be generalized for an arbitrary shape by taking into account the shape of the loaded area, the inclination of the load and an embedment depth factor [53]:
(8.2)
Where = = =
This formula may be used in combination with the sliding capacity formulation, to determine the stability diagrams for a combination of vertical and horizontal forces acting on the foundation. The diagram describes a stability envelope, in which the foundation is stable. The vertical and horizontal boundaries of the envelope determine the vertical and horizontal (sliding) capacity of the foundation, see figure 8.1 and figure 8.2.
70 Foundation design
Figure 8.1: Stability envelope undrained soils Figure 8.2: Stability envelope drained soils
It may be observed that the sliding capacity of drained soils increases for higher vertical loads, following Coulomb’s friction law. The sliding resistance of undrained soils however, does not improve for increased vertical stresses.
8.2 Design parameters
8.2.1 Soil To provide a quantitative estimation, general soil properties values for sand and clay are assumed. For sand it is chosen to take similar values to the soil used in the study by Bransby [3]. In this study the bearing capacity of a grillage foundation is analyzed. The discussed sand consists of uniformly distributed fine silica sand with a density of 1487 kg/m3. These properties allow the performance of the grating to be compared with the results in that study. The clay properties originate from the location where the reference subsea structure is installed. This is slightly over-consolidated clay.
Table 8.1: Soil properties
Soil Sand Clay Unit
Unit soil weight 14.6 7.5 kN/m3
Internal friction angle 30.8 0 °
Interface friction angle 21.7 16.7 °
Apparent cohesion 0 1 kPa
8.2.2 Friction The interface friction angle between the composite material and the soil differs from the interface friction angle between steel and soil. Frost and Han investigated the friction coefficient between composite material and angular sand ( ). They tested the friction for a large number of densities and normal loads. They found that the
peak interface friction angle of the composite/sand interface is in the order of 10 % larger than for the steel-sand interface. The experiments showed that the interface shear strength was a function of the normal stress, the relative roughness, and the angularity of particles and the initial density of the soil [54]. Composite/clay interfaces displayed similar benefits in drained and undrained conditions. Giraldo and Rayhani discovered composite/clay interface friction angles that were in the range of 5 % to 19 % higher than that of the steel/clay interfaces. Interface adhesion also showed favorable results with regard to composite material [55].
8.3 Drained conditions (sand) 71
As discussed before, the surface finish on gratings may be selected as smooth, concave or gritted. It is expected that the gritted surface, in which silicon-oxide grit has been incorporated in the manufacturing process, provides additional frictional resistance for the gratings. This further improves the stability of the subsea structure and especially the horizontal sliding resistance.
These effects display a high amount of uncertainty and vary depending on resin type and possible surface finish effects. Therefore, these are not included for the calculation of the bearing capacity of the composite grating. Neglecting these effects provides a conservative approach for the vertical bearing capacity.
8.2.3 Foundation The dimensions of the foundation and the bearing load on the structure are required for the foundation design. The dimensions of the base area of the protection structure are converted to an equivalent rectangular area. This allows easier calculation of the bearing capacity. These are specified in table 8.2.
Table 8.2: Structure parameters
Structure properties Symbol Value Unit
FLET + protection structure mass (submerged) 308,000 kg
Effective width foundation 18.98 m
Effective length foundation 34.73 m
Design bearing pressure 10.6 kPa
Skirt height 0.75 m
8.2.4 Skirt penetration The penetration of the foundation skirts provides additional bearing capacity. The penetration resistance of a skirt
may be determined from the following formula.
( ) ∫ ( )
(8.3)
This formula applies to both drained and undrained soils. For the empirical coefficients, see section 8.4.1.3. The skirts penetration is not increased by the arching effect described in section 8.3.1.1. The only discrepancy between the two
foundations would originate from the increased penetration for the grating foundation. By neglecting the generated bearing capacity of the skirts altogether, the vertical bearing capacity can be conservatively determined.
8.3 Drained conditions (sand)
8.3.1 Vertical bearing capacity Several enhancing mechanisms may improve the foundation capacity in drained conditions. These mechanisms are discussed, before including these effects in the generalized bearing capacity equation. This equation may then be used to determine the vertical bearing capacity for the grating foundation.
8.3.1.1 Arching When the grating foundation is subjected to a vertical load, the foundation will experience an increased amount of bearing capacity, larger than the sum of the individual beam capacities. This is the result of the larger volume of soil underneath the grating being pushed into the smaller open area of the grating. This consequently produces an increase in vertical and horizontal stresses in the soil and improves the base resistance of the beams and the frictional resistance of the sides of the beams. This mechanism is called the arching effect. Terzaghi explained the arching mechanism in more detail, describing what happens on a granular level. He described arching as the mechanism that may occur in soils when a certain section of the soil yields. The soil next to the yielding part stays in place and generates a shear resistance due to the relative movement at the interface [56]. This shear resistance attempts to keep the yielding material in its original position. This is supplemented by a decrease in pressure in the yielding material and an increase in pressure of the stiffer material. A large portion of the overburden pressure of the yielding part is then transferred to the non-yielding parts via the frictional forces. This results in an enhanced vertical effective stress compared to the free field solution. This effect increases non-linearly with increasing embedment depth [57].
72 Foundation design In the study by Bransby, the effect of arching was analyzed by examining a soil element between two adjacent grills. As the two adjacent plates penetrates the soil, the wall friction increases and eventually the friction becomes so large that the soil between two plates plugs and moves down together with the grillage foundation. The increase vertical effective stress may be determined by assuming equilibrium between the forces on the soil element. Assuming uniform vertical stress along the base and the top of the soil element (conservative) the acting forces are shown in
figure 8.3.
Figure 8.3: Forces acting on soil element [2]
Equating the vertical forces leads to:
(8.4)
Where = =
Given that the skin friction is equal to:
( ) (8.5)
These equations are combined to the following:
( )
(8.6)
This expression is rearranged and integrated over the boundaries, to find the distribution of the vertical stress over the depth.
∫
( )
∫
(8.7)
From which follows:
( )
(8.8)
Where is a factor for the arching effect:
( )
(8.9)
8.3 Drained conditions (sand) 73
And the lateral earth pressure coefficient used in this equation was defined by Kulhawy for large displacement piles as . Where the neutral coefficient was first suggested by Jaky [58, 59]: ( ) (8.10) For the grating foundation, the soil is confined in the horizontal plane in both directions. Therefore, the arching effect experiences additional skin friction, and the displaced volume is pushed into a smaller area. Performing the above derivation for the grating foundation, results in an altered expression for . The forces acting on a soil element within a grating is illustrated in figure 8.4.
Figure 8.4: Forces acting on a soil element in a grating perforation
( )
(8.11)
The base resistance and skin friction of the gratings are effectively increased as they depend on the depth the foundation has penetrated. The arching effect consequently creates a higher effective stress in comparison to the free field solution. As a result of this mechanism the soil stresses increase non-linearly with depth and diverge from the original solution for increasing penetration. Comparison of the vertical stress distribution of the grillage and grating solutions with the free field solution is presented in figure 8.5.
74 Foundation design
Figure 8.5: Vertical effective stress profile in grating and grillage foundations
8.3.1.2 Interference Another effect that may provide additional bearing capacity is the interference effect between closely spaced footings. The mechanism results from the failure mechanism of a shallow footing, see figure 8.6. If an additional footing is positioned within the passive zone of the adjacent footing; the total bearing capacity is greater than the sum of its parts. The radial transition zone of two adjacent footings will overlap and generate an extra resistance. Stuart referred to this mutual influence as interference and suggested a modified expression for the last term in equation (8.2) [60].
(8.12)
Where =
This efficiency factor depends on the relative footing distance and the soil friction angle . Graham suggested that the efficiency of two equal footings is maximum for a spacing of 1.5, with decreasing values to a spacing of 4 footing widths. At this spacing the footings act independently and carry an equal load. The efficiency was observed as high as 150 % at the spacing of 1.5 footing widths [61].
Figure 8.6: Failure mechanism of a single footing [62]
0
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0 1 2 3 4 5 6 7 8P
enet
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on
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Grating shape
Grill shape
Undisturbed soil
8.3 Drained conditions (sand) 75
The extent of this effect on the actual bearing capacity is difficult to establish. The relative distance between adjacent bars in the suggested grating foundation is quite large, due to the thickness of the bars. Furthermore, different footing geometries and material roughness are expected to also influence the efficiency. Studies indicate that the interference effect may be observed for footing spacing/width ratios up to 4. For this distance between adjacent bars, the load response and the bearing capacity are close to the single footing capacity as suggested by Terzaghi,
indicating no further interference effects [63]. The considered grating foundation has a bar spacing of 8 and the interference effect can be expected negligible. At the bar nodes, the effect may occur, but this is only expected for 25 % of the open area of the foundation. This has a limited effect on the total bearing capacity of the foundation and neglecting this effect is conservative. For a spacing of 4, the grating may give full interference effects, due to grating bars in both horizontal directions, but this is not investigated. The studies describing this phenomena mainly focus on larger footings (> 1 meter). It is questionable if the interference effect translates to the small dimensions considered here. Neglecting the effect altogether is therefore recommended [64].
8.3.1.3 Grating foundation To determine the bearing capacity of a grating in a fully drained soil, several additional assumptions are required. The increase in effective soil stress increases the normal force on the individual grating bars and thus the bearing capacity due to skin friction is increased. The interface friction angle and lateral earth pressure coefficient are assumed to remain unchanged by the pressure increase. Additionally, the base capacity of the grating bars is assumed to be affected by the increase in effective pressure. The analytical solution assumes that the base resistance of the bars increases non-linearly for increasing depth. The factors and are assumed to be unaffected.
The base and skin resistance on the outer grating bars are not expected to benefit from the increased effective stress as one of the sides is exposed to the undisturbed soil stress. The arching effect does not occur and therefore the vertical effective stress is not increased. The effective stress at the edges is equal to the undisturbed vertical effective stress
. The bearing capacity of a grating foundation is more difficult to obtain than a plate foundation, because friction generates additional capacity. The contribution of the bearing capacity obtained by the base of the structure is combined with the generated friction capacity on the inside of the perforation holes. The bearing capacity factor for the grating is different than the one used for the flat plate. Berezantzev suggested
that this factor was dependent on the embedment depth , relative to the width of the foundation [65]. For the grating, each bar has a small width and the local has a different value than the bearing capacity factor of the mud
mat foundation.
Figure 8.7: Schematic diagram of soil resistance on penetrating bars [3]
The total resistance of the grating at a particular depth is determined by the combined contributions of the side friction and the end bearing resistance, see figure 8.7:
76 Foundation design (8.13)
The outer base resistance and the outer skin resistance may be determined using the normal effective stress, whereas the inner resistances are calculated by the enhanced vertical effective stress. Due to the significant foundation area, the base and skin resistance along the perimeter are significantly smaller than the internal contributions. Therefore, these contributions are neglected. Equation (8.13) now reduces to: (8.14)
The base resistance on the inner bars may be determined by: (8.15)
In which the bearing capacity generated in the projected area is equal to:
(8.16)
Where
= = = - [65] The inclination terms and are considered equal to unity, as the load on the foundation is assumed to be applied
in the CoG of the foundation and perpendicular to the seabed. =
The shape factors and are a function of the inclination factors and are specified as:
(8.17)
(8.18)
The depth factors and follow from DNV [66]:
( ( )) (8.19)
(8.20)
And the bearing capacity factor for the gravity term is defined as:
{ ( ) ( )
( ) ( ) (8.21)
The resistance generated by the skin friction is the product of the friction over the penetrated depth and the linear distance of the skin area:
∫ ( )
(8.22)
The skin area per penetration depth for a grating foundation may be calculated by:
( ) (
)(
) (8.23)
8.3 Drained conditions (sand) 77
The friction on the insides of the walls of the grating may be determined by including the arching effect in the shear stress equation on a wall, see equation (8.5). This results in a definition for the generated side friction capacity as a function of its embedment depth:
( ) ( )
( ) (8.24)
The factor is defined in equation (8.11).
8.3.1.4 Mud mat foundation The mud mat foundation is modelled as a flat plate. The formula for the bearing capacity of a flat plate in fully
drained (sand) conditions is derived from equation (8.2) by assuming cohesion-less sand. (8.25)
The second part of the equation is the gravity term. The bearing capacity factor follows from:
( )
( ) ( ) (8.26)
The total vertical bearing load for the flat plate mud mat may now be defined as: (8.27)
8.3.2 Horizontal bearing capacity The behavior of the grating under combined vertical and horizontal motions is important to determine, as horizontal loads may occur due to fishing loads or due to thermal expansion of the pipeline. This was investigated by Knappet et al. for a grillage foundation, under a constant vertical loading [50]. The modelled grillage foundation generated additional capacity over equivalent mud mat foundations for loose and medium-dense sands, and similar for dense sands. This additional capacity was determined to be the result of the enhanced interface friction due to the soil/soil shearing and the increased shear area from the penetrated grills. This effect was less prominent in the denser sands,
as a reduced penetration was required to obtain similar capacity. For grating foundations, this increased capacity is still expected, but to a reduced extent, as the closed structure in the horizontal direction will barely have an increased shear area. The soil-soil interface however is still present and still induces improved horizontal resistance. Tapper et al. determined that an over penetration of a grillage foundation in the soil resulted in a large improvement in horizontal resistance. This effect may provide benefits for the gratings when additional horizontal capacity is required for an application. The gratings may then be installed using additional ballast to improve its horizontal
capacity in service [67]. The horizontal capacity of the grating is expected to differ from the original mud mat foundation. To determine this change, the capacities of the foundations are investigated for both sand and clays. The skirts surrounding the foundations, dictate the major part of the horizontal resistance. As we are mainly interested in the difference between the two foundations, the effect of these skirts is omitted to allow a better comparison and give insight into the application of a grating foundation without skirts.
The horizontal bearing capacity is determined as the sum of the lateral resistance by displacing a volume of soil and the sliding resistance caused by the friction. The lateral resistance is stated in ISO [68] as: ( ) (8.28) Where = = = The drained horizontal soil reaction factor may be determined by:
78 Foundation design
(
) (8.29)
The passive lateral earth pressure coefficient is:
( )
( ) (8.30)
The sliding resistance of the shallow foundation results from the shear stress: (8.31)
is the contact area of the foundation with the soil and is the friction generated between the foundation and the
soil, resulting from Coulomb’s friction theory: ( ) (8.32)
Where = =
Figure 8.8: Mechanics horizontal resistance grating foundation
Considering the grating foundation, the soil volume with the perforations provides additional horizontal resistance. This additional resistance follows from the minimum capacity of two failure criteria, see figure 8.8. The first failure criterion is assuming that the grating bars shear the soil at the same depth as the tip of the bars. The embedded soil then displaces along with the grating bars and the capacity follows from the shear stress of the soil/soil interface: (8.33)
8.4 Undrained conditions (clay) 79
Where the open area of the total foundation ( ) and follows from:
( ) (8.34) The pressure on the friction interface is the result of the weight of the soil within the mesh. The increased soil
pressure resulting from the arching mechanism is not included as this only expected to be a small factor of the total horizontal resistance. Additionally, this allows a conservative approximation of the resistance caused by the soil within the mesh. The second criterion assumes that the friction is sufficient to resist the sliding bars. The force provided by the soil within the mesh is then equal to the lateral earth pressure acting against the movement of the bars. This pressure as function of the embedded depth is, from [69].
√ (8.35)
By integrating this over the embedded depth and multiplying it by width of mesh and the number of perforations in the entire foundation, this leads to a total horizontal force of
(
√ ) ( ) (8.36)
Where = This results in a drained horizontal capacity of the foundation of: ( ( ) ) (8.37)
8.4 Undrained conditions (clay)
8.4.1 Vertical bearing capacity The soil bearing capacity of a mud mat and grating foundation is determined differently for undrained soils. As the codes and standards describe different methods, the bearing capacity in undrained soils will be determined for both DNV and API methods. The internal friction angle of the undrained soil , resulting from Mohr’s circle showing a horizontal failure envelope. The cohesion intercept is equal to the undrained shear strength . Experiments performed by Koopman on the penetration of a grill foundation in Kaolin clay showed that it is still difficult to predict the behavior of a grillage foundation in clay. The only hypothesis he was able to verify with an acceptance level of 5 % was that a grill in a grillage environment mobilizes more resistance than a grill without surrounding members. This suggests that there is an enhancing mechanism for the bearing capacity of closely spaced bars [4].
8.4.1.1 Upheaval An apparent increase of soil level between the bars will occur when the foundation penetrates in clay. This is the result of the displaced volume of soil. Assuming the clay has a constant volume (fully saturated) and the particles and
water are incompressible, the original volume in one mesh now has to fit in an area of ( ) . The constant
volume generates an increase of height of the clay within the perforations. This upheaval effect is in the order of
( ) (8.38)
Where is the penetrated depth of the foundation. The increased height within the gratings may improve the vertical stress within the mesh and the increase the frictional area. This effect is not included in the calculation of the bearing resistance of the grating in clay, ensuring a conservative design.
80 Foundation design
8.4.1.2 Remolding The application of the grating foundation in soft clays will result in remolding along the grating inner surface. This redistributes the horizontal soil pressure and effectively limits the skin friction. For significant embedded depths, this reduces the increase in undrained shear strength of the soil and lowers the expected vertical capacity.
8.4.1.3 Grating foundation The method of determining the bearing capacity of the grating foundation is derived from the equations in DNV and API. These methods are different and result in different required penetration depths to achieve sufficient capacity for the structure. The bearing capacity of the gratings in clay follows from the formula described for the penetration resistance of skirts in in soil from DNV. The bearing capacity method specified by DNV uses the results of a cone penetration test, determining the cone resistance of the soil. The lower bound cone resistance is used in the
determination of the end bearing resistance and the skin friction. This gives a conservative estimation of the capacity. The bearing capacity in clays follows from the summation of the end bearing resistance and the skin friction resistance.
( ) ∫ ( )
(8.39)
Where ( ) = = =
and are the contact areas of the gratings, split into the base area and the penetrating friction area.
The empirical coefficients for North Sea conditions are given by DNV:
Soil Most probable Highest expected
kp kf kp kf
Clay 0.4 0.03 0.6 0.05
Sand 0.3 0.001 0.6 0.003
The resistance of skirts in API is described in a similar way, adding the resistance resulting from the projected area and the side area. The factors in API are determined from the undrained shear strength of the soil, in contrast to the cone resistance in the DNV method: (8.40)
Where = =
The unit end bearing capacity in cohesive soils is determined from the undrained shear strength . (8.41) The skin friction resistance of the gratings may be determined from the undrained shear strength in clay, modified by the roughness of the soil: (8.42) For soft clays (< 20 kPa), the clay will remold during penetration, so the soil will make full contact with the object.
The dimensionless factor α will then approach unity. For stiff clays (> 150 kPa) however, the soil will not remold and only provides partial contact with the sides of the grating. For very stiff clays, the value nears zero. The dimensionless factor from the Kolk and Van der Velde method (1996) may be computed by:
{
(8.43)
8.4 Undrained conditions (clay) 81
Where for the penetration depth [70]. Both methods do not take into account any interaction effect such as interference or arching.. As the quantifiable benefit of these effects in clay remains unclear, the exclusion of these positive effects may result in a conservative bearing capacity.
8.4.1.4 Flat plate The bearing capacity of the mud mat follows from DNV. The DNV method utilizes the overburden pressure of the soil and the roughness of the plate to determine its bearing capacity.
Figure 8.9: Correction factor F for rough and smooth footings [71]
The bearing capacity of a flat plate in undrained conditions for linearly increasing shear strengths is
(
) (8.44)
Where = - , see figure 8.9 = = =
The correction factors are: =
=
= The resulting bearing capacity of the total foundation in undrained conditions follows from: (8.45)
8.4.2 Horizontal bearing capacity The horizontal capacity of the foundations in undrained conditions is determined different from the drained conditions. The lateral resistance of the foundation is specified in ISO as:
(8.46)
Where the undrained horizontal soil reaction factor . The undrained shear strength is the average value over the embedded depth. The sliding resistance in undrained soils is determined by:
82 Foundation design (8.47)
Where is the total foundation area and the undrained shear strength at base level. This sliding resistance is assumed equal to the sliding resistance of a grating, as the clay/clay interface will likely fail before the clay/foundation interface. Therefore, for undrained soils the only difference between the steel mud mat foundation and the grating foundation is the increased embedded depth of the grating, due to the increased height. This gives a result for the horizontal resistance of the foundations in undrained conditions as: (8.48)
8.5 Settlement
8.5.1 Immediate settlement of foundation The settlement of the newly suggested foundation will show more settlement than the original plate. This is due to the reduction in bearing area with respect to the flat mud mat. Due to the interference and the load transfer in the soil, the calculated settlement for the gratings will be greater than in practice, as the calculation method described in
DNV 30.4 is based on a rigid flat foundation and does not take the reduction factors into account [66]. The average settlement of a rigid mud mat foundation embedded in the soil at a depth may be determined by the formula in DNV:
( ) (8.49)
Where is the equivalent foundation diameter. The influence factors include the shape and
dimensions of the foundations and allow the use of the formula for the grating foundation. The factors may be determined using the charts of Janbu, figure 8.10 and figure 8.11.
Figure 8.10: Influence factor for settlements of embedded foundations [72]
8.5 Settlement 83
Figure 8.11: Influence factor for settlement of embedded foundations [72]
The modulus of the soil is determined by:
(8.50)
The Poisson’s ratio is
(8.51)
The constrained modulus is estimated by Janbu as:
(
)
(8.52)
Where is a reference stress ( ),
is the stress level of the soil and is a dimensionless modulus number and differs for various soils: Common modulus number for sand are: Loose: Medium:
Dense: And normally consolidated clays may be classified by: Soft: Medium: Stiff: The factor in equation (8.52) describes the reaction of the soil. The investigated clay is assumed to be fully elastic ( ) and the sand is assumed to behave elastic-plastic ( ). These values allow an estimation of the immediate settlement of the mud mat foundation and the grating foundation in sand and clay.
8.5.2 Consolidation settlement The long-term settlement of the foundations is mainly of interest for clays. In courser-grained soils, drainage takes place almost instantly with the change in stress level. The ventilated configuration of the grating foundation may provide improved drainage initially. However, when the clay is located within the grating perforations, providing similar vertical bearing capacity to steel mud mats, the possible gain in drainage is assumed negligible. Additionally, the reduction of structure weight by using a composite material may provide a small reduction in the long-term settlement of the entire structure.
84 Foundation design Concluding, the long-term settlement of the structure is not expected to alter, as a result of the different foundation. The consolidation settlement is therefore, mainly dependent on the soil properties. Changes in the structure foundation likely provide a benefit regarding the long-term settlement and are therefore not further investigated.
8.5.3 Objects below the seabed surface When placing a foundation on the seabed, the possibility exists that there are still rocks or small boulders located just below the surface. A Remotely Operated Vehicle (ROV) may remove these prior to installation. If the grating foundation is placed upon these boulders, the foundation will be subjected to an additional force. It is assumed that large boulders (> 630 mm) are located by the pre-lay survey and removed from the target location. The remaining boulders are expected to exert a load on the foundation. This is modelled by a patch load acting on the grating. The magnitude of the boulder load is equal to the required force to displace over the penetration depth of the foundation. Using the estimation from DNV for the settlement of a circular foundation:
( ) (8.53)
Assuming the load area is equal to the cross-section of the boulder and the displacement is equal to the penetrated depth , the load on the grating now follows from:
( )
(8.54)
For a maximum boulder size of 630 mm and a displacement of 0.05 m, this results in a point load on the foundation of 51 kN in clay and 174 kN in sand. This is determined using the methods described in section 9. The combination of this load with the in-service loading does not cause excessive stresses within the composite material.
8.6 Results
8.6.1 Assumptions Before determining the bearing capacity of the grating foundation in the two considered soils, several assumptions are required. These provide conservative assumptions and simplify the calculation methods by neglecting small contributions to the bearing resistance. To avoid unnecessarily complicating the analysis the eccentricity of the load is assumed equal to zero. This ensures the stability of the structure and allows the bearing capacities of both foundations to be determined for the entire foundation area. To help mitigate this overestimation of effective bearing area, the vertical load caused by the structure weight is doubled, before determining the required penetration depths. Furthermore, the stability of the structure is assumed similar or better than the original foundation. The grating foundation embeds more into the soil, thus improving the overturning resistance. Uniform soil properties are assumed over the area of the foundation. In reality, this is never true, as soil is anisotropic due to different compositions within the soil. To mitigate this, material factors are applied. The increased soil stress in drained soils as a result of the arching mechanism is assumed to also increase the vertical effective pressure at the grating tip area. This is therefore included in the calculation of the end bearing capacity. The grating will deflect under the load, as will be discussed in chapter 9, leading to a change in capacity at every location. This deflection is very small relative to the grating height, the grating is assumed infinitely stiff for the bearing capacity determination and this deflection is neglected. Considering the foundation in clay, the gratings will likely penetrate the entire height of the grating. The steel frame located above and to a lesser extent, the connection clamps then provide additional bearing area, reducing foundation penetration. This increase is neglected in the analysis. For the determination of the settlement, the influence factors based on the theory of Janbu are determined assuming the grating as a single bar. However, as the grating is consists of a network of such bars the geometry of the grating may provide additional resistance against settlement.
8.6 Results 85
8.6.2 Vertical bearing capacity sand The foundation capacity of the protection structure is expected to increase non-linearly for increasing embedment depth, up to the point where the soil within the grating perforations provides enough friction for it to move downwards, in line with the structure. This then provides equal resistance to a closed flat plate foundation. The required bearing capacity of the foundation is likely already reached, before the point that the soil forms plugs within the mesh. The determined plugging depth is therefore not required and full plugging may not occur. It is assumed that the arching effect increases the skin friction within each vent in the grating. Additionally, the internal friction angle and the lateral earth pressure coefficient are expected to be unaffected by the plugging behavior. As discussed earlier, the enhanced effective stress increases the end bearing resistance of the grating. For very large foundations, as is the case for offshore structures, the unenhanced resistance of the foundations at the edges is considered very small compared to the resistance of the foundation at the internal gratings. These contributions are therefore neglected. Furthermore, for any significant penetration depth in sand, the end bearing resistance is approximately 10 times larger than the generated side friction. Due to the small width of the bearing bars of the grating, the gravity term in the bearing capacity becomes very small as result from the relation between embedment depth and width of the bars. These simplifications lead to a much easier formula to describe the bearing capacity of the grating foundation. The shape factor will become equal to unity, due to small width of the grating bar and the internal area of the grating
nears the total grating area . The simplified equation can be written as:
( )
(
(
)
)
(8.55)
The vertical bearing capacity for the grate and mud mat foundations were investigated by the methods provided by API and DNV. For sand, both theories predict very similar penetrations for the grating foundation to provide the required bearing capacity. This results in a required penetration of , see figure 8.12.
Figure 8.12: Vertical bearing capacity in drained soil
8.6.3 Vertical bearing capacity in clay The bearing capacity of the grating foundation is not enhanced by the arching effect in clay. However, the increase in skin friction for increasing penetration significantly increases the bearing capacity of the foundation. The required penetration to attain sufficient bearing capacity in clay may be determined from figure 8.13. In this figure, the grating capacity, based on the API and DNV methods is displayed. As the grating capacities are determined using different
0
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50000
0 0.02 0.04 0.06 0.08 0.1
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tica
l bea
rin
g re
sist
ance
[kN
]
Penetration depth [m]
Vertical bearing capacity in drained soils
Vertical bearingcapacity grating
Vertical bearingcapacity grating noarching effect
Factored vertical loadon foundation
86 Foundation design methods, the required penetrations are also different. The API method estimates a required penetration of and the DNV method estimates the required penetration at .
Figure 8.13: Vertical bearing capacity in undrained soil
8.6.4 Horizontal bearing capacity Inserting the design parameters in the equations for the horizontal resistance one obtains the horizontal bearing capacity for the different foundations. As stated earlier, the effect of the skirts is omitted in order to determine the relative sliding resistance. Additionally, the effect of the steel base frame is not included as this will be similar for both foundations. For drained soils, the steel mud mat foundation is assumed fully embedded in the soil and sliding area is assumed equal to the foundation area. For the grating foundation, an embedded depth of 0.05 m is assumed (half of the height) and the projected area of the foundation is again 158 m2. For any significant penetration, the friction resistance of the soil/soil interface is much smaller; therefore, this additional force is included in the determination of the horizontal capacity. For undrained soils, the horizontal bearing capacities of both foundations are expected to be very similar. Only the increased embedded depth of the grating foundation provides additional capacity. The horizontal capacity of the
foundations, without the skirt resistance is displayed in table 8.3.
Table 8.3: Horizontal sliding resistance foundations
Soil Mud mat Grating Unit
Sand 1476 1700 kN
Clay 674 680 kN
These loads are still quite larger than the expected horizontal loads for the reference structure at Laggan. The design horizontal resistance for this structure consisted of fishing loads and piping expansion and contraction, amounting to 525 kN.
8.6.5 Settlement The immediate settlement of the foundation follows from equation (8.49). Assuming the ratio of the foundation dimensions is , and the depth ratio is equal to the influence factors follow from figure 8.10:
The distributed load is the resulting bearing pressure from the structure weight. The factor in equation
(5.48) is the equivalent diameter of the foundation and is determined by assuming the foundation area as a circular foundation with equivalent area. The soil specific factors νsoil, m) are used to calculate the settlement, see table 8.4.
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0 0.05 0.1 0.15 0.2 0.25 0.3
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l bea
rin
g re
sist
ance
[kN
]
Penetration depth [m]
Vertical bearing capacity grating in undrained soils
Vertical bearingcapacity grating DNV
Vertical bearingcapacity grating API
Vertical bearingcapacity flat plate
Factored vertical loadon foundation
8.7 Sensitivity analysis 87
Table 8.4: Soil specific parameters
Soil Poisson’s ratio ν Modulus number m Unit
Sand 0.2 250 -
Clay 0.3 20 -
This results in an average settlement of a flat foundation:
The grating foundation is likely to settle more, as the effective vertical stress and the open area are increased. A
single bar of the grating is used to determine the new geometrical influence factors. This bar is 0.05 m wide, has a thickness of 6 mm and a height of 0.1 m. From figure 8.10 the factors are determined:
The equivalent diameter of the bearing area of the grating is used to determine the corresponding pressure on the grating.. The distributed load on the grating is considerably higher than for to the mud mat solution. The vertical effective stress just below the grating foundation is expected to be similar to the stress below the flat plates. The load is quickly redistributed over the soil, resulting in a similar average effective stress. The other factors used in the settlement equation are the same for both foundations. The new settlements are:
The settlement of the grating foundation sees quite a significant increase from the original flat plate foundation. As the surrounding soil also settles, this may not cause immediate problems. The attached equipment will see a similar settlement and will keep the relative motion to a minimum.
8.7 Sensitivity analysis The sensitivity of the gratings as a foundation is determined for varying several parameters. As soil properties are
usually quite uncertain and anisotropic, this may help design a safe foundation. The sensitivities are determined by changing the parameters by ±10 %. First, the sensitivity of the vertical boundary capacity of the gratings is checked. This is done by determining the capacity of the gratings in drained and undrained soils assuming a penetration of 0.1 m. the vertical bearing capacity is determined for the drained soil by varying the projected area, the bar width and internal friction angle of the soil. As the bar width varies, the ratio between bar distance and width changes. The results are shown in table 8.5 and
table 8.6.
Table 8.5: Sensitivity vertical bearing capacity in sand at penetration of 0.1 m
Sensitivity vertical bearing capacity sand (0.1 m)
Description Symbol -10 % +10 %
Projected area Ap -24 % +39 %
Bar width tgrate -11 % +11 %
Internal friction angle φ' -4 % +2 %
Table 8.6: Sensitivity vertical bearing capacity in clay at penetration of 0.1 m
Sensitivity vertical bearing capacity clay (0.1 m)
Description Symbol -10 % +10 %
Projected area Ap -8 % +10 %
Bar width tgrate -2 % +2 %
Lower bound cone capacity qc -1 % +1 %
This shows that changing the dimensions of the gratings has a large influence on the maximum bearing capacity of the foundation. This is less pronounced in clays, as the bearing capacity largely depends on the frictional resistance.
88 Foundation design A more telling property of the foundation is the penetration that is required to obtain similar vertical bearing capacity to a flat plate. The penetration is calculated for the same parameters as the vertical bearing capacity. Varying the properties is compared with original required penetration depth calculated in sections 8.3.1.3 and 8.4.1.3. The sensitivities are indicated in table 8.7 and table 8.8.
Table 8.7: Sensitivity required penetration depth in sand
Sensitivity required penetration depth sand
Description Symbol -10 % +10 %
Projected area Ap +10 % -10 %
Bar width tgrate +7 % -6 % Internal friction angle φ' +1 % -1 %
Table 8.8: Sensitivity required penetration depth in clay
Sensitivity required penetration depth clay
Description Symbol -10 % +10 %
Projected area Ap +12 % -12 %
Bar width tgrate +3 % -3 %
Lower bound cone capacity qc +1 % -1 %
This indicates that additional horizontal projected area reduces the required penetration depth. The increased bar width for constant spacing, provides less improvement. The immediate settlement of the foundation is expected to be mostly dependent on the projected area, the applied load and the modulus of the soil. The sensitivity of the settlement has been listed in table 8.9 and table 8.10.
Table 8.9: Sensitivity immediate settlement in sand
Sensitivity immediate settlement sand
Description Symbol -10 % +10 % Projected area Ap +5 % -5 % Vertical load Fv -5 % +5 % Constrained modulus M +11 % -9 %
Table 8.10: Sensitivity immediate settlement in clay
Sensitivity immediate settlement clay
Description Symbol -10 % +10 %
Projected area Ap +5 % -5 % Vertical load Fv -10 % +10 % Constrained modulus M +11 % -9 %
The horizontal resistance of the foundation in reality is dominated by the height of the skirts. The sensitivity of the horizontal bearing capacity of the grating foundation without skirts depends on the projected area of the foundation and several other factors shown in table 8.11 and table 8.12.
Table 8.11: Sensitivity horizontal bearing capacity in sand
Sensitivity horizontal bearing capacity sand
Description Symbol -10 % +10 %
Projected area Ap +0.4 % -0.3 %
Bar width tgrate -0.3 % +0.5 %
Internal friction angle φ' -11 % +11 %
Vertical load Fv -9 % +9 %
Table 8.12: Sensitivity horizontal bearing capacity in clay
Sensitivity horizontal bearing capacity clay
Description Symbol -10 % +10 %
Undrained shear strength Su -10 % +10 %
The sliding resistance in clay is determined as a product of the undrained shear strength, giving trivial results for the sensitivity.
8.8 Discussion 89
8.8 Discussion
8.8.1 Bearing capacity Influence of skin friction on penetration resistance. The dominant parts providing the bearing capacity of the foundation are different for sands and clays. The ratio between the base resistance and the total bearing resistance is plotted in figure 8.14. This shows that the contribution of the skin friction to the total bearing capacity in sand is far less than the contribution of the base resistance. It may be determined that the influence of end bearing resistance is a factor 10 larger for relevant penetrations. In clays this ratio is different due the cohesion properties of the clay. For a grating penetration of more than 0.05 m in clay, the skin friction becomes the dominant contribution to the total bearing capacity.
Figure 8.14: Base contribution to total bearing capacity of foundation
Following the large sensitivity of the projected area on the required penetration of the grating (table 8.5), the influence of different mesh size is further investigated. The mesh is assumed to remain square and the thickness is constant, but the spacing ratio is varied from 2 to 12. The spacing ratio is defined as:
(8.56)
When plotting the required penetration of the grating foundation against different mesh sizes, the relationship of increasing penetration for increased mesh dimensions is displayed in figure 8.15. As the mesh dimensions further increase, the total projected area decreases and more penetration is required to obtain similar bearing capacity. Additionally the divergence between sand and clay is expected. The sandy soil provides a better support for the foundation, resulting in less penetration. For increasing mesh dimensions, the two calculation methods for clay converge, implying that the skin friction further increases in importance for the total vertical bearing capacity. This is also seen in figure 8.14.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Bas
e b
eari
ng
cap
acit
y ra
tio
[%]
Penetration depth [m]
Base contribution to total bearing capacity of grating foundation
Sand
Clay API method
Clay DNV method
90 Foundation design
Figure 8.15: Required penetration depth against spacing ratio
The design of a grating seems dependent on the distance between two adjacent bars, as the penetration shows a near linear increase for increasing spacing. By normalizing this penetration to the actual distance ( )
between adjacent bars, a converging relationship is revealed, see figure 8.16. The two different values for clay converge to the same value, as the bearing capacity due to the base area becomes negligible. The normalized penetration for sand also levels out for increasing mesh sizes, as the reduction in bearing area becomes smaller for increasing spacing distance.
Figure 8.16: Normalized required penetration depth to spacing ratio
Assuming the exact soil properties at the target location are known and the behavior of the grating foundation in the soil can be perfectly modelled, the height of the grating foundation can be equal to the required penetration depth. A higher spacing ratio indicates a lower projected area of the foundation, therefore requiring more penetrated depth and grating height for the bearing capacity. This way a minimum material volume and cost may be determined.
Figure 8.17 indicates that the lowest foundation weight is for small spacing ratios. If this spacing ratio becomes too small, reduction in added mass is lost and the installation becomes more difficult again. If the spacing ratio is too large, the grating loses its lateral stability and may deform and the material may be damaged. Additionally, a lighter foundation also improves installability of the subsea structure. Therefore, an optimum between the difficulty of installation, the cost and the strength of the foundation is desired.
0
0.05
0.1
0.15
0.2
0.25
2 3 4 5 6 7 8 9 10 11 12
Pen
etra
tio
n d
epth
[m
]
Spacing ratio (s/t)
Required penetration depths grating for gratings
Sand
Clay API method
Clay DNV method
0
1
2
3
4
5
6
7
8
2 3 4 5 6 7 8 9 10 11 12
No
rmal
ized
pen
etra
tio
n d
epth
(z/
(s-t
))
Spacing ratio (s/t)
Normalized required penetration depth for gratings
Sand
Clay API method
Clay DNV method
8.8 Discussion 91
Figure 8.17: Required grating weight for penetrated depth to spacing ratio
The structures investigated by Bransby et al. and Koopman are grillage foundations. The grating foundation however, shows an increased tendency to arch in sand, as the soil is confined in two principal directions instead of one for the grillage foundation. This means that the grating foundation provides improved bearing capacity for the same bar spacing. This improved bearing capacity correlates to the increase in bearing area. The results plotted in figure 8.18 indicate that to achieve the same bearing capacity, the grillage and grating foundations require roughly similar projected area. For smaller projected areas, the two clay solutions converge to similar values. This is caused by the increased dependence on the skin friction for larger penetrations.
Figure 8.18: Required penetration depth for grillage and grating foundations
As discussed in section 8.2.2, the interface friction between the composite and the soil is larger than the interface friction between steel and the soil. The friction coefficient may be further improved by applying a grit surface on the bottom of the grating, but this results in limited improvement in bearing capacity, as shown in section 8.7. The interference effect is not expected to provide a substantial contribution to the bearing capacity of the grating, as the spacing between the grating bars is too large to provide additional bearing capacity. The square perforation holes may see interference at the corners, as the passive zones overlap and increase the effective stress in the soil. This effect however, is not investigated for the considered foundations.
0
10000
20000
30000
40000
50000
60000
2 3 4 5 6 7 8 9 10 11 12
Fou
nd
atio
n w
eigh
t [k
g]
Spacing ratio (s/t)
Required weight of the grating foundation
Sand
Clay API method
Clay DNV method
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 100 200 300 400 500 600
Pen
etra
tio
n d
epth
[m
]
Horizontal projected area [m2]
Required penetration depth related to horizontal projected area
Grating sand
Grating clay API
Grating clay DNV
Grillage sand
Grillage clay API
Grillage clay DNV
92 Foundation design The arching effect is shown to provide a positive effect on the bearing capacity of a grating in sandy soils, but the quantitative effect in clays is unclear. Further research may provide a basis to design for this effect. The required penetration of the grating in sand to generate sufficient bearing capacity for a stable footing is calculated using the methods from DNV and API. The two calculation methods show similar results in sand. The
arching effect in sand allows the bearing capacity of the grating to quickly attain sufficient bearing resistance for the factored vertical load. The bearing capacity in sand is mainly provided by the horizontal projected area of the gratings and the discussed arching effect. The frictional contribution is small. It is shown that the arching effect in gratings in theory is more prevalent than the effect in grillage foundations, but for equal open area of the foundation, the larger distance between adjacent bars effectively negates this benefit. This means that the grillage configuration has a better aptitude of improving the bearing capacity by arching. Despite on these findings, grating foundations are still the preferred solution for a composite shallow foundations, as it provides improved bi-directional load transfer, lateral buckling support and improved connectability. The generation of bearing capacity of the grating penetration in clay is more complicated as the extent of the arching mechanism in clay is uncertain. Koopman’s experiments revealed it did have a minor beneficial effect on the bearing capacity of grill foundations, but not enough to provide a quantifiable theory. The bearing capacity resulting from arching in clay is likely reduced due to remolding of the clay along the grill sides. For this reason, the arching is not taken into account while determining the bearing capacity of the foundation in undrained soils. The vertical bearing capacity of the gratings in clays is mainly generated by the penetrating skin area. As the foundation penetrates further into the soil, it reaches the equivalent bearing capacity of plate foundation in clay. The clay will stop generating additional friction within the perforations and the structure as a whole will penetrate further into the soil. At this point the perforations will have effectively plugged and the foundation will only generate additional bearing capacity corresponding to the increase of an equivalent plate foundation. The grating foundation at this point may still generate additional capacity due to the roughness of the grating configuration, compared to a flat plate. Additionally, the DNV and API theories for the bearing capacity in clay do not fully agree with each other. DNV calculates the capacity using the values obtained by a cone penetration test, whereas API uses the undrained shear strength of clay to calculate it. The frictional area increases for increasing penetration of the gratings, resulting that the bearing capacity reaches required penetration relatively fast. The result of the investigation was that the penetration in clay is very dependent on the friction generated along the sides of the gratings, and for the penetration in sand, this effect is negligible. This may allow designing the foundation based on the type of soil at the desired location. For clay soils this indicates that the grillage configuration provide a better solution, providing more side area for the same amount of material, see figure 8.19. The grating configuration is more efficient for a sandy soil, providing a more stable and stronger structure.
Figure 8.19: Side area length against projected area of foundations
0
20000
40000
60000
80000
100000
120000
0 100 200 300 400 500 600
Pen
etra
tin
g sk
in a
rea
[m/m
]
Horizontal projected area [m2]
Penetrating skin area vs horizontal projected area of foundations
Grating foundation
Grillage foundation
8.9 Conclusion 93
8.8.2 Horizontal bearing capacity The horizontal bearing capacity is calculated for the two types of foundations. The horizontal capacity of the skirts surrounding the foundation were omitted in order to provide an effective comparison between the two foundations. This showed that the grating foundation provides additional capacity for both drained and undrained soils. This effect is more dominant in drained soils, as the additional friction of the soil within the mesh of the grating provides extra resistance. Introduction of the skirts however, will again reduce the difference between the two foundations. These results support the findings of Knappet et al. in which the capacity of a grillage foundation was investigated. An improved interface friction angle attained by using a composite material may further improve the lateral resistance of the foundation.
8.8.3 Settlement The immediate settlement of the original mud mat foundation and the newly designed grating foundation are investigated. This showed that the settlement of the grating foundation increases by a significant amount for both soils, due to the more ventilated foundation and the higher local pressure on the material. This increased compaction of the soil may further increase the soil stress beneath the foundation and result in a lower penetration depth. This increased immediate settlement is difficult to prevent and should be included in the design of the structure.
8.9 Conclusion Considering the foundation design of a grating foundation, it is shown that the mesh configuration provides several benefits over the original mud mat foundation and the grillage foundation discussed by Bransby and Koopman. The bearing capacity of the foundation in sand is improved by the arching mechanism, but in clay this effect is uncertain. The immediate settlement of the foundation sand is increased compared with the original mud mat foundation with even further settlement in clays. The horizontal capacity of a grating foundation shows improved properties over the original mud mat solution.
The gratings therefore provide an acceptable replacement for the solid mud mat under combined vertical and horizontal loading in drained soils. The behavior of the gratings is clays requires additional investigation.
9. Grating deformation
9.1 Introduction
9.1.1 Load cases The grating foundation is subjected to many different loads before the structure is located on the seabed. To determine the internal stresses of the material and the loads on the supports, the deformation of the new foundation is investigated. Two different load conditions are considered to determine the deformed shape of a single grating. The first is simply the in-situ loading of the foundation, where the gratings rests on the clay and the foundation is subjected to the weight of the subsea structure. The structure is subjected to this load for its entire lifetime on the seabed. To investigate the extent of deformation in clay, the soil deformation is first investigated for an infinitely stiff plate. This allows a comparison with the flexible grating foundation. The second load case occurs during the lifting of the structure. It is assumed that a dropped object falls on the foundation as it is prepared for the lift through the splash zone. This accidental loading exerts a dynamic load on the foundation, causing a high load for a short duration. These load cases are assumed to be the extreme loadings the composite will experience during its lifetime. It is therefore important to determine the behavior of the grating under these conditions. This will provide an indication for the loads in the supports and allows the connection details to be designed. The analytical process of determining the grating deformations and forces is first explained, before analyzing the performance in the different load cases.
9.1.2 Plate theory The deflection of the orthotropic composite grating may be modelled with the use of plate theory. Lagrange first properly suggested the general differential equation for plates. He corrected the differential equation proposed by Germain by adding the missing middle term. The first theory that successfully presented the bending of plates was proposed by Navier, who included the thickness of the plate within the differential equation by the flexural rigidity of the plate . He was also the first to introduce an ‘exact’ method of solving the differential equation by the use of Fourier trigonometric series. Kirchhoff provided the two basic assumptions for the bending in of thin plates. Kirchhoff’s theory states that the transverse shear and transverse normal effects, including shear deformations, are negligible. Furthermore, he showed that only two boundary conditions exist on a plate edge. This implies that the bending of a plate is entirely the result of bending and in-plane stretching of the plate. This plate theorem is termed the classical plate theory (or CPT) [73]. The first-order shear deformation theory (or FSDT) will be briefly assessed in section 9.7, to provide an estimate for the magnitude of the additional deflection on plate due to shear deformation. This theorem, often attributed to Mindlin and Reissner, extends the CPT by including the transverse shear stresses.
9.2 The Navier solution
9.2.1 Plate mechanics The differential equation for a plate results from the equilibrium of a small element. At the boundary, it is assumed that the edges of the plate are free to move in the plane of the plate. Therefore, the reactive forces at the edges are normal to the middle plane and the strains within the middle plane may be neglected during bending. The forces acting on the plate may be determined by assuming equilibrium on a small element of the plate, see figure 9.1.
96 Grating deformation
Figure 9.1: Moments and forces acting on an element [74]
The shear forces and are determined by the summation of shear stress along the - and -plane.
∫
∫
(9.1)
From equilibrium of the forces acting on the z-axis follows, where is the load intensity acting on the element:
(9.2)
This simplifies to:
(9.3)
Likewise, the equilibrium of the forces and moments acting on the -axis:
(9.4)
This simplifies to:
(9.5)
In the same manner, balancing the terms with respect to the -axis:
(9.6)
Since the forces in the - and -directions are not present and there are no moments acting along the z-axis, equations (9.3), (9.5) and (9.6) completely define the equilibrium of the element. By rewriting the shear forces, the following is obtained:
(9.7)
Substitution into equation (9.3) yields:
(9.8)
Which for becomes:
9.2 The Navier solution 97
(9.9)
The plate rigidity is the flexural stiffness of the plate:
( ) (9.10)
Where = = For the bending of a plate, the moments may be defined as a factor of the plate rigidity and the second derivative of the deflection. Here the quantity replaces the factor in the bending of Euler-Bernoulli beam equations. The moments in the plate may now be determined.
(
) (9.11)
(
) (9.12)
And the twisting moments:
( )
(9.13)
By substituting this into equation (9.9), the governing differential equation for the bending of a plate is derived:
(9.14)
This is the differential equation for the deflections for a thin plate bending analysis based on Kirchhoff’s assumptions. Lagrange obtained this equation in 1811. To find the deflection of the plate at any given point, a solution to the differential equation is required. For a simply supported plate with dimensions and (figure 9.2), the boundary conditions for the edges of the plate may be defined. For simply supported edges, the deflections and the bending moments are equal to zero.
Figure 9.2: Coordinate system of a plate
98 Grating deformation The boundary conditions are defined as:
( ) ( )
(9.15)
( ) ( )
(9.16)
9.2.2 General solution The solution to this problem for an arbitrary load may be determined by using the double Fourier series, first solved
by Navier. This solution uses the notion that any load distribution may be rewritten by the sum of infinite number of sines and cosines. Therefore, the deflection surface ( ) and the distributed load surface ( ) are sought for in the form of an
infinite Fourier series:
( ) ∑ ∑
(9.17)
( ) ∑ ∑
(9.18)
The coefficients and are still to be determined. The suggested equation for the deflection of the surface
satisfies the boundary conditions, which can be confirmed by entering the limits into the equation. To find the
coefficient of the load configuration , the equation ( ) is multiplied on both sides by
and
integrated twice between the limits (0 to a) and (0 to b). Simplifying and rewriting the equations results in an expression:
∫∫ ( )
(9.19)
Now by substituting the Fourier series for the deflection into the governing differential equation yields the follow equation:
∑ ∑{ [(
)
(
)
(
)
(
)
]
}
(9.20)
The above equation must be true for all values of and . Therefore, the term within the brackets must be equal to zero, leading to a definition for the coefficient :
[(
)
( ) ] (9.21)
The deflection equation follows by substituting this equation into the Fourier series for the deflection:
( )
∑ ∑
[(
)
( )
]
(9.22)
By substituting in the solution, one may determine the deflection of the plate under a particular kind of load. For example, a constant distributed load over the plate, ( ) results in a value for :
( )( ) (9.23)
9.3 Elastic foundation 99
For a patch load distributed load at ξ, η) over a small area (u, v), see figure 9.3, this becomes:
(9.24)
Figure 9.3: Dimensions patch load [73]
Reducing the area to zero (u, v → 0), effectively creates a point load and the term becomes:
(9.25)
These solutions may be combined to find the solution to a combination of load configurations
9.3 Elastic foundation
9.3.1 Mechanics As the structure lands on the seafloor, the reaction of the subgrade acts on the grating foundation. For a plate on an elastic foundation, the pressure on the plate results from the elastic reaction of the subgrade. This reaction is assumed linearly proportional to the deflection at that point.
Figure 9.4: Schematic representation of plate pressed into soil at the edges [74]
For the considered grating foundation, the outer edges of the plate are pressed into the soil. Therefore the deflection curvature resulting from the subgrade reaction is actually upwards, see figure 9.4. The reaction pressure on the plate may then be written as ( ). Including this term in the governing differential equation (9.14) results in:
(9.26)
100 Grating deformation Where = = =
The modulus k is dependent on the soil properties and the foundation dimensions. The values for sand and clay may be approximated by 80,000 and 40,000 , respectively [75]. The assumption is made that loads of the protection structure and the FLET itself are transferred via the frame and the steel beams underneath the structure to the grating foundation. The gratings are not fully flexible, leading to a non-uniform contact pressure between the soil and the foundations, see figure 9.6. The maximum contact pressure is
therefore located near the edges, where the subgrade reaction maximum. The exact contact pressure distribution is difficult to predict and to mitigate this, the bearing pressure is assumed to produce a resulting contact pressure at twice the actual load . This prevents underestimating the deformation and stresses within the materials. As the frame on the base of the structure initially takes the load, the edges of the gratings are pushed further into the soil, resulting in an additional upward distributed load on the gratings ( ).
Figure 9.5: Contact pressure and deflection profile flexible footing
Figure 9.6: Contact pressure and deflection profile rigid footing [76]
The vertical stress in the soil reduces with increasing depth and distance from the plate center, see figure 9.7. The resulting pressure profile on the rigid plate indicates that grating deforms more near the supports and only slight deformation is shown in the middle of the grating.
9.4 Orthotropic plate 101
Figure 9.7: Comparison of vertical stress distributions for flexible or rigid slabs [77]
9.3.2 General solution Substitution of the Fourier series for ( ) and ( ) into equation (9.22) results in the solution for the deflection
of a plate on an elastic foundation:
( ) ∑ ∑
[(
)
( )
]
(9.27)
The term kw0 may be regarded as a distributed load and is incorporated into the coefficient. As an example, the deflection of a simply supported plate subjected to a distributed load ( ) results in:
( ) ∑ ∑ ( )
( )( )
[(
)
( )
]
(9.28)
9.4 Orthotropic plate
9.4.1 Material properties
9.4.1.1 Isotropic material The theory above assumes that the plate material is isotropic. This suggests that the material properties at a point
are equal in all directions. If an isotropic material is loaded at a point, the material will react similar in every direction. The deformations are thus mainly dependent on two properties, the modulus and the Poisson’s ratio . The most common structural materials to belong to this category are steel and aluminum.
9.4.1.2 Anisotropic material Certain materials have directional dependency on their properties. Materials that behave like this are termed anisotropic. If these anisotropic materials are loaded at a point, the material may deform differently depending on the load direction. Common materials which show this behavior are wood and fiber reinforced plastics. These materials contain natural anisotropy. The anisotropy is the result of the material they consist of. Another form of anisotropy is structural anisotropy. These are materials which show anisotropic behavior, not due to the material they are composed of, but due to the shape or form of the body. For example, corrugated and stiffened plates are good examples, as they show improved properties in the direction of the stiffeners.
102 Grating deformation
9.4.1.3 Orthotropic material Anisotropic materials showing three perpendicular planes of symmetry of its properties are called orthotropic. Orthotropic materials are seen quite often in practice, for instance: reinforced concrete, gridworks and reinforced plates. The composite gratings are considered both natural and structurally orthotropic. The deflection of an orthotropic plate is derived in the section below. As the elastic properties of the orthotropic plate are dependent on the direction, the elastic properties are different in all three directions. The flexural rigidity of the orthotropic plate is therefore also different for the principal directions.
9.4.2 General solution The flexural and torsional rigidities of an orthotropic plate are given as:
(9.29)
(9.30)
And the shear rigidity is:
(9.31)
Where , , , , are the moduli of elasticity and Poisson’s ratios in the and directions and is the shear
modulus.
Concluding from
, that , the shear force expressions may be rewritten:
(
) (9.32)
(
) (9.33)
Where =
The governing differential equation for an orthotropic plate becomes:
( ) (9.34)
With the general solution:
( ) ∑ ∑
(
)
(
)
(
)
(9.35)
9.4.3 Grating parameters As the composite grating is a gridwork configuration, see figure 9.8, the flexural and torsional rigidities differ from the conventional orthotropic plate. The grating consists of two systems of parallel beams which are rigidly connected at their point of intersection. The beams are simply supported at their ends and the flexural rigidity of a single beam is converted into plate rigidity by dividing it by the distance of two parallel beams.
9.4 Orthotropic plate 103
Figure 9.8: Grating parameters
Where = = =
The second moment of inertia of the rectangular bars in the - and -direction follow from:
(9.36)
Using the moduli of the material and the grating rigidity in the - and -direction is determined:
(9.37)
Due to the grating shape: (9.38)
And the torsional rigidity of the grating becomes:
(
) (9.39)
Where and are the torsional rigidity of the beams: ( ) ( ) (9.40)
Where:
(9.41)
As the above-explained characteristics all apply to the considered composite grating, these effects are required to find the solution for the deflection of the plate. The governing differential equation for the naturally (composite material) and structurally (gridwork) orthotropic plate on an elastic foundation now follows:
104 Grating deformation
( ) (9.42)
The flexural and torsional rigidities are described in equations (9.37) and (9.39). By inserting the Fourier series for ( ) and ( ), and making sure the coefficient is equal to 0 for all and , the solution for the differential
equation becomes:
( ) ∑ ∑
(
)
(
)
(
)
(9.43)
9.5 Membrane stresses If the gratings are connected to the steel frame, the edges may rotate, but horizontal movement of the gratings is restricted. Bending the gratings causes an extension of the grating bars. This strain in the material generates tensile stresses, which act in addition to the bending stresses discussed in section 9.6.1. The maximum membrane stresses within the grating plate are located in the center bar for both principal directions. The membrane forces may be determined by equating the strain of the center bar to the strain by Hooke’s law. The
strain in the principal plate directions are related to the deflection by equation (9.44) [78].
∫ (
)
∫(
)
(9.44)
Hooke’s law ) may be rewritten for the grating configuration and dimensions, resulting in:
(9.45)
Due to the grating configuration, the membrane stresses in other directions and the mutual interaction of the principal directions are expected to be low. These are therefore presumed independent from one another. The second part of Hooke’s law can therefore be neglected, which allows the membrane forces to be directly determined in the principal directions by equating equations (9.44) and (9.45). The strain in the material is expected to be higher in the shorter dimension, as the plate deflects over a shorter distance, resulting a larger extension. Introducing the membrane forces in the differential equation results in equation (9.46) [74].
( )
(9.46)
This changes the general solution into:
( ) ∑ ∑
(
)
(
)
(
)
(
)
(
)
(9.47) To determine the new deflection, the membrane forces are initially omitted. The initial deflection then causes a strain from which the membrane forces follow. The determined membrane forces are included in the deflection series, equation (9.47), and the resistance against bending increases, reducing the deflection of the grating. This lower deflection decreases the membrane stresses, again increasing the deflection of the grating. By iteratively repeating this process, the deflection and the membrane forces quickly diminish to an equilibrium. Due to the relatively low initial deflection, considering the other dimensions, the membrane forces are low in comparison to the bending forces. Converting the membrane forces to a tensile stress within the individual bars, provides the maximum tensile stresses resulting from the horizontal extension of the grating. The strain of the bars reduces to zero towards the supports. Therefore, by including the maximum membrane forces
in the differential equation for the deflection, the reduction in deflection is overestimated. However, including this
9.6 Internal forces 105
reduction in membrane forces in the solution, needlessly complicates the solution and significantly increases the computation time. To mitigate this underestimation of the deflection, the maximum membrane stresses are assumed constant over the entire grating. Additionally, to avoid a reduction in flexural stresses, the increased rigidity due to membrane forces is not included when determining the maximum bending moments.
The axial stresses in the grating bars due to the membrane forces result from:
(9.48)
9.6 Internal forces
9.6.1 Section forces Now that the general deflection solution for the designed grating has been determined, the sectional forces within the parallel beams may be determined. The bending moments may be derived from the constitutive relations for the bending of a plate, equations (9.11) and (9.12). By adapting these relations for the orthotropic material, the bending moments with respect to the - and -axis result in [74]:
[
] (9.49)
[
] (9.50)
Considering equation (9.38) for an orthotropic plate the equations reduce to:
(9.51)
(9.52)
The twisting moments in the bars of the grating are determined by:
(9.53)
(9.54)
And the shear forces within the bars are:
(
) (9.55)
(
) (9.56)
To determine the sectional forces within the grating bars, these equations can be adjusted to determine the forces within the grating. The maximum moments and shear forces within the system of beams may be assumed to be parabolic between adjacent intersections. By first locating the coordinate ( , ) of the maximum absolute value of the
section forces, one may use the parabolic correlation between preceding and succeeding intersection points to approximate the forces at the node in question. The shaded area of figure 9.9 may be assigned to investigated node.
106 Grating deformation
Figure 9.9: Moment distribution between successive nodes
The maximum bending moments in the principal directions are most likely near the application point of the load. If a patch load is applied at ( ), the maximum bending moments at this point may be approximated by:
[(
( )
) (
( )
) (
( )
)] (9.57)
[(
( )
) (
( )
) (
( )
)] (9.58)
The maximum values of the twisting moments are located at the grating corners. This value is determined analogously to the bending moments:
[(
( )
) (
( )
) (
( )
)] (9.59)
[(
( )
) (
( )
) (
( )
)] (9.60)
The maximum shear forces are located at the application point of a patch load (depending on the magnitude with respect to the distributed load). For a distributed load, the maximum values are located at the supports.
[(
( )
) (
( )
) (
( )
)]
[(
( )
) (
( )
) (
( )
)]
(9.61)
[(
( )
) (
( )
) (
( )
)]
[(
( )
) (
( )
) (
( )
)]
(9.62)
The stress components resulting from the maximum bending and twisting moments are the design stresses which the composite material needs to resist to avoid damage. The resulting in-plane stresses vary linearly over the plate thickness and are maximum in the outer fibers of the element, see figure 9.10.
9.6 Internal forces 107
The critical bending stresses within the bars in the - and -direction:
Figure 9.10: Stress profile over height for bending moments
(9.63)
(9.64)
And the stress due to the twisting moments:
Figure 9.11: Stress profile over height for twisting moments
(9.65)
(9.66)
The shear stresses result from the shear forces and are distributed according parabolic law over the cross-section. The critical shear stress is therefore located in the middle plane of the bars:
Figure 9.12: Stress profile over height for shear forces
(9.67)
(9.68)
By combining the bending, torsional and membrane stresses, the maximum stresses within the fibers are determined. The bending and torsional stresses vary linearly over the cross-section of the plate, and its neutral line is located at the middle. The membrane stresses are assumed to provide a constant tensile stress over the height. Therefore, the compressive stresses due to bending are partly compensated by the constant tensile stress of the extension of the material. The maximum stress is located at the outer fibers where tensile stresses are combined. The critical stresses occur in the direction of the shortest plate dimension.
(9.69)
These stresses are not maximum in the same locations, but as the torsional stresses are located near the corners and are rather small, the maximum stress within the fibers may be assumed as the sum of the stress generated by the membrane stresses and the bending stresses. By assuming constant membrane forces over the entire grating, the maximum tensile stress is located where the bending moment is maximum.
108 Grating deformation
9.6.2 Reaction forces The reactive forces at the edges of the plate may be determined from the shear forces and the twisting moments at the edge. The bending moments are zero, as the edges are assumed simply supported:
(
)
(9.70)
(
)
(9.71)
Total resultant of the external load carried by the plate:
∫∫ ( )
(9.72)
This load acts in the positive -direction (downward). The resultant of the transverse effective shear forces acting on
the plate edges follows from:
∫ | ( )| | ( )|
∫ [| ( )| | ( )|]
(9.73)
This reaction of the supports acts in the negative -direction (upwards). These loads are balanced by the corner forces. By subjecting a rectangular plate to a load, corner forces are generated which act upwards. This is caused by
the effect that the corners of a uniformly loaded rectangular plate have the tendency to rise, but this is restricted by the supports. The corner force is given by: | | (9.74)
The total load of the corner forces is then:
(9.75) This results in equilibrium of the forces on the plate: (9.76)
The forces on the foundation do not fully transfer to the soil via the gratings, but a part is also directly transferred to the soil by the steel frame. Additionally, the soil below the grating changes the stiffness of the system and the load distribution within the gratings. The elastic reaction resulting from the soil is dependent on the subgrade modulus and the deflection of the grating at any point.
9.7 Shear deformation The composite material is quite sensitive to shear deformation and therefore this effect is investigated. Expanding the CPT to first order shear deformation theory (FSDT) allows the additional deflection caused by the shear deformation to be included in the differential equation. By evaluating the first order deformation of the plate, an estimate is provided for this additional deflection. The deflection solution for the classical plate theory (CPT) is described in sections 9.2 to 9.4. This value will now be denoted as ( ) [79, 80].
A definition for the Marcus moment for the plate may be given by: ( ) (9.77) This is equal for both theories due to the simply supported boundaries. This formula is transformed to its orthotropic equivalent:
9.8 Plate vibration 109
(
) (9.78)
The first-order plate deflection (FSDT), including the shear deformation, may now be defined as:
( ) ( )
(9.79)
Where ( ) =
The shear correction factor and is the shear modulus of the material. Solving the deflection for a simply supported orthotropic plate, subjected to an arbitrary load ( ) results in:
( ) ∑ ∑
(
)
(
)
(
)
(9.80)
Where
( (
)
(
) (
)
) (9.81)
And the load coefficient is still defined as the Fourier series expansion of ( ):
∫∫ ( )
(9.82)
Using equation (9.80) this is analyzed for an evenly distributed load ( ) . This results in an additional shear
deflection of the gratings in the order of 2.5% of the CPT deflection. This increase is relatively small with respect to the plate thickness. Including the elastic foundation in the definitions would further level the difference between the CPT and FSDT. Including the patch load in the determination of the shear deformation causes amplified deflection of the grating, but this load is only expected when the structure is placed on the seabed.
9.8 Plate vibration The frequency of natural vibration of the composite grating will be different from the original steel mud mat plates. If
this is in the range of any other resonance frequencies of the lowering operation or the structure itself, this may cause excessive lateral movement of the designed plate. Therefore, the natural frequency of the new grating is investigated. The free vibrations of the plate are only dependent on the material properties and the plate geometry. The natural frequency is therefore independent of any load. The membrane forces are assumed not to influence the vibration analysis. The governing differential equation now becomes [73]:
(9.83)
The last term in this equation is the mass moment of inertia. This differential equation may be analytically solved, by assuming the following periodic solution: ( ) ( ) (9.84) Substituting this solution into equation (9.83) results in:
( )
( )
( )
( ) (9.85)
110 Grating deformation Now by introducing the shape function:
( ) ∑ ∑
(9.86)
is defined as the vibration amplitude. Substitution of the shape function into equation (9.85) leads to:
∑ ∑ { (
)
(
) (
)
}
(9.87)
Since this equation must hold for every point ( ) in the domain and , the expression in the
braces should be zero for every and . This results in an expression for the frequency of an orthotropic rectangular plate:
[ (
)
(
)
(
)
] (9.88)
Using equation (9.88), it is determined that the fundamental natural frequency of the composite grating is higher than the original steel mud mat foundation frequency. Therefore, danger of resonance problems is not expected. The
fundamental natural frequency is obtained for ( ) ( ) → - The next four frequencies for the
discussed orthotropic plate for the modes may be determined for ( ) ( ) ( ) ( ) ( ).
9.9 Results The grating deformation and section forces are assessed for both the in-situ load case and for accidental loading. The general solutions of deflection profile are plotted using Mathcad 15.0 [81] for a single grating under the structure with dimensions of 4.2 m by 2.1 m.
9.9.1 In-situ loading For the in-situ loading, the load on the structure is assumed equal to the structure weight. This is the combined weight of the protection structure and the later installed FLET and roof panels. This weight is transferred via the steel frame of the protection structure and the gratings to the soil. The soil provides an elastic reaction, bending the grating upwards. The grating is first assumed infinitely stiff, to determine how far the grating is pushed into the soil. This assumes no soil moves through the perforations, but the required penetration depth (from chapter 8) can later be included to determine the actual displacement of the foundation. The actual deflection of the grating is then determined, assuming equal work done by the soil reaction.
9.9.1.1 Infinitely stiff grating The governing differential equation of an orthotropic plate on an elastic foundation is given by equation (9.46). Including the Fourier expansion of the distributed load, the general solution is now given as:
The grating is founded by clay and the distributed load and is the deflection at the edges. For the infinitely stiff grating, this deflection is equal to the entire plate, and the resulting work done by the displacement of the clay should equal to the total force of the load. As the grating can be considered stiff relative to the subgrade, the pressure resulting from the soil on the grating is not uniform. The pressure profile of the load is therefore parabolic, see figure 9.6 and figure 9.7. This pressure distribution is not important for the infinitely stiff grating, as the resulting total force remains the same. However, for the actual gratings, the edges will show more deformation than the center of the gratings. For sands, the total deflection of the foundation is even less, due to the higher subgrade modulus. The grating deformation is therefore, also less than in clays. For the infinitely stiff grating, the deflection in the soil is equal to 0.26 mm.
( ) ∑ ∑ ( )
( )( )
(
)
(
)
(
)
(
)
(
)
(9.89)
9.9 Results 111
9.9.1.2 Flexible grating Considering the actual grating, the grating is still stiff in comparison with the soil, but can now deform. The parabolic pressure profile results in a non-uniform deflection of the grating. The grating is pressed into the soil by the steel frame at its edges. The grating shows the most deformation at the outer edges of the grating. The flexible plate only requires the outer rim of the foundation to deform to generate enough reaction from the soil to withstand the weight of the structure. In comparison to the other dimension of the grating, these deflections into the soil are negligible. However, the deflection of the grating is used to determine the stresses and sectional forces. The deflection profile of the grating in the soil is plotted in figure 9.13.
Figure 9.13: Deformation of single grating in clay
This shows a maximum deflection at the edges of 1.26 mm, which is considerably more than the deflection of the infinitely stiff plate. The figure shows that only the outer of edges the gratings are pressed into the soil. The displaced soil volume by the deformation of the plate, equals the displacement volume of the infinitely stiff plate. This therefore results in a similar upward reaction of the soil. It is noted that the deflection shown in figure 9.13 is strongly exaggerated, to clarify the deformation of the plate. Due to the elastic reaction of the soil, the grating deforms more near the supports and the deflection levels off to the middle. Comparing the grating deformation with the infinitely stiff plate in figure 9.14 along the width of the foundation indicates the difference. Note that the deformation is very small in comparison with the plate width.
Figure 9.14: Deformation grating compared with infinitely stiff plate
Having a definition for the deflection of the grating also makes it possible to determine the moments and shear forces within the plate. The bending moments within the grating are plotted in figure 9.15 and figure 9.16 based on equations (9.51) and (9.52).
-2.5
-2
-1.5
-1
-0.5
0
0.5
0 0.3 0.6 0.9 1.2 1.5 1.8 2.1
Def
orm
atio
n fo
un
dat
ion
[mm
]
Foundation width [m]
Deformation of grating compared with infinitely stiff plate
Flexible grating
Infinitely stiff grating
112 Grating deformation
Figure 9.15: Bending moment in the x-direction
Figure 9.16: Bending moment in the y-direction
The maximum values for the bending moments are and . The difference between the
bending moments in either directions is low, due to the small deflection of the grating. This results in low membrane stresses and therefore the relative difference is small. Due to the orthotropic nature of the grating, the twisting moments are close to zero. Only near the corners of the plate a twisting moment is generated, which provides the corner forces for the grating equilibrium, see section 9.6.2. The twisting moments are shown in figure 9.17 and figure 9.18.
9.9 Results 113
Figure 9.17: Twisting moment acting in the x-direction
Figure 9.18: Twisting moment acting in the y-direction
The maximum twisting moments near the corners are quite small and negligible in comparison to the bending moments. The shear forces in the foundation result from equations (9.55) and (9.56). These are critical near the application point of the patch load and at the supports. The shear forces are shown in figure 9.19 and figure 9.20.
114 Grating deformation
Figure 9.19: Shear forces per unit length in the y-direction
Figure 9.20: Shear forces per unit length in the x-direction
The maximum values of the shear forces within the individual grating bars are and .
From these forces the flexural and shear stresses within the grating bars may be determined. Using equations (9.63) to (9.68), the stress within the composite material is investigated. This shows that the material strength of the gratings is sufficient to withstand the produced stresses from the in-service conditions for the considered grating dimensions. The stresses within the material were determined for a single bar. This resulted in maximum flexural stress of and . The torsional stress is neglected and the shear stress within the composite material
is and . As the composite material is far more susceptible to shear failure, the shear
strength of the material is considerably lower. The composite material strength is shown in table 9.1.
Table 9.1: Composite properties [82]
Property Glass-vinyl ester Unit
Flexural strength (LW) 241.3 MPa
Tensile strength (LW) 165.5 MPa
Shear strength 41.3 MPa
9.9 Results 115
Comparing the resulting stresses of the in-situ loading of the grating with the material strength, shows that the material is strong enough for this load case. The material is subjected to a parabolic soil pressure. This results from the stiff plate relative to the subgrade modulus. The material stresses stay well within the limits of the design strength of the grating.
9.9.2 Accidental loading The composite material is already being used on similar structures on the seabed as protection against dropped objects. These composites will consist of different additives and other fiber/resin ratios, as they are only intended for the impact protection, but the main materials are similar. A flexible resin keeping the fibers in place will still exercise good impact resistance. The difference between the composite and for example steel is that FRP will mostly deform elastically under a similar load. The FRP returns to its original form when the load is removed. The application of such gratings in a subsea environment shows the confidence of the oil and gas industry in the preservation of properties of FRP for the lifetime of the structures.
Assuming the composite grating is strong enough to withstand the impact of dropped objects, the dynamic impact may reduce the durability of the composite. Due to the elastic reaction of the material, the grating deforms to a large extent, before returning to its original state. This may induce high local stresses and cracking within the material. This facilitates the moisture-induced degradation of the material, causing premature failure. It is therefore suggested to determine the rate of degradation after the grating has resisted such an impact. The accidental loading considers the load case of the structure freely hanging in the air or still located on the barge. A shackle or other heavy equipment is dropped and causes a dynamic load on the gratings. The impact caused by a dropped object may either cause an elastic reaction of the grating, or if the dynamic impact occurs fast, by the plastic deformation of the foundation. This is modelled by the grating subjected to a patch load, varying in time.
9.9.2.1 Impact resistance Small deformations of the gratings may be predicted by assuming a linear elastic reaction between the mid plate deflection and a load. For larger impact loads, the bending and midline extension of the plate leads increased plate stiffness. Therefore, for any considerable impact, the reaction of the grating is non-linear. For high-velocity impacts, the composite deforms plastically and causes local damage. This is assessed in section 9.9.2.2. If the stress exceeds the strength of the material, the fibers are damaged, reducing the mechanical properties of the grating.
Table 9.2: Design impact energy for subsea production structures [83]
Load case Impact energy Impact area Object diameter
A 50 kJ Point load 700 mm
B 20 kJ Point load 500 mm
C 5 kJ Point load 100 mm
These load cases in table 9.2 are investigated for the grating. The maximum plate deflection and corresponding impact resistance for this deflection are determined. For high-velocity impacts, the punching shear failure is also checked. The impact resistance is determined by assuming a mass of 1500 kg dropped from a height of 3.3 meter. This coincides with an impact energy of 50 kJ (load case A). Load case C results in the maximum punching shear stress within the material. Following from the connection design, the gratings are assumed simply supported. As the grating deforms during impact, the kinetic energy of the object is absorbed into lateral bending and an increase of membrane stresses. As the grating deflects, the stiffness against deformation increases and more energy is absorbed. Once all the kinetic energy is absorbed, the grating is deformed to certain state and the resulting resistance force of the grating acts on the object. Due to increasing deflection of the plate, the membrane stresses increase and the resistance against bending becomes higher. This results in a non-linear plate stiffness. By first assuming the constant stiffness for the mid plate deformation, the mechanism may be modelled by a simple mass-spring system. Assuming no damping, the kinetic energy from the object will be converted to spring energy. This results in a maximum deformation of the spring. This analogy also works for a dropped object on a plate. The kinetic energy of the object plus the additional work done by the weight, is absorbed by the elastic deformation of the plate. The maximum deflection multiplied by the stiffness then results in the spring force of the plate.
116 Grating deformation As the plate stiffness is not constant, this is determined first. This is done by calculating the deflection of the grating under varying loads. The membrane forces are again determined iteratively. The stiffness at the center of the grating then follows by dividing the exerted load by the mid plate deflection. The relation between plate reaction and center deflection is shown in figure 9.21. The area below this line is the work done by the plate deflection and may be
correlated to the impact energy of the object.
Figure 9.21: Plate reaction for mid plate deflection
By assuming the impact load as a half sine pulse, see figure 9.22, the deflection during impact may be determined by solving the differential equation for the grating subjected to a time dependent load.
Figure 9.22: Assumed load profile: half sine pulse
The membrane forces are dependent on the deflection, and therefore indirectly by the magnitude of the load. Including this, simplifies the iterative process and allows the mid-plate deflection to depend only on the load magnitude. The differential equation is defined as [84]:
( ) (9.90)
Where the load may written in the form:
9.9 Results 117
( ) ( )∑∑
(9.91)
Where is the distribution of the dynamic load expanded into the double Fourier series, which is determined analogous to the distributed patch load, see equation (9.24). is the load frequency. The load term may be
separated in a part dependent of the position and a part varying in time.
( ) ∑∑ ( ) ( )
(9.92)
Solving this leads to a solution in the form of [85]:
( ) ( ) ∑ ∑
(9.93)
Where the vibration amplitude is expanded to include the membrane stresses,
(
)
(
)
(
)
(
)
(
)
(9.94)
The relation between plate resistance and center deflection is shown in figure 9.21. The area underneath this line now determines the work done by the grating, see figure 9.23.
Figure 9.23: Work done by grating deflection
By equating this area to the specified impact load of 50 kJ, the mid plate deflection is approximated at 0.13 m. This corresponds to an impact resistance of 780 kN for the considered grating. The maximum stresses in the material result from the bending moments and tensile forces in the material. These are determined using equations (9.48) and (9.63). The maximum stresses are again found in the shorter plate dimension ( -direction). The maximum bending stresses for this deflection are equal to 290 MPa, whereas the tensile stresses are determined equal to 120 MPa. Together, these stresses exceed the flexural and tensile strength of the material, causing permanent damage. To prevent this, the grating dimensions should be modified to lower the local material stresses.
118 Grating deformation Plotting the center deflection for varying time, based on equation (9.92) shows the previously determined maximum deflection of 0.13 m when the load is maximum (figure 9.24). Assuming an interaction time with a load frequency of ( )
the maximum load and deflection will occur at .
Figure 9.24: Mid plate deflection during impact for ti = 2 s
9.9.2.2 Shear punch resistance If the grating reacts plastically to the dropped object, the grating deforms accordingly. The maximum force the grating may resist may then be defined by the shear punch capacity. To determine the plastic resistance, the shearing area is first determined. This is the area which is sheared as the object punches through the grating. First, the number of grating bars that are hit are determined. The sum of the
cross-sections of a bar determines the total shearing area:
(9.95)
Where = = =
=
From the shearing area, the maximum shear resistance of the grating may now be calculated:
(9.96) Where is the shear strength of the composite material. The shear punch capacity is calculated by equation (9.96). This gives a grating capacity for each load case of: = = =
The grating reaction on the object is determined from the impact energies, see figure 9.23. The maximum reactions of the grating of each load case are: = = = All these reactions stay below the shear capacity of the grating. The lowest factor of safety is achieved for load case , as this energy is distributed over the smallest area.
9.10 Sensitivity analysis 119
9.9.2.3 Reaction forces The sectional forces also allow calculation of the reaction forces on the steel beams acting as supports for the gratings. These beams at the base of the structure transfer the loads from the structure to the gratings and allow the connection of the gratings to the structure. The reaction forces on the supports, act against the corner forces and the external load on the grating providing equilibrium for the system. The accidental loading subjects the material and the connections to the steel frame to the critical loading. Additionally, the splash zone entry and the landing operation cause considerable loads on the connections. The shearing forces acting upon the supports may be determined by equation (9.73). These forces are used to dimension the connection details in section 10.6. For the design load, a material factor of 2.0 is included to mitigate the uncertainty of the actual load on the connections.
9.10 Sensitivity analysis
9.10.1 In-situ loading The sensitivity of the deformation of the grating depends on a multitude of factors. By varying these factors, one obtains the sensitivity of the grating deformation and material stresses within the material. Placing the foundation on the soil will deform the individual gratings. The maximum deflection is dependent on the projected area of the foundation, which may be seen as the relative distance between two adjacent grating bars. Furthermore, the deflection is decreased by an increase in grating stiffness. Additionally the mid plate deflection is affected by the vertical load and the stiffness of the soil. The sensitivity is given in table 9.3.
Table 9.3: Sensitivity grating mid plate deflection in clay
Sensitivity mid plate deflection clay
Description Symbol -10 % +10 %
Projected area Ap +2 % -2 %
Grating height h +5 % -4 %
Vertical load Fv -10 % +10 %
Soil stiffness Kclay +10 % -8 %
Due to the stiff grating in comparison with the clay, a further increase in stiffness has little effect on the maximum deformation. Varying the load and the soil stiffness has similar effects on the grating deflection into the soil. As the maximum deflection of the grating into the soil is very small, compared with the other dimensions, the actual stresses within the material are low. The sensitivity of these values are therefore not meaningful. The stresses however, do affect the reaction forces acting on the connections. The sensitivity of the maximum reaction forces are evaluated by varying the parameters. This is shown in table 9.4.
Table 9.4: Sensitivity grating reaction forces in clay
Sensitivity reaction forces clay
Description Symbol -10 % +10 %
Projected area Ap -1 % 2 %
Grating height h -3 % +4 %
Vertical load Fv -10 % +10 %
Soil stiffness Kclay +2 % -1 %
Reducing the stiffness of the grating, makes it more flexible. This increases the maximum grating deflection, and the relative flexibility of the grating to the soil. This changes the soil pressure profile and results in a more distributed pressure on the grating. Therefore, the forces acting on the supports are reduced. For a more soft soil, the opposite
holds true.
9.10.2 Accidental loading The accidental loading is also influenced by various factors. The sensitivity of the deflection and the stresses within the composite material, due to the specified dropped object energy are determined by varying the projected area of the grating, the height of the grating, the impact energy and the impact duration. The results of the first three parameters are stated in table 9.5 and table 9.6.
120 Grating deformation
Table 9.5: Sensitivity grating impact deflection
Sensitivity grating impact deflection
Description Symbol -10 % +10 %
Projected area Ap +0.2 % -0.6 %
Grating height h +4.4 % -3.7 %
Impact energy Ek -2.8 % +2.8 %
Table 9.6: Sensitivity grating impact stresses
Sensitivity grating impact stress
Description Symbol -10 % +10 %
Projected area Ap +1.6 % -2.1 %
Grating height h +1.0 % -0.7 %
Impact energy Ek -4.1 % +4.1 %
The impact deflection and stresses are only slightly affected by the change in projected area. This can be explained by the increase in membrane stresses. As the bending resistance is reduced, the resistance by the membrane stresses increases. Therefore, the change in plate stiffness is low and the deflection and resulting stresses barely increase. The shear stress on the connections caused by the accidental loading is affected by the stiffness of the grating and the magnitude of the load. The sensitivities are shown in table 9.7.
Table 9.7: Sensitivity impact reaction forces on the connections
Sensitivity impact reaction forces
Description Symbol -10 % +10 %
Projected area Ap -7 % +9 %
Grating height h -28 % +38 %
Impact energy Ek -1 % +2 %
The stresses within the connection details are highly dependent of the grating stiffness. The higher the stiffness of the grating, the less membrane stresses are generated. This results in higher shear stresses on the connections. Decreasing or increasing the load has less influence, as this only results in a small change of maximum deflection of the grating. Varying the impact duration changes the maximum deflection of the grating, as shown in figure 9.25.
9.10 Sensitivity analysis 121
Figure 9.25: Sensitivity grating impact deflection
By reducing the impact duration, the maximum stress within the material is also increased, see figure 9.26.
Figure 9.26: Sensitivity grating impact stress
The shear punch capacity is affected by the varying grating parameters and load magnitude. The capacity is mainly affected by varying the projected area and the grating height. Additionally, the sensitivity on the factor of safety for a decrease or increase of the impact energy is determined. The results are shown in table 9.8.
Table 9.8: Sensitivity shear punch capacity
Sensitivity shear punch capacity
Description Symbol -10 % +10 %
Projected area Ap -9.1 % +11.1 %
Grating height h -10.0 % +10.0 %
Impact energy Ek +6.2 % -5.7 %
122 Grating deformation The shear punch capacity is shown to be mainly effected by projected area, which corresponds to the total amount of shear area. As expected, the grating height is directly correlated to the capacity, as a variation leads to a linear change in shear area. The change due to impact energy is limited as an increase leads to only a small increase in impact force.
9.11 Discussion The deflection of the grating is balanced by the plate bending and generated membrane stresses. The membrane stresses occur for significant deflection, causing the resulting stresses within the composite to be taken up by the tensile strength. This resistance against stretching of the material provides additional resistance against the deflection behavior. As the deflection of the considered grating is only limited, this effect is neglected, providing a conservative deflection. The grating deflection may be compared with the deflection of the original mud mat foundation. This deformation was determined using the same analytical method. A check for the magnitude using the Roark’s formula for a rectangular steel plate yielded similar results. The original plates are quite thin; therefore, the elastic analysis may not be used to determine the deflection. A significant difference with the composite is that the thin steel plate experiences yielding when the deflection becomes greater than the plate thickness. This is counteracted by the membrane stress within the material as this takes a part of the load, and increases the stiffness. This effect complicates the determination of the deflection of a thin steel plate under large deflection. The flexural rigidity of the steel plate is nearly 10 times smaller than the considered composite grating. This is caused by the larger height of the orthotropic grating. The deflection of the steel mud mat plates however, remains limited due to the better load transfer of bending and torsional moments. This also provides improved load transfer to the supports. The in-air deflection of the steel plate under similar load is therefore slightly larger than the composite grating. Comparing the composite grating with a steel grating of similar dimensions, a significant decrease in deflection is expected, as the better stiffness modulus of the steel now provides a better flexural stiffness of the grating. The flexural modulus resulting from the combination of a grating and the steel material makes for a very stiff foundation, with barely any deflection. This however, is coupled to a large increase in weight of the foundation. The steel grating as a foundation would result in an increase of the entire structure weight of approximately 25 %. This increase in total weight of the structure complicates the installation capability. By increasing the height of the grating even further, the deflection of the grating reduces, and the stresses in the material are lowered. This is coupled with an increase in foundation weight, and consequently the total weight of the structure. The height and the mesh size of the gratings will need to be determined to balance the hydrodynamic loads, the deflection and stresses within the grating and the penetration of the grating into the soil The vertical bearing capacity of the penetrating grating is an important factor. Once this is determined for the soil, the mesh size or the height of the grating may be adjusted, to lower the slam forces, reduce the foundation weight or mitigate the structure landing. Depending on the environmental conditions, soil characteristics and structure or project specifics, different grating characteristics can be optimized. The resulting flexural moments and shear stresses can put significant strain on the composite material. The susceptibility to shear forces is a dangerous characteristic of the composite. The possibility of boulders creating shear stresses should be analyzed, to determine if the composite grating shows sufficient strength. To allow a sufficient factor of safety for the shear stresses, the grating height may require need to be further increased. The reaction forces are taken up by the connections. As the material cannot be welded to the supports, the imposed connection length is a lot shorter. This redistributes the forces to a much smaller area, effectively creating more stress within the material. As shown in section 10, this is able to be resisted, but the required connection length is quite high, resulting in high amounts of connection hardware and additional increase in weight. This problem is difficult to mitigate, as increasing the height or the width of the grating bars only provides limited additional local strength. The deformation due to the shear forces within the grating is shown to be limited, but if the grating is subjected to a point load, the shear stresses increase significantly. This may lead to premature failure of the composite material or a large additional deflection. The elastic reaction of the soil does provide limited mitigation, as the grating is partially prevented from deformation, reducing the internal stresses. The additional shear deflection caused by a distributed load is quite low, but the extra deflection caused by a patch or point load may become quite large.
9.12 Conclusion 123
The stresses during impact loading of a dropped object, prescribed by Norsok N-001, exceed the strength of the composite materials. To provide a safe design regarding the impact resistance, the beam dimensions should be adjusted to resist this load. For high velocity impacts, the composite is able to resist direct shear failure. Section 9.9.2 displays that the gratings may be excessively damaged by this impact. To mitigate this, it is suggested to bring spare gratings, to allow replacement of damaged parts prior to installation. This will be a more economical solution than
increasing the dimensions of the plates to be able to withstand the dropped object loads. Additionally, redundancy in the foundation design is suggested, providing sufficient bearing capacity for the remaining foundation plates.
9.12 Conclusion The deformation of the foundation on the seabed was checked analytically, using classical plate theory and Fourier analysis to estimate the deflection of the grating under the loading. This showed that the deflection is limited and the resulting loads within the material are able to be transferred to the soil. Shear deflection, due to point loads, may cause significant shear stress in the material and may require additional investigation. Accidental loading by dropped objects exceed the material strength and redundancy or replacement of the grating plates is recommended. The reaction forces at the boundary of the grating were also determined, to be able to design an adequate connection technique. This will be investigated in chapter 10.
10. Connection design
10.1 Introduction The connection between the gratings and the base frame of the structure are to withstand the impact and dynamic loading, and carry the grates’ own weight. Unlike steels, composites may not be welded to the underside of the structure. Therefore, special attention is paid to the connection to the structure. The composite gratings are required to be fixed to the structure using a suitable joining technique. There generally exist size limitations due to the production process and the transportation, the joining technique of composites is an important design aspect. The joints are required to provide an adequate connection, to fully transfer the loads to the adjacent components. It is investigated which joining technique is most suitable for joining the composite grating to the structure. The following joining techniques are considered: adhesive bonding, mechanical fastening, interlock and welding. Mud mat plates are currently welded to the steel base frame of the structure. Multiple steel profiles are interconnected to form this base frame and to support the top side of the structure. The mud mat plates are welded to the flanges of the steel profiles, providing a rigid connection. The copying of knowledge of connection technology however does not transfer well to composites. It results in oversized composite components, due to the different behavior of the two materials. The linear elastic composites do not deform plastically, causing the stress concentrations created by the connection to be greater than in steel. Additionally, the anisotropic behavior of composites creates a vulnerability to the inevitable transverse stresses. This causes the design of composites to be governed by the load-bearing capacity of the connections, requiring uneconomical cross-sections. The design of FRP structures focuses more on the joints and not on the load carrying capacity of the material itself. This is not only as a result of the difficult joint design, but also due to the low stiffness modulus of the material, which prioritizes the allowed deflection over the stress capacity in the design process [86].
10.2 Adhesive bonding A less commonly used to connect composite material is adhesive bonding. This method sees limited use due to difficult quality control, especially for on-site connections. Furthermore, guidelines concerning the bonding of FRPs are not very advanced and long-term durability is not well charted. A benefit of adhesively bonded material is the better correspondence of the failure mechanism. Adhesives are anisotropic and fail in a brittle manner. Furthermore, adhesives may provide a smoother and more uniform load transfer, coupled with higher joint efficiency and stiffness. The largest benefit in adhesively bonding may be found in the lack of drilled holes. No drilled holes required in the composite make the composite less vulnerable to water ingress and stress concentrations are avoided. Adhesives are not deemed a viable connection, as the certainty that an adhesive bond is unaffected after ageing 30 years in a marine environment cannot be guaranteed. Furthermore, even though the failure mechanism is similar to the composite grating, this is not preferred for a steel/composite connection.
10.3 Welding The welding of polymers is a promising technique, but thermosetting polymers do not re-melt. Additionally the interface between the weld and the material is prone to defects, and difficult to produce a sufficiently strong connection. For thermoplastic resins this is a more viable option as re-melting allows the polymer chains to connect. However, introducing reinforcement at these locations is difficult, as a good intertwined network is required to fully transfer the loads from fiber to fiber. This joining technique may be applied to thermoplastic composites, but the use of these polymers is still more technically limited than thermosetting polymers. It is difficult to obtain a quality of the weld similar to that of the base material, due to the different application method. The welding of composites is not yet sufficiently advanced. This technique would also prove to be very difficult for the
selected thermosetting resins. Another drawback is that only allows a composite/composite connections, and an additional method is required to provide the connection to the steel. If the current growth in use of thermoplastics continues, they may eventually replace thermosetting polymers. In theory they are able to be welded together, but currently still fall behind of thermosets in terms of fiber adhesion and impregnation, processing and mechanical properties. As the thermoplastics see more use, the costs reduce and the understanding of the material improves. When the confidence in thermoplastics further improves, this joining technique may become the preferred option. Especially in the future if full-composite structures are considered.
126 Connection design
10.4 Interlocking Interlocking may provide a useful joint by design. One way is by making the connection direction different from the in-use loading direction. Alternatively, an insert that connects to both parts of the joint can be applied. The interlocking mechanism makes use of the friction and geometrical arrangement to keep the elements in place. The difficulty of this technique is the strict geometrical tolerances required to produce a proper joint. For the current design case, a secure fit is a requisite, as the grating would otherwise experience extra dynamic forces during transport and installation. Another possibility is to mount the grating plates in the space between the flanges of the profiles. This secures the gratings horizontally. Vertical movement is still possible, as the height of the profiles is larger than the plate thickness. To fix the gratings vertically, they are required to be connected to one of the flanges, either by adhesively bonding or mechanical fastening. Using interlocking to join the steel and composite is not regarded as a suitable technique, as the joint would require high dimensional precision and geometry of the FRP components. The gratings would have to be designed to allow such a specific connection. A combination of two joining techniques may take advantage of the beneficial attributes of both techniques and compensate for their unfavorable properties.
10.5 Mechanical fastening Mechanical fastening usually comprises of bolting or riveting two parts together. Bolting allows for easy assembly and more important, disassembly. Bolted connections can be tensioned with a specified torque, granting high controllability. Rivets provide extra joining strength due to the interface shear conceived when the rivet is fastened. Both these mechanical fasteners are applied in the same fashion as in steel mechanical connection.
If mechanical fastening it the selected joining technique, the use of stainless steel hardware is preferred. Using composite joining hardware is only recommended, if the stainless steel is not expected to maintain its strength in the marine environment. It is of vital importance to prevent damage to the material, and as such, drilling holes to allow for a connection is discouraged. Exposing the inner resin, no longer protected by the outer veil, enables the wetting of the material. This may eventually lead to a detrimental strength reduction of the fibers and the resin and may cause failure of the joint. Therefore, it is preferred to use the geometry of the composite grating to allow a connection. This may be done with clips and angles gripping into the composite mesh and bolting it to the steel profiles. This way the FRP gratings may be attached securely to the steel frame, without losing the integrity of the composite mesh. Various clips and angles exist on the market and are used to connect the grating to the steel frame. The most relevant ones for this application will be discussed [87]. Type M or saddle clips: The M-clip consists of an M-shaped steel shape. The
two arms of the clip clamp two opposite load bars to the support. This secures the grating in two principal directions. The clips are connected to the steel profiles by bolting it in the middle of the clip. The tooling required for this type of connection is only the drilled hole in the steel profile. Labor cost is also relatively low due to the straightforward connection.
Figure 10.1: Grating M-clip
Type C clip: These clips may be used to connect two unsupported edges of the plate. The C-shape clamps around the load bars of the two plates and the clip itself is closed with a bolt. This minimizes difference in deflections if the joints fall in between supports. This will only be used in locations where the grating is not supported by stiffeners.
Figure 10.2: Grating C-clip
10.5 Mechanical fastening 127
Type E clip: This shaped as a more flat M-clip. It also has two arms preventing movement in two directions. The only significant difference is that the height of the grating is bridged by the shaft of the bolt in contrast to the M-clip, where the gap is bridged by the clip itself. Ease of installation may slightly improve at the cost of a less secure fit.
Figure 10.3: Grating E-clip
Paw clip: This clip is relatively flat and is similar to the E-clip. The four arms
clamp all four of the surrounding load bars to the support and prevent movement in all three principal directions. This clip produces the highest holding capacity.
Figure 10.4: Grating Paw-clip
The Talon system - Another mechanical connection may
consist of a series of J-clips in a row, similar to the Talon™ system, developed by AIMS international. This fastener system is developed for securing composite walkway gratings in the wave zone of an offshore platform. The Talon system was designed for resisting the severe wave forces exerted by hurricanes and typhoons. The arms of the clamp grip clamp onto the mesh and lock it in place. The larger area of the clamp redistributes the loads of the connection, effectively reducing the local stresses in the grating. Additionally, the labor costs of these clamps are considerably less, as the clamps require less bolting for the same amount of load transfer area. The bolts only connect the clamp to the steel frame, and the gratings are locked in place between the clamp arms and the bottom flange.
The most promising joining technique is therefore to connect the composite gratings to the structure using mechanical fastening. By using a configuration similar to the discussed Talon claws, the loads are distributed over a large area and damage may be prevented. It is suggested to clamp the gratings in between the clamps and the bottom flanges of the steel profiles of the frame, see figure 10.6. Vertical movement of the grating is then prevented. The arms of the clamp grip into the mesh of the grating and limit the horizontal movement. Employing a tolerance for the location the arms grip into the mesh, allows compensation for the differences in thermal expansion and the resulting mutual displacement. This connection system has proven its applicability in the offshore industry, in arguably worse conditions than it will endure in the lifetime of the structure. This is therefore the preferred option for the connection between the gratings and the structure.
Figure 10.6: Clamp layout
Figure 10.5: Grating clamp [94]
128 Connection design
10.6 Results Mechanical fastening is the preferred connection method to connect the gratings to the structure foundation, as this provides the most reliable and safe joint. Riveting is not considered a viable option, as pre-tensioning is not a requisite. The most suitable option is using bolted connection in combination with claws to clamp the gratings to the steel frame underneath the structure. This provides protection against the wash-out of gratings during lifting through the wave zone and keeps the gratings in place during the landing of the structure. The reduced stiffness of the composite gratings may limit the maximum span distance. In order to prevent excessive deformations, additional steel supports may be required to reduce the maximum span. This adds extra weight to the structure, but assuming the composite gratings are designed for from the start, a much more optimal design can be achieved. As the composite grating cannot simply be welded to the flanges of the structure, an alternative connection design is desired. The alternatives are to fit the grating either in between the profiles, and letting it rest on the bottom flanges, or by suspending the gratings under the flanges, see figure 10.7. Inserting the grating foundation above the steel frame negatively influences the immediate settlement of the structure, therefore this is not considered.
Figure 10.7: Gratings suspended under bottom flange
Figure 10.8: Gratings resting on bottom flange
The first option of letting the gratings rest on the bottom flanges has the advantage of better load transfer during installation and transportation, see figure 10.8. The loads are directly transferred to the profile flanges. Additionally, a stronger connection to the steel frame is possible, as the grating may be connected to flanges and webs of the profiles. However, reducing the integrity of the webs of the steel beams should be avoided. The flanges of the profiles provide protection to the connections during installation through the splash zone and having the gratings above the flanges provides a more esthetically sound structure. A downside is the installation of the gratings to the structure. The composite plates will have to be situated in between the four webs of the steel frame, but it is difficult to maneuver the gratings between the steel beams without causing damage. In contrast, a grating suspended to the underside of the steel frame has the benefit of providing a better load transfer in service, see figure 10.7. Additionally, the extra exposed grating provides improved bearing capacity and the grating is located lower in the structure, providing the bearing resistance at a lower location, and effectively making the structure settle less. This also improves the horizontal capacity, as more grating is inserted into the soil. As the gratings are located in a more convenient location, they may be installed to the structure in a later stage, reducing the possibility of damage. The joint is less secure as it is only attached to the flange of the profile. The structure landing loads are better distributed, due to direct load transfer to the flanges.
The failure mechanisms of the clamps are investigated to determine the forces and stresses on the steel flanges, the connection hardware and the composite gratings.
10.6.1 Connection method It is suggested to use 12 clamps per grating. These clamps span 10 perforations for a total distance of 0.5 m. These
are mechanically connected to the gratings and the beam flanges using four M16 × 150 mm bolts. Washers are used
10.6 Results 129
to provide an even load distribution and avoid damage to the clamps and bolts. The stainless steel clamps have a thickness of 5 mm. For the specified reaction loads in equations (9.71) and (9.72), the maximum reaction is assumed to over the entire support. From this the forces in a single clamp may be determined. The reaction forces are distributed over four clamps in the -direction and over two clamps in the -direction.
{
(10.1)
This results in a force per clamp of 65 kN for the considered accidental loading. A material factor of 2.0 is used to mitigate the uncertainties of the connection loads. The clamp is assumed to be made of the same material as the bolts. The stainless steel properties are given in table 10.1.
Table 10.1: Stainless steel hardware properties
Description Symbol Value Unit
Diameter bolt Ø 13.27 mm
Effective cross-section area bolt AM16 138.3 mm2
Modulus of elasticity E 193 GPa
Ultimate tensile strength σuts 517 MPa
Shear strength unthreaded shaft σsu 114 MPa
Shear strength threaded shaft σst 88 MPa
10.6.2 Connection stresses The clamps are used to grip into the mesh on both sides. In contrast to the Talon grip systems, this is attached vertically to the flanges of the frame profiles. This allows the bolts to be loaded predominantly in tensile strength, considerably improving its performance and reducing the required amount of mechanical fastening. This connection method may be applied either below or on top of the bottom flange of the steel profiles. Presuming the gratings are attached vertically to the flanges, the most obvious failure mode is the tensile failure of the bolts. This occurs when the tensile stress exceeds the ultimate tensile strength of the bolting equipment and fail. The load on one boundary is distributed over the number of clamps and the number of bolts attaching the clamp to the flange of the steel profile. The stress in the bolts is then:
(10.2)
Another possible failure mechanism is shear failure of the clamp itself. This occurs when the gratings exert a large force on the bolted connection, resulting in the bolt being pulled through the clamp material. The load distribution
may be improved by including washers. The shear area of the pulled through thickness and circumference determines the maximum shear stress in the clamp material.
(10.3)
The shear area is the product of the thickness of the clamp and the circumference of the washers.
The profile flange may fail in a similar way as the clamp, with the bolts being pulled through. The steel beam is made of s355 steel, having lower shear strength than the stainless steel clamp. The shear area is determined by the
flange thickness and the circumference of the washer.
(10.4)
The FRP of the composite may also fail by shearing of the grating bars. The shear strength of the composite is a lot lower than steel, but the force is spread over a larger area. The bars may shear over its width, over the entire length of the clamp.
130 Connection design
(10.5)
One way of improving the failure strength, is to fill the ventilation holes during the molding process, where the structure is to be connected. This greatly increases the shear area of the composite. The gratings are attached to the flanges of the profiles. This means the flanges act as a support for the gratings, and the forces are acting on these flanges. This results in a stress on the flanges, for which they are not designed. To check if the flanges can withstand this force, the flexural forces within the flanges are determined, based on the support reactions and the locations of the clamps. If the flanges yield due to excessive stresses, the steel profiles will lose part of the buckling resistance, thereby reducing the integrity of the entire structure. The force of the clamps is assumed to act on the outer edge of the flanges , creating a bending moment within the flanges.
The stress may be estimated from the section modulus of the flanges.
(10.6)
Where the moment per unit length of the flange is determined by:
(10.7)
Where the longitudinal distance of a single clamp . The section modulus is determined by:
(10.8)
Where the thickness of the flange .
10.7 Discussion The stresses remain below the strength of the respective materials, providing a safe design. To provide extra safety additional clamps can be added at the cost of reducing the integrity of the flanges. The gratings are fixed only in the vertical direction, but horizontal movement is limited due to the clamps gripping into mesh. This still allows for thermal expansion, preventing possible damage. The critical failure mechanisms are expected to be the clamp shear failure, but this can easily be mitigated by choosing a thicker clamp or increasing the washer diameters. The shear stress within the composite material stays quite low for the in-service loads, but for a dynamic impact this may cause excessive stresses and the material may fail. Finally, the bending stresses within the profile flanges are taken into account. The local application of the support reactions may cause deformation in the flanges. This can be avoided by increasing the amount of connections per plate or by using thicker lower flanges.
Attaching the grating to the underside of flanges provides a better solution as the installability is improved and the immediate settlement is lowered. A downside is that susceptibility to damage and losing grates is increased. Additionally, the accessibility of the connection is considerably improved, reducing the required labor time to connect the grating to the steel frame.
10.8 Conclusion Considering the connection method to connect the grating to the subsea structure, it becomes clear that mechanical fastening is the best solution. Attaching the composite gratings to the underside of the flanges is likely the best solution, considering the installation possibilities and required labor. Additionally, the reduced secureness of the gratings during transport and installation is less important than the reduction in total settlement achieved and the improved bearing capacity of the structure in the soil.
11. Cost analysis
11.1 Introduction The benefits of the new foundation are coupled with an increase in cost due to new material and additional connection costs.. An analysis may be performed to estimate the extra costs for the foundation. To give an initial estimate of the costs of the new foundation, the process costs are determined separately and combined.
11.2 Cost breakdown The suggested foundation is an already existing product, allowing a good estimate of the expected costs. The grating material cost may be determined from the fiber and resin costs. Due to the high quality material required for this application, the amount of fillers and additives are likely of low volume weight and are neglected for simplicity. The fiber to resin ratio of the grating is assumed to be 40 % to 60 % with a resin density of 1200 and a fiber density of 2700 . Off the shelf products are also available, but these vary considerably in costs. The costs for
the composite raw materials were taken from [10] and increased for the average inflation over the years. The raw
steel cost for the mud mat plates was determined from [88] by the cost per tonnage for hot rolled plate. To convert the resin and a fiber into a composite grating, the materials are compression molded into shape. This molding process is assumed to be of slightly lower cost than the pultrusion process. Even though the pultrusion process is semi-automated, the equipment cost required for the molding process is lower and the process is easier. The steel plates still require cutting the plate to the desired dimensions and preparing the sheets for welding. The
ventilation holes, to improve the splash zone entry are also required to be drilled. After welding the steel plates to the base frame, the plates are coated for improved protection. Labor and overhead costs for manufacturing is assumed to be incorporated in the costs. Due to the specific dimensions of the foundations, the composite grating will be custom made to size, which may require special equipment to fabricate the foundation. This may result in an increase of the material costs, but this investment likely partly diminished by the high volume of purchase. This influence is therefore neglected.
The transportation costs for the foundations are not expected to be very different. For one, the foundation weight is only a small part of the entire structure and secondly the outer dimensions of the gratings differ only slightly from the steel plates. The higher transport volume of the gratings makes up for the higher weight of the steel foundation. Assuming a maximum transport volume of 48 and a maximum transport weight of 36500 of a single truck, the
composite is limited by volume and the steel by weight, leading to an equal amount of trucks. Using a truck operating cost calculator, an estimate can be made on the transport costs of the foundations for transporting the gratings over a distance of 750 km. [89]. This shows that the increased truck load of the steel foundation does not significantly increase the transport costs. Additional costs may arise from additional measures to prevent damage to the gratings during transportation. If the composite is damaged in any way, its integrity is lowered and its durability may be significantly reduced. The contribution of the foundation transport is expected to only be a small part of the total transportation costs of the structure. The installation costs of the two different foundations are quite different. The gratings are mechanically connected to the structure. This means the time of installation is a greater than the original solution. As shown in chapter 10, the preferable option to connect the gratings to the structure is by fastening it to the underside of the bottom flanges of the structural beams. The costs to connect this foundation to the steel structure consists of the clamps and bolting hardware, in addition to the extra labor and inspection costs. For the mud mat plates, the plates are welded to the structure. The costs for this process consist of the welding costs, the labor costs and eventual NDT on the welds. Prior to connecting the foundations to the structure, they will need to be lifted and positioned in the correct location. For the composite gratings this process is relatively easy, due to the lighter weight of the individual plates and the mechanical fastening does not require strict positioning. The steel plates on the other hand, are welded to the structural beams and require high positioning accuracy. This is complicated by the higher weight of the plates and the difficulty to weld upside down, requiring upending of the steel frame. These factors significantly increase the amount of time to install the steel plates.
132 Cost analysis As the gratings are made from composite and not from corrosion susceptible steel, some costs may also be saved by the anodes that do not need to be installed in order to account for the corrosion of the steel mud mat plates. For the reference structure, 13 anodes are required to protect the exposed area of the mud mat plates from corrosion.
The costs of end of life removal of both foundation is expected to be close. The gratings may be easier removed, due to the mechanical connection, but the material itself is difficult to recycle. The steel mud mats have to be cut away at a higher cost, but the leftover steel may be sold as scrap metal.
11.3 Results The costs of the new foundation are determined by analyzing the costs of the separate parts of the production process. A literature study was performed to determine the price range of the off the shelf gratings. These show a high variation in costs from different manufacturers. The volume ratios and the densities of the resin and fibers were used to determine the mass of each component within the gratings. The material costs [10] were increased by 50 % to account for the inflation. The raw material costs of the current steel mud mat plates are determined from its mass and the current hot rolled steel plate price. The processing cost of hot molding is assumed to be close to the cost for the pultrusion process [10]. By including the inflation over the years a processing cost is determined. The processing costs for the steel plate is assumed to be equal to $2.50 per kg incorporating the weld preparation, cutting to size, labour and overhead. Only the transport costs of the finished gratings and steel plates to the fabrication yard are considered. The transport of the entire structure is not expected to change negatively, by changing the foundations. The transport costs of the foundations are almost equal due to similar amount of truck loads. The higher transported load in a single truck for the steel plates reduces the transporting cost per mass, but this is balanced by the lower total weight of the composites. Considering the reference structure, a total of 76 of gratings or mud mat plates are required. To withstand the support forces, the gratings are attached using stainless steel clamps gripping into the grating mesh. These clamps are required at every 1 m of support length, resulting in 12 clamps per grating plate. The stainless steel clamps are assumed to consist of 10 consecutive saddle clamps interconnected to provide extra strength. The clamps are connected to the support frame using four M16 × 150 mm bolts for each clamp. Additionally, some steel PFC beams are to replaced by I-beams in the design to allow all gratings to be attached to the flanges of the structural beams. Off-the-shelf saddle clips, intended for 0.05 m high gratings are $4 each. As the designed gratings are twice the height of off-shelf-products, the saddle clips are expected to cost double. The stainless steel bolting hardware is determined at $4 [90], leading to an estimated cost of $80 per clamp. A stainless steel clamp provides support for a grating length of 0.5 m. The welds required to connect the steel mud mat plates to the structure base are the installation costs for the current foundation. Assuming the weld length required for the plates is similar to the sum of edge length of the gratings, the total weld costs may be determined. Assuming a welding speed of 2 meters per hour and assuming two workers required for the welding operation and NDT for a wage of $60 per hour. The filler metal and shielding gas are expected to be included in these costs. The lifting and positioning is expected to take 1 hour for each grating, requiring four workers for this operation. The increased accuracy required for the steel mud mat plates is expected to increase the positioning time by 30 minutes per plate. Additionally, upending of the entire structure may be required to prevent welding difficulties due to welding upside down. The total costs are defined as the sum of the material, fabrication, transportation, connection, installation costs and the cost saving due to fewer anodes. This shows that the grating costs are slightly more expensive. It can be seen in table 11.1 that the raw material costs of the composite are higher, but the major contribution to the higher cost is caused by the connection costs. This is expected as mechanical fastening is a time- and labor-intensive joining technique.
11.4 Sensitivity analysis 133
Table 11.1: Cost breakdown shallow foundation
Material costs Value Unit Cost/unit Workers Composite Steel
Composite Resin 11357 kg $1.79
$20,381
Fiber 17035 kg $2.28
$38,908 Steel Steel plate 52831 kg $0.80
$42,264
$59,289 $42,264
Processing
Composite Molding 28392 kg $6.53
$185,278 Steel Coating 1346 m2 $25.00
$33,650
Post processing 52831 kg $2.50
$132,076
$185,278 $165,726
Transport
Composite Truck 28392 kg $0.113
$6,418 Steel Truck 52831 kg $0.061
$6,423
$6,418 $6,423
Connection
Composite Bolts M16x150 3696 pc $4
$14,784
Clamps 924 pc $80
$73,920
Labor 231 hr $120 2 $27,720
Steel Welding + labor 481 hr $120 2 $57,720
$116,424 $57,720
Installation
Composite Lifting 38.5 hr $240 4 $9,240
Positioning 38.5 hr $240 4 $9,240
Upending 6 hr $360 4 $2,160
Steel Lifting 38.5 hr $240 4
$9,240
Positioning 77 hr $240 4
$18,480
Upending 6 hr $360 6 $2,160
$20,640 $29,880
Anode costs
Steel Anodes 13 pc $1,000
$13,000
$13,000
Total costs $388,049 $315,014
11.4 Sensitivity analysis The dimensions of the gratings may require adjusting for different types of soil, thereby changing the resulting material costs. To determine the sensitivity of the cost model, the bar width and height of the grating parameters are adjusted by ±10 % to determine their effect on the total cost of the foundation. Changing these values additionally effects the mass of the grating and the cost of the connection hardware. The results are shown in table 11.2.
Table 11.2: Sensitivity grating costs
Sensitivity grating costs
Description Symbol -10 % +10 %
Projected area Ab -5.5 % +6.7 %
Grating height h -6.5 % +6.5 %
Raw material cost $/kg -1.5 % +1.5 %
Manufacturing cost $/kg -4.8 % +4.8 %
Labor cost $/hr -1.2 % +1.2 %
11.5 Discussion The new foundation is expected to cost more than the original mud mat foundation. Even though the raw material and processing costs are in the same range as the steel counterpart, a significant amount of costs arises from the
134 Cost analysis connection to the subsea structure. In comparison to the steel plates, more time, labor and materials are required to connect it to the structure. Cost saving due to reduced anode placement is limited. It is questionable if the increased cost for the foundation weighs up against the reduced risk of waiting for weather during installation. Further research is required in the possible cost saving for improving the installation window. If the installation window is improved by a large amount for a certain location, the new foundation is likely to save
costs. For narrow wave spectra, e.g. for swell waves, the weather uncertainty is low and wave heights will not vary a lot. If the average wave height is low enough, the added value of using composite gratings for the structure is then low. However, if the structure is installed in very rough seas and a structure equipped with mud mat plates only has a small window for safe installation, it may be useful to consider the composite gratings. If the risk of missing the installation window outweighs the added cost for the grating foundation, the grating becomes a relevant alternative. The application of the composite grating foundation may therefore be quite location and season dependent.
11.6 Conclusion The composite gratings created from E-glass and vinyl ester are considerably more expensive than the original steel plates. This is caused by more expensive material, the increased material volume and more time- and labor-consuming connection to the structure. However, as the operability is improved, the vessel may not have to wait on favorable weather to install the structure, reducing the actual costs. The improvement in operability depends on the environmental conditions at a location and this may determine the choice for a composite grating foundation.
12. Sustainability
12.1 Introduction Sustainability of the material is a vital aspect in design phase. Degradation of the resin matrix of the composite may incite the release of dangerous chemical to the environment. To determine the risk, the environmental impact of using a composite grating to its surroundings is investigated. This will be analyzed throughout the different phases of the life cycle and compared with the steel mud mat foundation.
The environmental impact during the production phase of the foundation includes the acquisition of the components for the eventual product. In addition to the base material, the environmental impact also includes the energy required for production and any waste materials produced.
The service life considers the time when the product fulfills its main purpose. The long-term durability and the energy consumption are of vital importance here. Special consideration has to be given to the examination of materials dissolved in the seawater during its lifetime. If this harmful to the environment, measures are to be taken to prevent this from happening or the material design has to be re-evaluated.
At the end of the lifetime of the structure, the foundation is to be removed from the steel structure and dismantled where possible. Subsequently the material is sent for recycling or reused in a different product with another function. The use of materials in structural applications is expected to be the first use of the material, as these are coupled to strict requirements. However, this does not mean it cannot be reused in a lower function product with similar proficiency. This is particularly the case for thermosetting polymers, which cannot be remolded. Instead of thermal recycling, these materials may be mechanically recycled, incinerated or end up in a landfill [86].
12.2 Life cycle assessment The environmental impact of a product is usually evaluated as part of the Life Cycle Assessment (LCA). The impact may be measured by six main categories, which groups various emissions into a quantified measure on the effect of the environment. These six categories are general issues having a fundamental impact on the environment and a scientific approach exists to quantify the effects. The main six categories are briefly described below:
Global warming potential: This is an index to measure the contribution to global warming. It consists of
greenhouse gas emissions, which retain the heat of the earth by absorbing the reflected radiation, resulting in global warming. It is measured in equivalents.
Ozone depletion potential: The ozone layer protects life on the planet from harmful UV-radiation. The emissions of substances which reduce the ozone layer, determining the influence of a product. It is measured relative to
- .
Photochemical ozone creation potential: This is better known as smog and is formed by a reaction of a volatile organic compound and nitrogen oxides in the presence of heat and sunlight. It may be measured by the release of nitrogen oxides equivalents.
Acidification potential: The acidification results from the emissions of sulphur dioxide and nitrogen oxides. These react with water vapor and precipitates to the earth. This is also known as acid rain. It is measured in in equivalents.
Eutrophication potential: This is generally caused by release of nitrogen and phosphorus. These nutrients promote the growth of algae and vegetation in water and degradation of this organic material consumes oxygen, resulting in oxygen deficiency. It may be quantified by the release of substances into the water or soil.
Energy use: This is the process of using natural resources and the effort to convert and shape the considered product to its eventual form. As it uses primary energy resources it may be seen as an environmental impact category, even though it is effectively only a conversion. It may be measured in gigajoules.
An extra impact category considered is amount of water used to produce the product. Water is consumed in the production and completion of products. As potable water is a scarce resource, this is included in the analysis of environmental impact.
Other impact categories are: human toxicity, aquatic toxicity, thermal pollution, noise pollution, light pollution, visual pollution, and vibrations. These effects are more difficult to quantify, due to their high uncertainty and additionally are mostly of local impact [91].
136 Sustainability
These environmental impacts of products may be quantified to determine its performance. The steel mud mat plates and the composite gratings are compared to determine the change in environmental impact for the new foundation. This gives an indication of the difference in sustainability between the two foundations.
The emissions and release of harmful substances are assessed and quantified in every step of the product life cycle. The block diagram for determining the environmental impact of composites gratings may be simplified for the production process by:
Figure 12.1: Raw material flow diagram composite [92]
Whereas the process of creating of the steel mud mat plates is simplified in the block diagram below:
Figure 12.2: Raw material flow diagram steel
12.3 Results The environmental impact of a pultruded grating has been quantified in an LCA study performed for Strongwell composites. In this report the composites are compared with other structural materials for certain shapes. This study only considered the energy and environmental impact up to the manufacturing of the actual product, not the impacts due to in-service use and its end of life. Other limitations are that the emissions for various shapes were normalized to an area covering 9.3 m2 and the linear extrapolation of mass loading is a reasonable assumption, but this is less appropriate for human health and toxicity related impacts.
12.3.1 Emissions In particular, the environmental impact of a pultruded grating and a steel plate were determined for the same area. The determined values for emissions and released substances were up scaled to the dimensions of the considered foundation. This is done by determining the additional weight and assuming a linear correlation in environmental impact. Comparison with a steel grating shows this to be an accurate estimation. The composite grating and the steel plating may now be compared. The results are shown in table 12.1.
Table 12.1: Environmental impact shallow foundations
Impact aspect Composite grating Steel plate Unit
Global warming 54001 71220 kg CO2 equivalent
Acidification 31898 34515 H+ moles equivalent
Eutrophication 16.1 17.6 kg N equivalent
Ozone depletion 7.90E-04 2.16E-04 kg CFC-11 equivalent
Smog formation 226 335 kg NOx equivalent
Metered water 346216 72185 kg
Energy consumption 998 1389 GJ equivalent
12.3 Results 137
This shows that the composite grating foundation performs better in almost all aspects. Only the ozone depletion potential is larger, but this quantity is small. The additional amount of water used in production of the grating however, is significantly larger. The toxicity of the material to human health and the environment is not quantified, but due to the high use of styrene and other chemicals, this is expected to more dangerous than steel production.
12.3.2 Embodied energy
Figure 12.3: Embodied energy diagram pultruded grating [92] The energy consumption of creating a composite may be displayed in an embodied energy flow map, see figure 12.3. This shows the energy consumption from the raw materials to the eventual product for each step of the production process. Embodied energy may be defined as the sum of energy required to produce a product, considering all that energy is integrated in the created product itself the above diagram displays this energy flow map for the composite grating created by the pultrusion process. The flow map for molded grating is expected to be quite similar in its raw
138 Sustainability materials, with the exception of distribution of glass fibers and resin within the product. As the resin fraction is larger, this will have increased energy consumption and glass fibers will show a reduction. The resin for this pultruded grating is polyester, but because the production process of vinyl ester is quite similar, this is assumed a reasonable comparison.
The energy flow map shows various methods of creating ‘greener’ product. For instance, increasing the glass to resin ratio results in a lower energy product and another option would be to replace the styrene within the resin mixture with filler materials. [92]. It is worth noting that carbon-composites require significantly more energy than glass fiber-composites for producing the end-product. This is due to significant amount of energy required to produce these fibers.
12.3.3 Waste management As indicated before, this study does not take into account the recyclability. The processes to recycle steel mud mat plates are established, but the composites are more difficult to recycle. Due to the cross-linked resin matrix, the glass and the resin can no longer be reprocessed. Likewise, reuse of the composite gratings is unlikely, due to the high standards in the offshore industry. For this reason the use as a structural component is also unlikely as the residual mechanical properties are difficult asses due to material degradation. Reuse in a different application may be possible, but the options are limited, as composites are made to order and usually designed for a particular application. Using mechanical recycling to produce recyclates from thermosets, allows the composites to be included in other products as reinforcement or filler materials. Thermoplastic composites may see some form of sustainable recycling, as this resin softens again under application of heat and pressure and retains most of their mechanical properties. The most common option for thermosetting composites is thermal processes to break down the composite into materials and energy, but otherwise they may end up in a landfill [86].
12.4 Discussion The performance of the grating during the processing phase with respect to the environmental impact is improved over the steel mud mat foundation. The extent of the improvement is limited due to the larger volume required for the composite foundation. The composite performs worse considering the ozone depletion potential, but the magnitude is very low in comparison to the CFC-11 equivalent [93]. The production process of the composite gratings requires a lot more metered water. In addition to the human health issues when mixing the resin and the handling of styrene, these are the critical environmental issues. Emissions during service life of a composite consist of solvents from the resin released into the seawater, in contrast to the water contamination due to the release of ionized metals from the sacrificial anodes for the mud mat foundation. The end of life emissions of the composite is a consequence of its inability to reprocess the material. Incineration to separate the constituent materials is expected to release a significant amount of harmful emissions to the environment and therefore this should be prevented. End of life steel is expected to show limited emissions and release of substances into the environment. The embodied energy of composites is lower than the steel foundation for the production process. The main contribution for the total energy to create the final product originates from the styrene production. The steel creation is the main contribution for the mud mat plates. Changing the fiber/resin ratio within the composite and may significantly change the embodied energy of the eventual product. This ratio is determined by the durability of the composite, due to the high standards required to maintain their mechanical properties. Modification of the fiber/resin ratio to provide a ‘greener’ solution is therefore only limited. The difference in used energy for the foundations during the service life is limited. The same transport benefits apply for the end of life, in addition to the energy difference for waste management possibilities. As discussed before, the possibility of recycling the composite gratings at the end of life is limited. Therefore the performance of the steel with regard to the end of life sustainability is significantly better. Steel may be reused in lower quality products or recycled for new steel. The mechanical recycling of composites is promising and may allow use of the produced recyclates. These particles may be used in different applications, such as incorporation into thermoplastic matrices, reinforcement in wood particle boards or included in road asphalt and concrete. The commercial benefit of these applications is not yet clear, but in summary, it is apparent that the end of life value of steel is higher than composites.
12.5 Conclusion With regard to the sustainability of the newly discussed foundation, the performance is slightly better. The process of manufacturing the composite foundation requires less energy and additionally the composite has a lower impact on the environment. The incompetence in recycling the thermosetting composites is a critical downside of the material. This leads to mechanical recycling to allow further applications for the material. If no further application is
12.5 Conclusion 139
determined, the material is incinerated to separate the materials and return some of the embodied energy. The limited material reprocessing ability puts a large strain on the environment.
13. Results By considering an actual subsea structure, the methods described give insight in the benefits and drawbacks of using a composite grating as a foundation. The grating foundation is investigated from manufacturing to its in service behavior. By quantifying the loads, a better comparison between the two foundations is made. A brief recollection of the results found will be described in this section.
13.1 Material selection The selected configuration of the material needs to provide the foundation for a structure with a base area of 670 square meters. The maximum span the material needs to bridge is 2.1 meters. To carry the weight of the structure, an average bearing capacity of 10 kPa is required over the area of the structure. The degradation of material properties has to be limited in order to provide sufficient strength after 30 years in the marine environment. Thermosetting composites are well-known materials in the world of plastics, with predictable properties. They are therefore preferred over thermoplastic polymers as they offer higher reliability in the environment. The low viscosity of thermosets allows good wetting of the fibers and improves manufacturability. The resin in the composite thermoset is mainly dependent on the properties of the material and the environment in which it is placed. Vinyl ester is reasoned to be the most appropriate resin. It has the best corrosion-prevention capabilities of the thermosetting resins. Additionally, its low viscosity provides a good wetting ability. Vinyl ester is relatively cheap compared with the high performance polymers, which keeps the total expenditure of the foundation low. Furthermore, the resin is often applied for the manufacturing of molded gratings. The reinforcing fibers within the matrix material provide the strength and stiffness of the composite material. Of the commonly used fibers, E-glass is proposed for the first assessment. If E-glass fibers are deemed insufficient in a later stage, the alternatives are carbon and S-glass fibers. These are stronger and improve the eventual product, but increase the cost of the composite by substantial amount. E-glass fibers show better corrosion resistance than carbon fibers and the strength properties are less affected by moisture ingress. Additionally, the strain to failure coincides with the resin materials. The E-glass with vinyl ester composite is often used in environments where corrosive protection is vital. It displays good mechanical properties and the components create a strong bond, due to the good wetting abilities. The composite materials are displayed in table 13.1.
Table 13.1: Composite material properties
Property E-glass and vinyl ester
Steel S355 Unit
Flexural strength (LW) 241 355 MPa Flexural modulus (LW) 13.8 205 GPa Shear strength 41.3 266 MPa
Poisson’s ratio (LW) 0.32 0.3 - Density 1800 7850 kg/m3
Water absorption 0.6 0 %
Coefficient of thermal expansion (LW) 8 12 10-6 /°C
The critical durability issue of the composites is the hydraulic stability. The immersion of the composite causes reduction in mechanical and physical properties. A good understanding of the diffusion of the polymer is required in order to apply the material to a structural application. The combination with moisture and sustained stress may cause a significant increase the creep deflection of the composite. The creep behavior may be satisfactory predicted by the existing models, but to fully understand the long-term effect of creep on the selected composite, additional testing is be required. Additionally, the current methods of predicting durability by accelerated ageing may not comply with composites. Therefore, the end of life properties of the material are difficult to predict and additional safety factors are required.
142 Results
13.2 Manufacturing For the manufacturing process of gratings, the molding process is selected over the pultrusion process. Even though the pultrusion process of bars and subsequent creation of gratings creates much stronger and stiffer gratings, the molding process is preferred. This is because the molded gratings have a thick outer layer of resin, protecting the fibers. Furthermore, these gratings consist of only one part and this inherent advantage provides additional protection against the ingress of moisture. The pultrusion gratings compose of multiple pultruded bars connected to each other with stiffeners, through drilled holes, facilitating further damage. Another advantage of the molded gratings is that the gratings are bi-directional. The load may now be transferred in two directions, allocating the total load over a larger area and reducing the forces on the supports.
13.3 Structure transport The transport of the structure is assumed not to be significantly affected by the change in foundations. The re-hitting of the barge during lift-of is reduced due to the reduced total weight of the structure.
13.4 Lifting through the splash zone The magnitude of the loads on the structures during lowering through the splash zone depends on the wave period. For a grating foundation this correlation is less evident. The hydrodynamic loads differ only slightly as a result of changing wave periods. This effect may be attributed to the significant reduction in added mass of the new foundation. The added mass of the considered grating is assessed at around 1/10th of the added mass of the mud mat foundation. Additionally, replacing the mud mat foundation with a grating foundation changes the dominant load case for determining the critical hydrodynamic loads. Whereas the loads on the mud mat foundation are predominantly determined by a combination of the mass forces and drag forces, the prevalent load on the grating is the result of the
slam forces at water entry. The workability diagram shows the structure equipped with a grating can be installed in rougher sea states. The considered grating dimensions allow installation of the structure in waves with a significant wave height of 2 meters for all wave periods. In comparison, this is only valid for a structure with a mud mat foundation up to a maximum of 1 meter significant. For the considered location, this provides an increase of installability of at least 25 %, throughout the year.
13.5 Lowering to seabed Analysis of the lowering operation of the structure revealed that the installation may become easier. The lowering phase is basically a spring-mass system, which may oscillate with a certain period. Due to the large reduction in added mass, and consequently the dynamic mass, the resonance period of the system is reduced. The new dynamic
mass is approximately 14 % of the original, resulting in the resonance period being approximately √ of
the period of the structure with the mud mat foundation. This has the effect that the resonance period of the hoisting system is further removed from the crane tip oscillation period. The period of the hoisting system enters the range of wave periods, which may cause difficulties during the lifting through the splash zone.
13.6 Landing on seabed Investigation of the landing problem for the original mud mat foundation shows a gentle approach to the seabed. The added mass underneath the footing effectively damps the structure and lowers the approach velocity. The water beneath the structure is pushed aside and allows the structure to land on the seabed. When the skirts penetrate the soil the structure slows down further and once the mud mat reaches the seabed the final settlement occurs before the structure comes to a stop. The velocity during this landing operation is reduced gradually, limiting the maximum forces on the foundation. The landing problem for the grating foundation shows a different result. The highly ventilated configuration of the grating has an increased area to which the water body may relocate and the added mass of the structure is considerably lower. Therefore, the velocity of the structure is barely cushioned and the structure velocity stays equal to the lowering velocity. The structure therefore only sees significant reduction in velocity when the skirts penetrate the soil. However, due to the relatively high lowering velocity, the gratings also quickly hit the seabed and structure lowers further. The increasing bearing resistance and friction eventually halt the structure at a lower depth than the mud mat foundation. The lowering velocity only reduces when the skirts penetrate the soil and more when the grating itself hit the soil. The landing for the grating foundation is therefore quite rough.
Results 143
This difference is also observed in the force contributions on the structure during the landing phase. Up until the skirts penetrate, the total external load comprises of the hydrodynamic forces on the structure. Once the skirts penetrate the soil, the skirts slowly start to carry a part of the total load. In the last phase as the mud mat plates hit the soil, the water beneath the structure is fully displaced, and the soil carries the full weight of the structure.
For the grating foundation, before the skirts penetrate, the hydrodynamic forces are considerably lower. In the second phase, when the skirt tip penetrates the soil, the total resistance on the structure is slowly increased in-sync with the skirt load. Eventually, the gratings hit the soil and the gratings carry the total load. As the structure velocity is hardly reduced before the gratings hit the soil, the impact duration is quite short. This causes a high peak in maximum force on the grating, but the reduced dynamic mass of the structure limits the effective pressure on the grating. This causes the structure to penetrate the soil further than required, to obtain sufficient bearing capacity.
13.7 Foundation design The stability of the grating foundation is compared with the original mud mat foundation. This resulted in a required penetration depth in order to generate sufficient bearing capacity. The bearing capacity in drained soils is significantly improved by the arching mechanism within the grating perforations. The dominant contribution to the capacity in drained soils is the base area of the foundation and the skin friction is approximately 10 times smaller. The grating foundation requires a penetrated depth of 0.04 m in drained soils. In undrained soils, the skin friction within the perforations mainly generates the bearing capacity. This is calculated using the contribution of the friction and the projected area of the foundation. The required penetration depth for undrained soils is considerably higher than in drained soils, leading to a greater required grating height. The grating foundation requires a penetrated depth of 0.12 m according to the API standards in undrained soils. Application of the grating foundation shows improvement in the horizontal sliding resistance, due to the soil located in the holes of the grating, providing extra resistance. The immediate settlement is compared with the original mud mat foundation and this shows a large increase in settlement depth of both drained and undrained soils. This is partly mitigated by the lower position of the foundation on the structure.
13.8 Foundation deformation The deformation of the foundation as a result of the loading is determined. From the grating deformation, the internal stresses are analytically determined using classical plate theory. The in-service stresses within the material did not exceed the material strength for the proposed grating dimensions. Due to the behavior of the composite material, shear deformation gives extra deflection of the grating because of the shear loading on the foundation. When the structure is located on the seafloor, this is not expected to cause problems. Dropped object loading is specified by the Norsok codes, and occurs during the installation phase causing excessive loads on the gratings. These stresses during impact cannot be fully absorbed by the elastic reaction and exceed the material strength, causing damage to the grating. Full plastic failure of the material is prevented.
13.9 Connection design To maintain the properties of the composites, a connection technique is preferred which protects the material from damage. By examining adhesive bonding, mechanical fastening, welding and interlocking as possible joining techniques against the design requisites, the best solution is a mechanical connection. The other techniques do not provide the strength or durability for a lifetime of 30 years. By using a clamp, tooling of the material is avoided and a direct steel/composite connection is not required. This clamping angle grips into the mesh of the grating and may be mechanically connected to the flanges of the steel profiles of the base frame. Several different connection methods were considered. By determining the failure modes and their respective material stresses the optimal connection could be determined. This showed that connecting the grating to the webs of the steel profiles resulted in undesirable stresses. By attaching the grating to the flanges of the profiles a better loads distribution is attained, mainly as the bolts are now loaded in their strongest direction. By attaching the gratings to the underside of the flanges, the installation of the gratings becomes much easier, lowering the labor costs. Additionally, positioning the gratings here, slightly improves the settlement behavior of the structure on the seabed.
144 Results
13.10 Cost analysis The cost analysis showed an increase in total costs for the foundation. The cost is determined by splitting up the costs for each of the contributions during the manufacturing process. The cost of the raw materials and the manufacturing and of the product is compared to the costs of the raw steel and the eventual mud mat plates. Furthermore, the costs of transporting it to the fabrication yard is compared for the change in weight and volume. The installation costs due to the labor and connecting hardware are compared and lastly the reduced costs due to omission of anodes. The new foundation shows an increase in cost of 25 %.
13.11 Sustainability A brief environmental impact analysis on the new foundation is performed in order to check the emissions, the embodied energy and the waste possibilities for the composite material. This resulted in lower harmful emissions in comparison to the steel mud mat fabrication. The waste management of the composite material clearly showed decreased possibilities in comparison to the steel. This is caused by the limited reprocessing abilities of the composite.
14. Discussion The results show that the composite grating foundation is an interesting alternative to be used as shallow foundation for subsea structures. The general performance of the composite foundation is briefly discussed. The required properties are easily acquired by using high performance composites, but the high costs of these materials make the cheaper thermosetting polymers more attractive. Similar to the matrix material, the cheaper fibers are selected in order to keep the cost of the shallow foundation low. The proposed E-glass vinyl ester composite in the grating configuration is successfully applied in the water treatment and chemical industry, being exposed to many harmful substances. Additionally, the gratings are applied in the offshore industry as walkways, located in the splash zone of platforms. This provides confidence in the durability of the material. The chosen molded gratings, significantly improve the workability for the installation in the splash zone. This allows subsea structures to be installed rougher seas, reducing the cost of waiting for favorable weather conditions. The critical loads on the grating foundation occur during the splash zone entry, due of the slamming loads. These slamming loads, are significantly lower than the loads on the original mud mat foundation. The lowering resonance period is decreased as a result of the lower dynamic mass, causing earlier resonance amplification with the crane tip heave period. This is quite predictable and should be avoided by changing the vessel heading or by using additional heave compensators. The reduced kinetic energy, causing a reduced impact pressure on the foundation, counteracts the reduced cushioning of the landing operation. As the material strength is lower, the resulting stresses should be mitigated by controlling the lowering velocity. For the proposed grating foundation, the lowering and landing operations increase in difficulty. The foundation stability is assured for significant penetration of the foundation into the soil. The base resistance in sand and the skin friction in clay generate sufficient bearing capacity for the structure weight. The structural integrity of the gratings remains intact during in-situ loading, showing limited deflection. The foundation deforms approximately 1 mm, reduced by the elastic reaction of the soil. Dropped impact loading exceeds the material strength and occurrence will likely cause damage. Stability of the foundation should be assured, regardless of losing a grating plate, therefore redundancy is proposed. The suggested connection method to the structure is strong enough to withstand the support reactions caused by the accidental loading, securing the gratings safely to the structure. The costs of the foundation are increased, due to the higher costs of connecting the foundation to the structure. The mechanical fastening requires an increased amount of labor and connection hardware, causing the main factor of cost-increase for the grating foundation. The environmental impact of the foundation shows improved values over the steel mud mat foundation with regard to the emissions. However, the reduced capability of recycling the materials increases the strain on the environment.
15. Conclusion The feasibility and design of using a composite material as a ventilated foundation for a subsea structure is investigated. Analysis of the design requirements and material properties of different composites displayed a preference towards an E-glass vinyl ester composite. This thermosetting composite showed good mechanical properties, while resisting water degradation and other ageing effects. The existing applications of the material in a similar environments, allow confidence in the performance of the composite for the period of intended use. In contrast to previous studies on similar foundations, constructed from steel, the considered configuration is a grating foundation. This mesh allows for easier construction, installation and load transfer to the steel superstructure. The composite grating is molded in one piece, providing protection for the fibers. Analysis of the failure modes of the connection to the steel frame indicated that the optimal way of attaching the gratings was to clamp it underneath the steel profiles. The flanges are able to take up the highest load and the clamping equipment is loaded in their strongest direction. Using the simplified method of DNV for estimating the loads on a structure lifted through the splash zone, indicates that the new ventilated foundation lowers the hydrodynamic loads by a significant amount. This improves the operability and allows the structure to be installed in rougher seas. As a result of the reduction in added mass of the foundation, the resonance period of the lowering operation is lowered and the period may experience resonance amplification with the crane tip oscillation for significant lowering depths. The landing operation of the structure equipped with the new foundation becomes more complicated. The hydrodynamic forces close to the seabed no longer reduce the structure landing velocity. Therefore, the grating foundation approaches the seabed at a fast pace and this creates a significant impact. The lower dynamic mass limits the impact pressure on the material, but to avoid damage on the composite material, the lowering velocity will have to be regulated. The slamming loads during the splash zone lift create the maximum forces on the grating. The required penetration for the grating foundation to obtain sufficient bearing capacity is investigated. The arching mechanism leading to plugging of the perforations is adjusted for the grating type foundation and the bearing capacity is expected to show reasonable results in sand. The required penetration in clay is less certain, as the extent of the arching mechanism in clay is unclear. The friction dominates the bearing capacity of the grating in clay and for sufficient penetration; this will generate the required bearing capacity. The material stresses and deformations occurring due to the exerted loads during installation and in service operational use are investigated using classical plate theory. The stresses and deflections are shown to be limited, only exceeding the material strength for accidental loading. It will be uneconomical to design for this situation. Redundancy of the grating panels is therefore recommended, to mitigate the possible loss of gratings and assuring foundation stability. The newly proposed foundation is estimated to be 25 % more expensive than the original mud mat solution. This is mainly caused by the expensive connection method. If the increased costs weigh up against the expected low operability of the structure installation, the new foundation may be considered. The sustainability of the composite foundation displayed improved performance over the original mud mat foundation regarding the emissions during fabrication. However, the composite material shows reduced waste management possibilities
Future research and recommendations
Recommendations In order to allow the application of the discussed foundation in practice, several subjects and operations need to be investigated in further detail. The following subjects require further work. In order to determine the durability of the composite material a long-term practical assessment is required. By
determining the properties of this material after a large period of time, its performance as a shallow foundation may be assessed. This may allow extrapolation to the assumed lifetime of the structure. Additionally, the
quantity of released solvents and agents is important for the impact on the environment. If this analysis shows that the chosen composite is not satisfactory, a new material is to be selected that fits the criteria.
A small scale test is required in order determine the improved bearing capacity of a mesh-type foundation in clay. This testing is required to allow adequate predictions of the foundation. This may provide some insight in the micromechanics of the soil, before scaling up the test, to a larger size.
A larger scale test is also required, preferably the size of a single grating. This may allow disregard the reduced bearing capacity of the outer holes. The force and stresses within the material, the horizontal bearing capacity and the overall stability may then be determined, and compared to the calculations. It is advised to also include the surrounding steel frame, as this allows the connections to be tested.
For the lifting through the splash zone, the method stated in DNV was used. To generate a more exact approximation, it is recommended to utilize a software package for the dynamic analysis. This may provide a better estimation of the viscous effects of water flowing through the gratings and a more realistic view of the forces on the structure. This is expected to generate a less conservative result.
Perform an FEA using a soil model for a grating foundation to determine the micromechanics of the load transfer within the soil.
Retrieval of the structure at the end of life is not covered in this report. Due to the shape of the foundation, this may require additional force in addition to the weight of the structure. However, the suction effect as seen in mud mat plates is not expected. Hence, a detailed investigation of this problem is desired.
The possibility exists that a grating plate may be lost during the subsea lifting operation by slamming, dropped objects or landing the structure on a boulder. It is interesting to investigate the consequence of losing a grating on the stability of the structure. Redundancy for the reference structure is easily achieved, as the foundation would consist of 76 gratings. For smaller structures, this effect may be more important.
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Developments Several promising developments exist, which may alter the design of the composite gratings in the near future. These are briefly discussed below. Basalt fibers are worth mentioning as an alternative to E-glass fibers. The manufacturing cost of these fibers is
currently still higher than E-glass fibers, but the mechanical properties are considerably higher. In the future these fibers may replace the glass fibers.
Nanoclay fillers may be used in FRP to obtain greatly improved properties with regard to the strength, stiffness,
dimensional stability and interfacial bonding. Additionally, the fillers accelerate the curing reaction of the composites and improve the hydrolytic stability of the composites. Inclusion of these fillers may allow the use of
the materials with more confidence for their long-term durability. The development of smart structures may greatly affect the monitoring of subsea structures. By integrating fiber
optic sensors within the structures, the structural health monitoring can provide information about the structure conditions such as strain and temperature. This may allow close monitoring of the composite material and the structure foundation.
Should the material show good performance in the subsea environment, this may encourage the development of full-composite structures. Especially for protection structures, this may greatly improve the lift and ease of installation. The composite material may require additional improvement to allow this to be realized.
References
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