COWI AS STRAIGHT BRIDGE – NAVIGATION CHANNEL IN · ADRESSE COWI AS Grensev. 88 Postboks 6412 Etterstad 0605 Oslo TLF +47 02694 WWW cowi.no OPPDRAGSNR. A058266 DOKUMENTNR. NOT-KTEKA-020

ADRESSE COWI AS

Grensev. 88

Postboks 6412 Etterstad

0605 Oslo

TLF +47 02694

WWW cowi.no

OPPDRAGSNR. A058266

DOKUMENTNR. NOT-KTEKA-020 STRAIGHT BRIDGE_SOUTH – SUMMARY OF ANALYSES.DOCX

VERSJON 1.0

UTGIVELSESDATO 19.02.2016

UTARBEIDET Prosjektgruppen, ledet av Per Norum Larsen

KONTROLLERT Rolf Magne Larssen

GODKJENT Sverre Wiborg

Table of Contents

Summary 5

1 Introduction 7

1.1 Nomenclature and Coordinate System 7

2 Description of Concept - Design Philosophy 9

2.1 Concept 9

2.2 Abutment in Axis 1 9

2.3 Tower in Axis 2 10

2.4 Cable Stays 10

2.5 Bridge Girder 10

2.6 Columns 11

2.7 Pontoons 11

2.8 Abutment at Flua 11

2.9 Mooring System 11

3 Basis for the Design 13

3.1 Functional Criteria 13

3.2 Codes 13

3.3 Permanent and Variable Loads 14 3.3.1 Permanent Loads 14 3.3.2 Traffic Loads 14 3.3.3 Temperature Loads 16

STRAIGHT BRIDGE – NAVIGATION CHANNEL IN SOUTH

NOT-KTEKA-021 CURVED BRIDGE_SOUTH – SUMMARY OF ANALYSES 2/159

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3.3.4 Wind Loads 16 3.3.5 Wave and Current Loads 19 3.3.6 Tidal Variations 20

3.4 Accidental Load Cases 20 3.4.1 Ship Impact 20 3.4.2 Flooding of Pontoons 22 3.4.3 Loss of Stay Cables 22

3.5 Material, Load and Combination Factors 23 3.5.1 Material Factors 23 3.5.2 Load Factors and Load Combinations 23 3.5.3 Combination Factors (Correlation) 24

3.6 Additional Project-Defined Motion Criteria 25

3.7 Mooring Design Procedure 26

4 Analyses 28

4.1 ULS 28

4.2 Ship Impact 31

4.3 Simplified Wave Analysis Model in the Frequency Domain 31

4.4 Assumptions and Simplifications 32

5 Cross-Sectional Properties 34

5.1 Main Girder 34

5.2 Tower 38

5.3 Stay Cables 45

5.4 Columns 47

5.5 Abutment South 50

5.6 Abutment Flua 52

5.7 Pontoons 54

5.8 Mooring Lines 59 5.8.1 Mooring Line Component Data 59 5.8.2 Fairlead Positions 61 5.8.3 Anchor Locations 62

6 Wave and Wind Response 63

6.1 Eigenmodes 63

6.2 Wave Response 68 6.2.1 Screening 69 6.2.2 Discussion of Screening Results 72 6.2.3 Second Order Load Effects from Waves 74 6.2.4 Damaged Condition – Two Compartments Filled 74

6.3 Wind Response 74

6.4 Movements and Accelerations 78


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7 Mooring System 82

7.1 General 82

7.2 Mooring Line Characteristics 82 7.2.1 Pretension 82 7.2.2 Catenaries 82 7.2.3 Individual Line Tension due to Pontoon Displacement 84 7.2.4 Mooring System Stiffness 84 7.2.5 Effects of Non-Linear Mooring System Stiffness 85

7.3 Capacity Check 87 7.3.1 Environment 87 7.3.2 Marine Growth 87 7.3.3 Material Factor, Load Factors and Load Combination Factor 87 7.3.4 ULS - Calculation of Maximum Line Tension 87 7.3.5 ALS - Calculation of Maximum Line Tension 90

7.4 Anchor Loads 90

7.5 Angle with Vertical 91

7.6 Further Work 92

7.7 Gravity Anchor 92

8 Design 96

8.1 Girder 96 8.1.1 ULS Forces and Moments 96 8.1.2 Stress Control in ULS – Cross-Sections used in Analyses 105 8.1.3 Stresses – Updated Cross-Sections 109 8.1.4 Comparison of Stresses Extracted by Combination Factors vs Directly Extraction from Time-Series in OrcaFlex 111

8.2 Tower 112 8.2.1 Tower cross beam 113 8.2.2 Tower Foundation 115 8.2.3 Bearings 116 8.2.4 Construction Stages 117

8.3 Stay Cables 120 8.3.1 Stay Cable Forces 120 8.3.2 Design of Cables 122

8.4 Columns 124

8.5 Abutment South 126 8.5.1 Bridge Girder Connection 126 8.5.2 Foundation on Rock 127 8.5.3 Caisson 128

8.6 Abutment North (Flua) 131 8.6.1 Bridge Girder Connection at Flua 131 8.6.2 Foundation on Seabed at Flua 133 8.6.3 Caisson at Flua 134

8.7 Pontoon 136


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9 Ship Impact 138

9.1 Head-on-Bow Collisions with Bridge Pontoons 138

9.2 Head on Bow Collision with Bridge Pontoon, Local Design 146

9.3 Deckhouse Collision - Local Design of Bridge Girder 146

9.4 Deckhouse Collision – Global Response 146

10 Correlation between Wind and Wave Response 147

10.1 Method and Results for Combination Factors 147

10.2 Description of Analyses 152

11 Benchmarking – OrcaFlex Wind Module 153

11.1 Description of Models 153

11.2 Comparison of Static Wind Results 153

11.3 Comparison of Dynamic Wind Results 155

12 Concluding Remarks 157

12.1 Key Challenges 157

12.2 Robustness 157

12.3 Improvements 158

12.4 Uncertainties 159

13 References 159


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Summary In this project we have shown that it is feasible to design a floating bridge structure for the crossing of Bjørnafjorden, given the available data on climate and accidental conditions. This entails that the floating bridge complies with the criteria for bridge structures given in Eurocode. Due to a lack of available motion criteria in Eurocode for floating bridges, the project group has proposed and implemented additional motion criteria, of which the most restricting criterion is the maximum vertical displacement of 1m due to traffic load, as this constrains pontoon design. The bridge has four lanes, each 3.5m wide, and is designed for a speed limit of 110km/h with a maximum incline of 5%. The floating bridge crosses Bjørnafjorden using mooring lines to seabed. From the abutment at “Flua” in the north to the abutment on land in the south the distance is approximately 4500m. The bridge girder is straight in the horizontal plane and consists of a single steel box, which for the floating part is supported by concrete pontoons spaced at 203 m. In the south end, the girder is supported by a cable-stayed bridge with a main span of 450m to provide for the required navigation channel placed just outside Svarvahelleholmen. The bridge girder is monolithically connected to the abutment in south, a prerequisite from SVV. In north at Flua, the bridge girder is allowed to move in the longitudinal direction only. Here the girder is fixed for rotation using an arrangement of sliding bearings. An A-shaped tower supporting the cable-stayed bridge is founded on Svarvahelleholmen. The tower is 215 m tall and made of concrete. The bridge girder is supported transversally and vertically at tower using sliding bearings. Thus, no imposed loads from temperature are induced in tower. The mooring system consists of 18 mooring lines. Six mooring lines are connected to pontoons 3, 9 and 15 (axis 5, 11 and 17). The mooring lines consist of bottom chain, wire and top chain. Data on soil-conditions are currently of a high degree of uncertainty. Anchor locations are therefore expected to change and the mooring system has not yet been optimized. The analysed mooring system satisfies the capacity check. The design is based on the limit state method. The partial factor method according to Eurocode NS-EN 1990 is the basis for the design process. Structural design of bridge girder is governed by ULS combination of permanent loads with dominant environmental loads with 100year return period. Most of the estimated cost of the floating bridge is connected to the cost of steel in the bridge girder. Thus, optimization of induced moments from environmental loads is an important driver. Permanent loads are also important and utilize approximately 50% of the bridge girder capacity. Wave loads induce large moments about bridge weak axis. Wind loads induce moments about bridge weak axis with roughly half the magnitude of the moments from waves. About bridge strong axis the wave and wind induced moments are of similar magnitude and are governing for abutment and tower design. Ship impact (ALS), only affects structural design of the bridge girder locally in connections between columns and bridge girder. However, ship impact loads govern the design of the pontoon walls, giving a wall thickness of 1.1m, which significantly contributes to the large pontoon displacement of 18kte. For other structural parts (abutments, columns, tower) the loads from ship impact have been of the same magnitude or lower than the ultimate limit state loads. Wave conditions are based on fetch analysis for local wind driven seas and swell is derived from diffraction analysis of the 100year extreme storm waves. The 100year maximum significant wave height is 3m with a peak period of 6s. These waves are due to local winds from a sector North-West to South-West. Waves from north and south are limited to a significant wave height of 1.6m with a peak period of 4s. Ocean swell waves have to pass through two straits before reaching the location. Due to large diffraction effects swell seas are limited to a significant wave height of 0.4m for peak periods between 12-16s and 0.2m for 17-20s. Two 100year design sea states, from West and North-West, each consisting of two wave trains are based on screening of wind driven waves and swell waves separately. As for wind conditions Eurocode is used, giving a mean wind of 31.7m/s at a height of 10m with frequency spectra derived from 10min wind time series. Spatial covariance is accounted for based on regulations defined by SVV. Global response from wave and wind is analysed separately and combined with combination factors. The combination factors are quantified by simultaneous wind and wave analysis in the time domain. Wave analyses are performed in the time domain taking into account geometric and hydrodynamic non-linear effects. Wind analyses are performed in the frequency domain. Geometrical non-linear effects are taken into account by extracting axial loads from permanent geometrical non-linear analyses in the time domain. The characteristic wave and wind loads are extracted by subtracting the nominal response due to permanent loads. This is because permanent and environmental loads shall be combined with different load factors.


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In order to minimize weak axis moments, one has to look at pontoon/bridge interaction in waves. The key to pontoon optimization is to ensure that eigen modes inducing moments about bridge weak axis are not triggered. There are two effects that can trigger eigen modes in the bridge weak axis system; Heave motion of the pontoons and pendulum motion due to pontoon surge motion. Heave affects the total bridge, while pendulum motion affects only the high part of the floating bridge. Therefore optimization toward minimizing moments from heave is prioritized. In order to ensure that the lowest heave eigen period is above wind driven seas the added mass is increased by attaching a flange to the pontoon. With the flange attached the full range of possible heave motion eigen periods is limited to between 7.8s and 10.8s, which is in a range where wave loads are minimal. In comparison, the same pontoon without the flange attached has a range of possible heave motion eigen periods between 6.4s and 8.9s, which is in a range where wave loads are significant. In addition, having a large water plane area reduces the span of eigen periods, thus making the design more robust toward changes in wave climate. Another factor adding to the robustness with the proposed design is the flexibility to changing the added mass by changing the flange width. In-place, if the actual wave climate differs from the design wave climate, an additional heave plate can be attached to the structure, ensuring that the heave added mass is sufficient. It should be noted that given a design where pontoon/bridge interaction is so critical, the accuracy of hydrodynamic pontoon properties should be assessed in a tank test, especially 2nd order wave drift and viscous effects. The pontoon flange is especially critical to assess. As for wind response the most important effect is moments about bridge girder strong axis, which are dominated by the first four eigen modes ranging from 32.5s to 78.3s. These modes are slowly varying with virtually no damping, and might cause a challenge for fatigue. Based on a study comparing linear and non-linear mooring stiffness with regards to response, it is found that used linearization of the mooring stiffness leads to conservative moments about bridge girder strong axis. Since data on wind climate is not yet available, region specific wind data from Eurocode is implemented, where frequency spectra are derived from 10min wind time series. Due to the long natural vibration period of the structure, classical formulation for obtaining dynamic wind response due to buffeting load might not give accurate results, as wind statistics is normally based on 10minute events. It is suggested that the effect of long natural vibration period in relation to the wind spectra and coherence function is studied in more detail at a later stage, and that the wind measurement at site is used to identify proper wind parameters. The initial studies performed, indicates that the used procedure produces conservative load effects. A study has been performed to identify stability issues for the structure. Among other things the possibility of vortex induced vibrations was addressed, and it was found that for the current configuration it is not expected that vortex shedding will be a problem, mainly due to the mass of the structure. With respect to flutter onset velocity the study concludes that aerodynamic derivatives for the cross section are needed before any conclusion can be made. No problems in relation to galloping or divergence were identified. Thus, based on the current knowledge the structure is aerodynamically robust. From the ship collision risk analysis, three events have been identified as potential risks for the concept, namely: head-on-bow collisions with bridge pontoons, deckhouse collision with bridge girder and head-on-bow collisions with bridge girder. The latter event is mitigated by ensuring that the bridge girder is placed high enough to avoid such collisions. The deckhouse collision is assumed to be a minor issue, evaluated from both local static considerations and global response analysis for the curved bridge concept. The key challenge is related to head-on-bow collisions with bridge pontoons, with resulting energies from Monte-Carlo simulations at 300MJ for axis 3 and 110MJ for other axes. The event is analysed by global response analyses of eccentric and centric impacts at each axis, as well as local dimensioning of pontoon walls. In order to ensure robustness against a change in loads from head-on-bow collisions with pontoons, due to changes in impact energies, two measures have been identified. First, increasing pontoon displacement decreases significantly the dynamic response in bridge during impact for axis 3-21. Secondly, a large fraction of the ship impact load acts in the connection between girder and column and reinforcement in this part will significantly increase robustness without much added steel weight.


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1 Introduction

The work presented in this report has been performed by a project group with COWI, Aas-Jakobsen, Johs Holt and Global Maritime as the main contributing companies. This report presents the main findings for a straight bridge with navigation channel in south. Marine operations and construction methods are presented in a separate document: /5/ NOT-MO-003 Method Statement, Bridge with Navigational channel in South.

An overall description of the concept is presented in chapter 2, with emphasis on important decisions for design. In chapter 3 the basis for the design is outlined. The reason for not calling this chapter design basis is that some results are presented and that a detailed design basis is a separate document, ref /1/ RAP-GEN-001 Design basis. Chapter 4 presents the analyses procedure and numerical models, with a list of important assumptions and simplifications. Cross-sectional properties are found in chapter 5. Important results from wave and wind response analyses are given in chapter 6. Mooring system design is covered in chapter 7. The design check in ULS is presented for main structural components in chapter 8, as well as ALS check for tower and abutments. The design check in ALS for other main components are found in chapter 9, Ship impact. In chapter 10 a study investigating the correlation between wind and wave response is presented. Finally, some concluding remarks about key challenges, robustness, improvements and uncertainties is given in chapter 12.

1.1 Nomenclature and Coordinate System

Figure 1-1: Nomenclature overview of whole bridge

Bridge girder Load effects (refers to local bridge axis) - Axial force (Nx) - Shear force vertical (Qy) - Shear force transverse to bridge axis (Qz) - Torque (Mx) - Bending moment about strong axis (My) - Bending moment about weak axis (Mz) Global displacements and accelerations (refers to global orientation) - Displacement west/east - Displacement vertical - Rotation about north/south axis


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- Acceleration west/east - Acceleration vertical - Rotational acceleration about north/south axis

Local displacements and accelerations (refers to bridge local axis) - Rotation about bridge axis - Acceleration transverse to bridge axis - Rotational acceleration about bridge axis Pontoons

Global displacements and accelerations (refers to global orientation) - Displacement north/south (surge, 1) - Displacement west/east (sway, 2) - Displacement vertical (heave, 3) - Rotation about north/south (roll, 4) - Rotation about west/east (pitch, 5) - Rotation about vertical (roll, 6) - Acceleration west/east - Acceleration north/south - Acceleration vertical


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2 Description of Concept - Design Philosophy

2.1 Concept The bridge concept presented here crosses Bjørnafjorden using mooring lines to sea bottom. The distance from abutment at “Flua” in north to the abutment on land in south is approximately 4500m. The concept is based on a bridge girder which is straight in the horizontal plane. The bridge girder consists of a steel box with stiffeners. The bridge girder is supported by pontoons at spacing of 203 m. In the south end, the girder is supported by a cable-stayed bridge.

The cable-stayed bridge in south has a main span of 450 m to provide for the required navigation channel placed just outside Svarvahelleholmen. The main elements of the high bridge consist of abutment at axis 1, tower at Svarvahelleholmen at axis 2, bridge girder with a back span of 310 m and main span of 450 m and stay cables in back and main span.

North of the cable stayed bridge the girder descends from approx. 51 m at axis 3 to 18 m over a length of approx. 1000 m and continues at an elevation of 18 m to the abutment at Flua. Floating pontoons at 203 m spacing support the bridge girder. This part of the bridge consists of bridge girder, columns in 18 axes, pontoons in 18 axes and abutment at Flua.

Figure 2-1: Straight bridge with ship passage in south, top and side view

2.2 Abutment in Axis 1 The bridge girder is monolithically connected to the abutment, which is approximately 40 m long. The abutment must have sufficient weight to counter for uplift forces from stay cables arising from the longer main span and from forces arising from environmental loading. The bridge girder goes all the way to axis 1.


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Beneath the girder, a 40 m long concrete caisson is placed and is filled with sand/gravel ballast. The bridge girder is fixed to the caisson using shear studs.

2.3 Tower in Axis 2 The tower consists of an A-shaped tower made in concrete and founded on rock on Svarvahelleholmen. The total height of tower is 215 m. Earlier investigation has shown that fixed end abutment attracts large bending moments about vertical axis from wave and wind loads. Thus, it was decided to introduce transversal support between tower and bridge deck in order to take such a moment as a force couple between tower and abutment. Thus, two 30 MN multi-directional elastomeric pot bearings are used to support the bridge girder in the transverse direction. Since the girder is fixed to abutment in axis 1, it is be beneficial to support the girder on sliding bearings at tower in order to eliminate imposed loads from temperature action. Two 20 MN multi-directional elastomeric pot bearings are placed on the cross beam of tower to support the bridge girder.

2.4 Cable Stays The back span and main span are supported by 2 planes of stay cables. There are 72 stay cables in total – 2 x 18 stays on each side of tower. The stay cables support the bridge girder every 20 m. It is suggested to use stay cables consisting of high strength steel strands (S1860), each with steel area of 150 mm2, which is individually galvanized, waxed and sheathed. The bundle of strands is covered by an external HDPE pipe equipped with small helical ribs. The problem with cable vibration can be solved by installing dampers at cable ends.

In Eurocode the stay cables can be utilized to 56 % of the tensile strength of the steel cables in ULS. For a traditional stay cable bridge the stays are usually utilized to 40 % of the breaking strength due to permanent loads only. However, due to the recently increase in load factor for permanent load from 1.2 to 1.35 and that the stay cables in a floating bridge is subjected to wave forces, the utilization ratio for permanent loads should be decreased. In initial design the stay cables dimension were determined using a utilization ratio of 28 % due to permanent loads. The resulting cable areas are then put into the analysis and response from permanent, traffic, wind and wave are combined to give ULS forces which is controlled for allowable stresses.

Results show that stay cables ranges from 25 to 59 strands based on initial hand calculations. The analysis results show that the inner cables must be increased to 27 strands and out outer to 60 strands. The analyses are not re-run after this change.

2.5 Bridge Girder In the cable stay bridge the back span is 310 m long and main span is 450 m long. The height of bridge section in back span and main span is 3.5 m. For the floating bridge the height of the cross-section is 6.5 m giving a span / height ratio of 31. Results show that permanent loads utilize approximately 50% of the ULS capacity at support sections. The thicknesses of plate and stiffeners vary along the length of bridge. The plate thickness varies from typically 12-14 mm in span section to 24mm at support section. The thickness of longitudinal stiffener vary from 8-12 mm. Transverse stiffeners are placed in steel box at approximately each 4 m. Steel quality of S460 is chosen for the bridge girder.

.


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2.6 Columns The bridge girder is supported by one column at each axis. All columns are made of steel and have a diameter of 10 m. The columns are governed by ship impact and by wave loading in ULS conditions.

2.7 Pontoons The floating bridge is supported by 18 equal pontoons with spans of 203m. The pontoons are made of light weight concrete of density class 2.0. The total height is 14 m with 10 m draft. In the analyses a draft of 10.5m is used. The freeboard of the pontoons are 4m. The displacement is approximately 18 000 tons. This is the same pontoon that were used for the curved bridge. The straight bridge has a lighter bridge-girder, than the curved bridge, therefore could the pontoons have a smaller displacement. This amounts to approximately 2000 tons.

The submerged boundaries of pontoons shall be watertight. To ensure this the bottom slab is prestressed in both directions, the outer walls are prestressed vertically and the upper part of outer walls are prestressed horizontally. In order to get the best effect, the prestress is applied before top slab is casted.

Concrete thicknesses, prestressed reinforcement and normal reinforcement are governed by hydrostatic and hydrodynamic pressure, permanent loads, creep & shrinkage and temperature gradients. In addition local ship impact governs the large wall thickness of 1.1m short side and 0.6m long side.

The pontoon has a 5 m flange at the bottom with the purpose of increasing the added mass in heave. This will improve the heave motion of pontoons from wave action due to a shift in heave eigenperiod.

Please refer to the pontoon optimization study in chapter 6 in /8/ NOT-KTEKA-021 Curved bridge South – Summary of analysis for a description of the pontoon design philosophy.

2.8 Abutment at Flua In north the bridge is monolithically connected to the abutment at Flua. The abutment is founded on 40 m depth and it consists of a caisson structure made of concrete with dimension 48 x 28 x 50.5 (L x W x H). The caisson is filled with sand/gravel ballast in order to withstand the large end moments from bridge girder. The bridge girder is fixed to the caisson trough shear stud connection.

Governing loading comes from the fixed end moment about vertical axis due to wave and wind loading. This moment is approximately 6 000 MNm, see section 8.1.1, dominated by wave loads and using a combination factor of 0.6 to represent simultaneous wind response. The factor of 0.6 is considered to be conservative as discussed in Chapter 3.5.3.

The large moment is taken by friction between caisson bottom slab and rock. A friction factor of 1/1.3 = 0.77 will be used.

2.9 Mooring System The mooring system consists of 18 mooring lines. Six mooring lines are connected to pontoons 3, 9 and 15 (axis 5, 11 and 17). The mooring lines consist of 100m bottom chain, 641m / 641m / 920m wire and 20m top chain.

There is high uncertainty related to the data on soil-conditions, and therefore the recommended anchor locations are expected to change. Because of this uncertainty and for modelling simplicity, the mooring system is modelled symmetric about both horizontal pontoon axes. The anchors for the mooring lines


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connected to pontoons 3 and 9 are located at a depth of 500m. The anchors for mooring lines connected to pontoon 15 are located at a depth of 350m, more appropriate for the location. The system is very not sensitive to changes in anchor location.

The components in the lines are designed for a minimum lifetime of 25 years. The inspection and maintenance related to this is covered in a separate document, see /9/ NOT-GEN-004 Operation and maintenance - Moorings.

The mooring system shows a non-linear characteristic, especially for large offsets (5-10m). This is because of the large self-weight of the mooring lines when accounting for marine growth (assuming no removal), and the high safety factors for moorings recommended by client. The safety factors are considerably higher than the project group anticipated.


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3 Basis for the Design

3.1 Functional Criteria The functional criteria are listed in Table 3-1.

Table 3-1: Functional criteria

Summary of functional criteria Description

Design road class H8

Design traffic volume 12000-14000 ÅDT (2040)

Speed limit 110 km/h

Carriage way with 4 lanes each 3.5m wide

Shoulder 1.5 m on both sides

Pedestrian lane 3m wide

Minimum horizontal radius 2350m

Min radius in a sag curve 3800m

Max radius of crest at shipping channel 14100m

Max radius of crest other places 20356m

Max incline 5%

Free-board pontoons 4m

Navigation channel 400m x 45m

Free clearance low bridge 11.5m (chosen)

Guard rail Strength class H2, working width 1m

Protective wind screen Not used

Structural weight contingency 4% of structural weight

3.2 Codes The design performed for this bridge is primarily based on the rules and regulations given by the bridge owner the Norwegian Public Road Administration (NPRA), i.e. the NPRA Handbooks. The most important of these being:

N100 Veg og gateutforming

N400 Bruprosjektering

The basis for these NPRA regulations is that design shall be performed based on the limit state method using partial factors according to the Norwegian Standard NS-EN199X, X being a figure from 0 to 9. The most important of these being:

EN 1990 Basis of Structural Design

EN 1991 Actions on structures

EN 1992 Design of concrete structures

EN 1993 Design of steel structures

For infrastructure the Eurocode system concerns structures fixed to ground. As this bridge is partly floating Eurocode is therefore not adequate and some rules and regulations from DNV are used as a supplement.


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Mooring design for the bridge will be performed based on the procedures as outlined in NS-EN ISO 19901-7:2013 and DNV-OS-E301 Position Mooring.

3.3 Permanent and Variable Loads

3.3.1 Permanent Loads Permanent loads due to bridge girder mass are applied according to Table 3-2. The plate thicknesses of the bridge girder have been updated in the final design, for some of the sectional lengths. The upgrade leads to a slight increase of the loads, ref Table 5-2. Table 3-2: Permanent loads applied on bridge-girder. (For explanation of cross-section types, see Chapter 5.1.)

Cross-section type H1 H2 S1 F1

Total girder weight [kN/m] 120.6 208.2 190.2 138.9

Asphalt, railings etc [kN/m] 54.3 54.3 54.3 54.3

Total permanent load [kN/m] 174.9 262.4 244.4 193.1

Self-weight of columns, pontoons and tower are included in the analysis. In the analysis, the permanent loads will be in equilibrium with the buoyancy of the pontoon such that the bending moments in girder will be similar to a bridge founded on ground. The stay-cables in the high bridge are pre-tensioned with the aim of minimizing the bending moments in the girder and tower due to permanent loads. The construction phases of the high bridge are analysed with simplified methods. The aim of the analysis is to introduce the correct final forces into the bridge from permanent loads and not to study required cantilever heights during construction. The final forces in bridge will to a large extent be independent of the construction method.

3.3.2 Traffic Loads LM1 is used for elements with influence lengths up to 500 m. This load case is governing for most of the structural elements, except for roll movement of girder for which LMV (defined on page 15) should be used.

Eurocode – LM1

An Illustration of the LM1 load case can be found in Figure 3-1.

Figure 3-1: Eurocode Traffic – example of leftmost adjusted.


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17 ∙ 2.5 / 3 ∙ 5.4 / 58.7 /

The carriage way width is 2x8.5m plus pedestrian/cycle path of 3m. The total distributed traffic load is 58.7kN/m. Calculation of the equivalent line loads for the uniformly distributed traffic loads are given in Table 3-3.

Table 3-3: Calculation of equivalent line loads for the uniformly distributed traffic loads.

Placement Axial loads [kN] Equivalent line loads [kN/m]

Notational lane nr. 1 2 300 5.4 / ∙ 3 16.2 /



Rest area 2.5 / ∙x

Pedestrian/cycle path 2.5 / ∙ 3 7.5 /

LMV

This traffic load is used for elements with influence length longer than 500m. Traffic lanes are located at the center of each lane of the road. The total distributed load is 38 kN/m.

4 ∙ 9 / 2 / 38 /

Figure 3-2: LMV Traffic.

Table 3-4 Load intensity LMV traffic

Equivalent line loads Description 9 / All traffic loading

2 / Pedestrian/cycle path


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3.3.3 Temperature Loads From design basis document constant temperature loads are:

T max = 32 ˚C

T min = -22 ˚C

Which gives +5 ˚C +/- 27 ˚C

It is optimal to have zero imposed stress in girder at temperature +5 ˚C, such that the stresses from max and min temperature are equal.

In addition to the constant temperature, there can be a temperature difference between top and bottom face of 18˚C.

Since the bridge girder is free to translate in global x direction at the bridge tower and at Flua, the girder will not receive any constraining forces due to uniform temperature variation, besides from the cables. The response from temperature is therefore believed to be insignificant for the girder.

The tower, cables, girder and columns is not exposed to temperature loads in the analysis (gradient or uniform loads), to verify that the response from temperature load is small.

3.3.4 Wind Loads Wind loading is based on the current codes, NS-EN 1991-1-4:2005, including national appendix NA:2009, as well as supplementation from experiences obtained from similar projects carried out in Norway.

No measurements of wind climate have been available when the design basis for this project was established. Some simulations of the wave climate have been performed and these indicate that the climate taken according to the code may be conservative, ref. Figure 3-3

Further investigations related to wind climate must be performed when results from wind measurements are available.

The mean wind is given in the table below.

Table 3-5: Mean wind at Bjørnafjorden

Return period Velocity at 10 m [m/s] Velocity at 52 m [m/s] 1 22.9 28.4

100 31.7 39.3

For analysis with 1year wind, instead of a separate analysis, results from analysis with 100year wind can be multiplied with a factor of 0.5. This assumption is based on the following equation.

0.52 0.5

Mean wind and turbulence intensity is assumed to vary with height as the red line in Figure 3-3.


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Figure 3-3: Mean wind velocity and turbulence intensity variation with height as applied in analysis (Red line) and from simulations of wind from three different directions (blue lines)

Mean wind force, Fm(z), is calculated using the following equation:

12∙ ∙ ∙ ∙ ,

For simplified calculations a static gust load can be calculated using the wind gust velocity by the following equation:

1 7 ∙ ∙

This gives the following drag forces on bridge girder for 100-year wind.

Table 3-6: Drag forces on bridge girder for 100-year wind

Section Fm Fq CD Vm Iu* H Z

[kN/m] [kN/m] [m/m] [m/s] [m] [m] Main bridge - top 1.8 3.3 0.529 39.3 0.117 3.5 52.0 Main bridge - low 5.3 9.7 0.867 38.9 0.117 6.5 47.5 Side span 4.0 7.2 0.867 33.6 0.117 6.5 15.0

*See chapter 5.2 and 6.4 in NOT-HYDA-018-Curved Bridge for details on calculation of turbulence intensity

The frequency distribution of the turbulence is described by the Kaimal spectrum for the along wind component in NS-EN 1991-1-4:2005. The remaining components are not described in the code, but NPRAs Handbook N400 gives some additional information.

The following plot shows the normalized Kaimal spectrum for the along wind component u with frequency n for a mean wind velocity 39.3m/s and height z=52m.


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Figure 3-4: Kaimal energy spectrum for the along wind component (wind velocity = 39.3m/s, height = 52m)

The statistical dependence between the turbulence components at two points for a given frequency shall be described by a co-spectrum. The following plot shows the co-spectrum for the along wind component u with distance ∆y between the points and frequency n for a mean wind velocity 39.3m/s and height z=52m.

Figure 3-5: Co-spectrum for the along wind component u at two points with distance ∆y and frequency n for a mean wind velocity

39.3m/s and height z=52m


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3.3.5 Wave and Current Loads Wave conditions are based on fetch analysis for local wind driven seas and diffraction analysis of the 100year extreme storm waves to derive swell. The 100year maximum significant wave height is 3m with a peak period of 6s. These waves are due to local winds from a sector North-West to South-West. Waves from north and south are limited to a significant wave height of 1.6m with a peak period of 4s. Ocean swell waves have to pass through two straits before reaching the location. Due to large diffraction effects swell seas are limited to a significant wave height of 0.4m for peak periods between 12-16s and 0.2m for 17-20s. Table 3-7 gives the 100year sea state scatter diagram. Table 3-7: 100 year sea-state scatter diagram. NB: between Tp=6s and Tp=12s sea states with Hs=0.2m are

applied Hs[m] Tp [s]: 3.0 4.0 5.0 6.0 12.0 14.0 16.0 17.0 18.5 20.0Wave dir: Wave dir [deg]: N 180 0.9 1.6 na na na na na na na na N-NW 202.5 0.9 1.6 2.5 na na na na na na na NW 225 0.9 1.6 2.5 3 0.4 0.4 0.4 0.2 0.2 0.2 W-NW 247.5 0.9 1.6 2.5 3 0.4 0.4 0.4 0.2 0.2 0.2 W 270 0.9 1.6 2.5 3 0.4 0.4 0.4 0.2 0.2 0.2

Figure 3-6: JONSWAP Spectrum for scatter diagram

A fetch analysis with 1year wind has been performed. Instead of running a separate analysis, results from analysis with 100year waves are multiplied with a factor of 0.5. This assumption is based on the following equation.

1.53

0.5

The fetch analysis gives a Tp of 4.4s, while we have chosen to scale from Tp=6s. The validity of this assumption has not been considered.


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Static loads Table 3-8 gives the 100year current velocity. For cross current it may be assumed that Vc = 2/3V0. Table 3-8: 100 year current velocitiy

Depth (m) 100 year Current velocity V0 [m/s]

0-5 0.70

Table 3-9: 100 year current and wave drift loads for each pontoon

Load Case Fx [kN] Fy [kN]

Current 270deg, 0.70 m/s 0.0 44.4

Current 270deg & 90deg, 0.47 m/s 0.0 19.7

Mean drift 180deg, Hs=1.6, Tp=4 68.3 0.0



As is evident from Table 3-9, current loads are so small compared to first order wave forces that they can be neglected for simplicity.

3.3.6 Tidal Variations The tidal variation given in the design basis /1/ is +/- 0.75 m from mean sea level. In the analysis +/- 1m will conservatively be used. The bridge road profile is defined at mean sea level. Thus, no imposed loads will be induced in the girder at this condition.

If tidal variations lead to a sea level different from mean sea level during installation, the pontoons at the ends of the free floating girders will be ballasted to align with the part supported by abutments. The bridge must be ballasted such that the two parts align perfectly. After connection the pontoons will be re-ballasted to the same level as before connection. In this way no imposed loads is induced in bridge girder at mean water level.

To simulate tidal variation of 1 m, the load to be applied to each pontoon equals the vertical water plane stiffness (C33) multiplied by 1 m, which is +/-17 447 kN.

3.4 Accidental Load Cases

3.4.1 Ship Impact Head-on-bow Collisions with Pontoons The impact energy distribution for the bridge axes has been estimated by Monte Carlo simulation of the ship traffic in area conducted by SSPA, ref /7/, and is presented in Table 12. Ship collisions with impact energy above these alternatives have an annual probability of exceedance less than 10-4. Alternative 4 is used for the final design. Table 3-10: Impact energy alternatives for head-on-bow collisions with bridge pontoons Alternative 1 Alternative 2 Alternative 3 Alternative 4

Axis 3 340 420 360 300 MJ Axis 4 120 160 110 110 MJ Axis 5 90 70 90 110 MJ Axis 6 90 70 90 110 MJ


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Axis 7 90 70 90 110 MJ Axis 8 90 70 90 110 MJ Axis 9 90 70 90 110 MJ Axis 10 90 70 90 110 MJ Axis 11 90 70 90 110 MJ Axis 12 90 70 90 110 MJ Axis 13 90 70 90 110 MJ Axis 14 90 70 90 110 MJ Axis 15 30 30 90 110 MJ Axis 16 30 30 90 110 MJ Axis 17 30 30 90 110 MJ Axis 18 30 30 90 110 MJ Axis 19 30 30 90 110 MJ Axis 20 30 30 90 110 MJ Axis 21 30 30 90 110 MJ

The indentation curve in Figure 7 has been determined to be representative for the design ship through a study conducted at NTNU, ref /5/ 1. To account for a possible effect of ice-strengthening for future vessels, the indentation curve used in the analysis is multiplied by a factor of 2. 1

Figure 3-7: Indentation curve for design ship for ship impact accidental load case For local design of the pontoon concrete wall the following pressure-area relation is proposed through a study at NTNU, ref /5/: 18 . , and is used in project. The maximum force is limited by the peak force from the indentation curve in Figure 3-7 multiplied by a factor of 2, as explained above. Deckhouse Collision For local evaluation of the bridge girder client has proposed using a static load of 25 MN, distributed over a length of 29 m. The load corresponds to a dissipated energy of 700 MJ uniformly distributed over a deckhouse indentation length of 29 m. 700 MJ is the maximum deckhouse dissipation energy identified from the Monte Carlo simulations conducted by SSPA, ref /7/. In the report by SSPA the deckhouse indentation curve is from Ship collision with bridges by O.D.Larsen. NOTE: A local design check has not been performed for the straight bridge, please refer to the curved bridge report /8/ for method and results. The results are assumed to be in the same magnitude.

1 The study at NTNU evaluated impact between striking ship and bridge pontoon for the design ships recommended by SSPA, a container ship and cruise ship. The purpose was to evaluate indentation curves and a pressure area relation for local design. The indentation force is higher for the container ship, and therefore it is used in all ship impact analyses.


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For the global response evaluation a rectangular impulse load with a peak force of 15 MN, distributed over 15 m, is considered. This is equivalent to what was considered in the Storebælt project.

3.4.2 Flooding of Pontoons Pontoons chambers may accidentally be filled, for instance due to ship collision. In that condition the bridge shall withstand 100year environmental loads.

In order to analyse this accidental case, the bridge is subjected to 100year environmental loads from waves and capacity is checked with all material and load factors set to 1.0. Two compartments are filled for one pontoon. Seven individual analyses are performed for filling of each of the first seven pontoons.

Two different scenarios exist:

1. Two of the large compartments near the centre of the pontoon are flooded (due to an impact to the long side of the pontoon). This case gives the largest flooding in terms of flooded water volume.

2. Two compartments at the short end of the pontoon are flooded (Due to an impact to the short side of the pontoon). This case gives the largest alteration of the roll stiffness.

For the first case, the pontoon looses 10% of its heave stiffness and displacement. See table below.

Table 3-11: Heave stiffness and volume of pontoon for intact and damaged condition for case 1

C33 intact C33 damaged Displacement intact Displacement damaged 17.5 MN/m 15.7 MN/m 17.8 kte 16 kte

Due to only minor changes in the eigen period of the damaged pontoon, there are no significant consequences with respect to dynamic loads in the bridge girder. Some more green sea on deck will occur since the new equilibrium position reduces the freeboard with 1m. More results and elaboration on this is given in section 6.2.4.

3.4.3 Loss of Stay Cables The bridge structure shall withstand a loss of any stay cable.


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3.5 Material, Load and Combination Factors

3.5.1 Material Factors An overview of the material used for main elements of the bridge is given in the table below. Material factors are taken from the relevant Eurocode.

Table 3-12: Description of materials and material factors used in the bridge

Main elements Material Quality Material factor (ULS)

Material factor (ALS)

Bridge girder Steel S460 1.1 1.0

Columns Steel S460 1.1 1.0

Stay cables Steel cables S1860 (VSL SSI 2000-C or D) 1.2 x 1.5 = 1.8

1.8

Abutment axis 1 Concrete B45 1.5 1.2

Abutment at Flua Concrete B55 1.5 1.2

Pontoons Concrete LB55 (Density class 2.0) 1.5 1.2

Tower axis 2 Concrete B55 1.5 1.2

Rebar in concrete B 500 NC 1.15 1.0

Prestress in concrete S1860 1.15 1.0

3.5.2 Load Factors and Load Combinations Load factors are taken from NS-EN 1990:2002/A1: 2005/NA:2010. The load factors for the ULS condition are given in chapter 7.2.2 of Design basis.

Table 3-13: Load combination for ULS (comb B) Dominant loads (γ x Ψ0) G-EQK Q-TrfK Q-TempK Q-EK(1y) Q-EK(100y) QK Permanent loads G-EQK 1.35/1.0 1.2/1.0 1.2/1.0 1.2/1.0 1.2/1.0 1.2/1.0 Traffic loads Q-TrfK 0.95 1.35 0.95 0.95 - 0.95 Temperatur loads Q-TempK 0.84 0.84 1.2 0.84 0.84 0.84 Enviromental loads with traffic Q-EK(1y) 1.12 1.12 1.12 1.6 - 1.12 Enviromental loads without traffic Q-EK(100y) - - - - 1.6 - Other loads QK 1.05 1.05 1.05 1.05 1.05 1.5 * γ is load factor in accordance to table NA.A2.4(B) i NS-EN 1990:2002/A1:2005/NA:2010. Ψ is combination factor in accordance to table NA.A2.1 i NS-EN 1990:2002/A1:2005/NA:2010

Only one load combination is considered for the serviceability limit state, namely infrequent combination given in Chapter 7.2.4 in the design basis /1/. This combination reflects a one year return period and will be used to evaluate tightness and crack width criteria of concrete pontoons. Table 3-14: Load combinations for the rarely occurring serviceability limit state Dominant loads (Ψ0) Q-TrfK Q-TempK Q-EK(1y) QK Permanent loads G-EQK 1.0 1.0 1.0 1.0 Traffic loads Q-TrfK 0.8 0.7 0.7 0.7 Temperatur loads Q-TempK 0.6 0.8 0.6 0.6 Enviromental loads Q-EK(1y) 0.75 0.75 1.0 0.75 Other loads QK 0.6 0.6 0.6 0.8

Static wind, dynamic wind and wave loads are treated as one load group, called environmental loads, for which the combination factors described in the next chapter are applied. Current loads induce small


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responses for this concept and are therefore neglected. For dynamic wind response, the characteristic 1 year and 100 year response is found by finding most probable 10-minute maximum.

For dynamic wave response, the characteristic 100 years response is at this stage the average maximum for 10 3 hours simulations multiplied by a factor of 1.25. The factor is used to obtain the 95 percentile 3 hour maximum, which Torgeir Moan at NTNU has recommended to use for the design against wave loads. The characteristic 1 year response is at this stage obtained by using the average maximum for 10 3-hours simulations (100 year conditions) multiplied by a factor of 0.5, see section 3.3.5.

In normal operating condition in ULS the following load groups are governing for the design of bridge girder, stay cables, columns and tower:

Permanent loads

Traffic loads

Environmental loads.

Each of these are treated to be dominant in each of the three main design combinations for ULS. Response from tidal loads and temperature loads are added with their respective load factor. For bridge open for traffic, one year wave and wind loading is applied.

Table 3-15: ULS Combination table

Perm

Traffic

Temp

Tide Wave 100 year

Wind 100 year

Description

ULS1 1.35 0.95 0.84 1 0.7 * 0.56** Permanent load dominant, 1 yr wave + wind

ULS2 1.2 1.35 0.84 1 0.7* 0.56** Traffic load dominant, 1 yr wave + wind

ULS3 1.2 0 0.84 1 2.0*** 1.6 Wave and wind load dominant (100yr) * Factor of 1.25 applied to get characteristic wave load. Non-dominant action (1.6*0.7=1.12). 1 year wave scaled from 100 year wave with a factor of 0.5. => 1.25 x 1.12 x 0.5 = 0.7 ** Non-dominant action (1.6*0.7=1.12). 1 year wave scaled from 100 year wave with a factor of 0.5. => 1.0 x 1.12 x 0.5 = 0.56 *** Factor of 1.25 applied to get characteristic wave load. Dominant action load factor of 0.6. => 1.25 x 1.6 = 2.0

3.5.3 Combination Factors (Correlation) In this project, the design checks are performed with method one and verified by method two and three below.

1. Maximum characteristic force components from dynamic wave and wind loading are determined from analyses. Force components from wave loading are combined assuming no correlation between them, using a combination factor of 0.4 for the coincidental force component. Characteristic dynamic wind is added using a combination factor of 0.6 on dominating force component. For other force components for dynamic wind, 0.4 is used. Static wind response is considered to be fully correlated with wave and dynamic wind and a combination factor of 1.0 is used.

2. The second method is to extract stresses at selected points in bridge girder directly from the time domain dynamic wave analysis in OrcaFlex and compare it with the stresses extracted by the first method. If the stresses in the last method are higher the combination factors should be increased accordingly. This is done with wave loads and permanent loads only and is a verification of the combination factors for waves. The study has not yet been completed for the straight bridge, and for now it is assumed that the compliance for the curved bridge concept also applies for this concept.

3. Dynamic and static wind is implemented in OrcaFlex, making it possible to extract the combined response from wave and wind loading and estimate combination factors for waves and wind. Analyses


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show that for bending moments about strong axis the combination factor for wind range from 0.0 to 0.6 for dominant wave response. The results from this study are presented in chapter 10.

The combination factors for the bridge girder are given in tables below. Both dominant waves with corresponding dynamic wind and dominant dynamic wind with corresponding waves are considered. For the non-dominant action a combination factor of 0.6 is used.

Table 3-16: Combination factors α for static and dynamic wind and dynamic dominant wave

Dynamic waves Static wind Dynamic wind

Dominant force N Mx My Mz N Mx My Mz N Mx My Mz

Axial force (N) 1.0 0.4 0.4 0.4 1.0 1.0 1.0 1.0 0.6 0.4 0.4 0.4

Torque (Mx) 0.4 1.0 0.4 0.4 1.0 1.0 1.0 1.0 0.4 0.6 0.4 0.4

M strong axis (My) 0.4 0.4 1.0 0.4 1.0 1.0 1.0 1.0 0.4 0.4 0.6 0.4

M weak axis (Mz) 0.4 0.4 0.4 1.0 1.0 1.0 1.0 1.0 0.4 0.4 0.4 0.6

Table 3-17: Combination factors α for static and dominant dynamic wind and dynamic wave

Dynamic waves Static wind Dynamic wind

Dominant force N Mx My Mz N Mx My Mz N Mx My Mz

Axial force (N) 0.6 0.4 0.4 0.4 1.0 1.0 1.0 1.0 1.0 0.4 0.4 0.4

Torque (Mx) 0.4 0.6 0.4 0.4 1.0 1.0 1.0 1.0 0.4 1.0 0.4 0.4

M strong axis (My) 0.4 0.4 0.6 0.4 1.0 1.0 1.0 1.0 0.4 0.4 1.0 0.4

M weak axis (Mz) 0.4 0.4 0.4 0.6 1.0 1.0 1.0 1.0 0.4 0.4 0.4 1.0

The tables above applies for design of girder.

For tower design, simultaneous force components from wave loading are used. Simultaneous wind is in general for the tower treated with a conservative combination factor of 1.0. For the critical part of the tower above and below bridge girder a combination factor of 0.6 is utilized. For design of bearings a combination factor 0f 0.6 on dynamic wind is used.

For design of stay cables full correlation is used between wind and wave responses.

3.6 Additional Project-Defined Motion Criteria In Table 3-18, the most relevant criteria regarding motions are given. These criteria are a result of the functional criteria in Table 3-1, of which the speed limit is particularly governing.

Table 3-18: Motion criteria governing the design Motion Load Criterion Vertical deflection due to traffic 0.7 x traffic Approx. 1 m Rotation about bridge axis (roll) due to traffic 0.7 x traffic 1 deg Rotation about bridge girder axis (roll) due to env. loads 1 year storm 1.5 deg Vertical acceleration 1 year storm 0.5m/s2 Horizontal acceleration 1 year storm 0.3m/s2


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In handbook N400 vertical deformation is limited to L/350 due to traffic, where L is the span length. For a floating bridge the span length is not clearly defined and it can be shown that this criterion is fulfilled for nearly all combinations of pontoon stiffness and girder stiffness, resulting in vertical deformations in the order of 2 to 3 m. Clearly, this is too large and thus the criterion is not suitable for floating bridges. It is instead, decided to limit the vertical displacement of bridge at pontoons to 1 m for 70 % of the characteristic traffic load for this project. Simplified calculations give a minimum vertical pontoon stiffness of: qLM1 x L x 70% / 1m = 58.7 x 203 x 0.7 / 1 = 8.3 MN/m, thus a lower limit of 10 MN/m is chosen for this concept.

The second criterion gives a roll stiffness of approximately 1100 MNm/rad,

The chosen pontoon has a vertical stiffness of approx. 17.4 MN/m and a roll stiffness of 3300-4900 MNm/rad. Hence, the pontoon geometry is not governed by the two first criteria.

The pontoon geometry is not a result of the criteria given above, but has been developed with the required weight of structure and optimization of heave response in mind. Larger pontoon area will tend to increase the lowest heave period. The pontoon area is chosen such that the heave period lies between wind driven waves and swell waves.

3.7 Mooring Design Procedure Mooring design for the bridge will be performed based on the procedures as outlined in NS-EN ISO 19901-7:2013 and DNV-OS-E301 Position Mooring. Safety factors are as requested based on NS-EN 1990.

Moorings should be checked for intact condition (ULS), for redundancy conditions having lost one or more moorings (ALS) and for fatigue conditions. Further a check should also be done for the transient condition between intact and redundancy condition. Checks for fatigue and transient condition are not included in this report.

The design for ULS will be based on the following design equation (from DNV-OS-E301) where the safety factor is split into a partial separate safety factors for mean tension and partial safety factor for dynamic tension:

where Sc is characteristic strength, Tc-mean is characteristic mean line tension and Tc-dyn is characteristic dynamic line tension.

Sc is taken as dimensioning strength of the mooring line and based on NS-EN 1993-1-11 this is taken as Suk/1.50 where Suk is characteristic value of breaking strength.

Main actions to be considered for mooring design are indirect actions from the bridge structure on the mooring lines. Importance of eventual direct actions on mooring lines from current and vortex-induced vibrations should be checked.

Indirect action originates from wave-induced actions, wind induced actions, current induced actions and from pre-tensioning of the mooring system.

Wave induced actions are taken from the non-linear time domain simulations for the complete bridge model in OrcaFlex as described in Chapter 6. The mooring system will be modelled fully in OrcaFlex using OrcaFlex standard line modelling technique and the mooring will consist of chain, wire and potentially rope. Estimated wave actions will be based on the same procedure as for the bridge structure itself; ten (10) 3-hour time domain simulations.


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Wind induced actions are taken from the NovaFrame wind analysis. In this analysis, the stiffness of the mooring system is linearized based on information from the OrcaFlex model. Procedure will ensure that appropriate linear stiffness is used.

Current induced actions are determined in the OrcaFlex model.

The characteristic mean line tension, Tc-mean, is taken as: pre-tensioning of the mooring system

The characteristic dynamic line tension, Tc-dyn, is taken as: wind induced actions, both static and dynamic parts (ref Section 6.3)

wave induced actions, including waves from local wind driven sea, swell waves, wave drift force, second order wave loading (ref. Section 6.2)

current induced actions

Regarding load combinations, for the ULS load we will use a partial factor of 1.1 for the mean load and a factor of 1.6 for the dynamic load. These factors are in accordance with load factors given for environmental loads in NS-EN 1990.

For the redundancy condition, we propose to use the same methodology as for ULS. Regarding load combinations, we will use a partial factor of 1.0 for the mean load and a factor of 1.0 for the dynamic load. If the definition of Sc should be based on NS-EN 1993-1-11, this still must be Suk/1.50 where Suk is characteristic value of breaking strength. This seems to be a rather conservative figure but is used as basis for the checks in this report.


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4 Analyses

4.1 ULS

Figure 4-1: Analyses flow chart. Notes in Figure 4-1: Analyses flow chart.

1. Stiffness in roll modified for pontoons for each bridge girder height taking into account the bridge inertia about the pontoon (z-coordinate)

2. Ignored because forces and moments from current loads are negligible 3. See Table 3-16 and 3-17 for combination factors 4. See Table 3-15: ULS Combination table


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Figure 4-2: Overview of model geometry as implemented in ULS analyses

A global model of the complete bridge including the cable supported bridge span is established. To properly account for all the different loading effects the model is established in three different analysis systems; OrcaFlex, NovaFrame and RM Bridge. Verification of each model is performed by comparing statically and dynamically behaviour. For an overview of the interaction between analysis programs see Figure 4-1 above. A description of the model geometry and numerical implementation is presented in Figure 4-2.

Post-simulation, the characteristic wave and wind loads are extracted by subtracting the nominal response due to permanent loads. This is because permanent and variable loads shall be combined with different load factors.

Wave analyses in OrcaFlex and wind analyses Novaframe are run with nominal permanent loads in order to account for inertial effects. In OrcaFlex geometric non-linear effects are also accounted for. Novaframe (being a frequency domain program) cannot account for this non-linearly. However, by including axial loads in NovaFrame extracted from permanent analyses in OrcaFlex, the non-linear effect of permanent deformations are taken into account.

Implementation of Hydrostatic Stiffness in Linear Software

A linearized form of the roll and pitch stiffness is implemented in NovaFrame and RM bridge.


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Roll and pitch stiffness are calculated according to the following equations.

C ρg KB KG ρgI

C ρg KB KG ρgI

The height of the bridge and the amount of ballast required varies along the bridge, and therefore KG varies. KB and area moment however remains constant for each pontoon. In general, the center of buoyancy and the water plane area moment varies with time, which cannot be accounted for in a frequency domain model such as NovaFrame. For small roll and pitch angles (<10°) however, the area moment can be considered constant.

Simultaneous Wind and Wave Analysis - Combination Factors

In order to verify the chosen combination factors between wave and wind used in the global model, simultaneous wind and waves are implemented in OrcaFlex.

The built in wind simulation tool in OrcaFlex is not able to represent spatial wind coherence, which is essential for the analysis of long slender structures. This shortcoming has been addressed by developing an external python function to calculate the wind forces and moments based on wind time series.

More details are found in chapter 10.


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4.2 Ship Impact

Figure 4-3: Ship impact analysis flow chart

4.3 Simplified Wave Analysis Model in the Frequency Domain A frequency domain model of one bridge section with one pontoon has been developed in Matlab. The aim of the frequency domain model is to

Get a fast estimate of the bridge girder moments.

Screen through all wave states and directions to make sure that the worst sea states are run in the full time domain model.

Full time domain simulations in OrcaFlex complete a 3-hour simulation of one sea state in roughly 3 hours. By comparison, the frequency domain model completes 6 pontoons for every combination of sea state and direction in less than one minute. Therefore, as a first level screening of pontoons and sea states this approach is very powerful.

The implemented method is in accordance with DNV-RP-C205 Environmental conditions and environmental loads, Chapter 7.


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Figure 4-4: Three degrees of freedom model applied for simplified frequency domain model

4.4 Assumptions and Simplifications Morison effect neglected (looked at and considered conservative to neglect, because the damping

effect is larger than the excitation effect).

Drift-forces are implemented using Newman’s approximation.

Hydrodynamic damping is neglected in the NovaFrame model. Hydrodynamic damping will give negligible effect to bending moment about strong axis from wind loading, which is dominated by the first four modes. The bending moments about weak axis will have a more significant reduction but here wave loads are dominating.

Wind spectra, length scales and turbulence intensities can only be calculated for one value of a reference height Z. For all analyses carried out for the complete bridge it is chosen to use the highest point of the bridge girder, Z=52m, which is believed to be a conservative approach taking into account that the majority of the bridge girder has a significantly lower elevation.

The applied calculation procedure In NovaFrame assumes that all modes are uncorrelated and not coupled. This is clearly the case for the modes contributing to the strong axis moment but is not so obvious for the modes giving contribution to the weak axis bending moment, but for weak axis moments wave loads are dominating.

In order to account for non-linearities in bridge centre of gravity due to rotation of bridge, a modified pontoon roll stiffness is implemented in linear analysis. Linearization is assumed valid due to small roll angles (~1.5deg). The linearization is necessary when using modal superposition.

Geometric stiffness in linear wind analysis is linearized about nominal permanent loads and static wind loads.

In time domain model of waves, the non-linear geometric stiffness due to static wind is neglected. The effect has been studied and found to be small. In the simultaneous wind and wave analysis this effect is accounted for and shown to be of no importance.

Instead of running a separate analysis for 1year waves, results from analysis with 100year waves are multiplied with a factor of 0.5. This assumption is based on the relationship between the significant


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wave heights for the 1year vs the 100year wave. However, the fetch analysis gives a Tp of 4.4s, while we have chosen to scale from Tp=6s. The validity of this assumption has not been considered.


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5 Cross-Sectional Properties

5.1 Main Girder

Plate Thicknesses used in Analyses

The plate thicknesses of the mono box girder vary along the bridge. Minimum plate thickness of top plate according to Eurocode is 14 mm. Using a 8 mm thick through stiffener spaced at 600 mm gives a minimum equivalent thickness of the top plate of 25 mm which will be sufficient for most part of the bridge, however, at some location the top plate will be additional reinforced.

In the analyses, it is chosen an equivalent thickness of 25mm for the top plate in the high bridge. For the bottom plate and the webs it’s chosen a thickness of 20mm (H1). Above the rigel, all plates have an equivalent thickness of 40mm (H2). In the side-spans there’s chosen a thickness of 25mm for the top and bottom plate. There is assumed 20mm thickness for the webs (F1). Above the supports and effective thickness of 35mm for top and bottom plate is assumed, while the webs have 30mm (S1).

Figure 5-1: Main-girder dimensions for the low bridge


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Section properites of girder used in analysis H1 H2 S1 F1

Length 724 50 480 1752

General dimensions

Total width m 31 31 31 31

Crossection height m 3.5 3.5 6.5 6.5

Height lower inclined web m 1.9 1.9 3.5 3.5

Width upper inclined web m 1.7 1.7 2.2 2.2

Width lower inclined web m 7.25 7.25 7.25 7.25

Equivalent plate thickness mm

Topplate Plate 1 0.025 0.04 0.035 0.025

Upper inclined web Plate 2 0.02 0.04 0.03 0.02

Upper inclined web Plate 3 0.02 0.04 0.03 0.02

Lower inclined web Plate 4 0.02 0.04 0.03 0.02

Lower inclined web Plate 5 0.02 0.04 0.03 0.02

Bottom plate Plate 6 0.02 0.04 0.035 0.025

Crossection properties

Area m2 1.41 2.55 2.21 1.55

Dinstance from centroid to bottom plate m 2.09 1.94 3.62 3.64

Distance from centroid to top plate m 1.41 1.56 2.88 2.86

Ix week axis m4 3.35 6.09 18.06 12.77

Iy strong axis m4 114.94 212.36 184.60 126.31

It tosrion (t=constant) m4 11.63 21.24 57.02 39.62

2*t*Enclosed area m2 3.68 7.36 10.17 6.78

Section modules

Weak axis in top plate m3 2.37 3.89 6.27 4.46

Weak axis in bottom plate m3 1.60 3.14 4.99 3.51

Strong axis in top plate m3 8.33 15.39 13.88 9.50

Strong axis in bottom plate m3 13.93 25.74 22.38 15.31

Weight

Steel skin (including longitudinal stiffeners) tons/m 11.1 20.0 17.4 12.2

Transverse stiffeneres tons/m 1.2 1.2 2 2

Total steel weight tons/m 12.3 21.2 19.4 14.2 Table 5-1: Sectional properties of girder used in analysis


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Updated Plate Thicknesses

After design checks were performed, the plate thicknesses were updated. The analyses are not re-run due to these changes. The girder above the two first pontoons were additional reinforced to 40mm equivalent thickness (S2*). The spans between axis 7/8, 8/9, 13/14 and 14/15 are also reinforced top 25mm in the webs (F2). There were also included another section type called (S1*), which takes into account the local longitudinal stiffening arrangement, which transfers the forces from the girder to the columns.

Section properties Updated H1 H2 S1 F1 S1* S2* F2

Length 724 50 480 1752 432 115.5 730

General dimensions

Total width m 31 31 31 31 31 31 31

Crossection height m 3.5 3.5 6.5 6.5 6.5 6.5 6.5

Height lower inclined web m 1.9 1.9 3.5 3.5 3.5 3.5 3.5

Width upper inclined web m 1.7 1.7 2.2 2.2 2.2 2.2 2.2

Width lower inclined web m 7.25 7.25 7.25 7.25 7.25 7.25 7.25

Equivalent plate thickness mm

Topplate Plate 1 0.025 0.04 0.035 0.025 0.035 0.04 0.025

Upper inclined web Plate 2 0.02 0.04 0.03 0.02 0.03 0.04 0.025

Upper inclined web Plate 3 0.02 0.04 0.03 0.02 0.03 0.04 0.025

Lower inclined web Plate 4 0.02 0.04 0.03 0.02 0.03 0.04 0.025

Lower inclined web Plate 5 0.02 0.04 0.03 0.02 0.03 0.04 0.025

Bottom plate Plate 6 0.02 0.04 0.035 0.025 0.035 0.04 0.025

Force transferer Plate 7 0.04 0.04

Force transferer Plate 8 0.04 0.04

Crossection properties

Area m2 1.41 2.55 2.21 1.55 2.73 3.19 1.67Dinstance from centroid to bottom plate m 2.09 1.94 3.62 3.64 3.55 3.52 3.58

Distance from centroid to top plate m 1.41 1.56 2.88 2.86 2.95 2.98 2.92

Ix week axis m4 3.35 6.09 18.06 12.77 19.95 23.05 13.23

Iy strong axis m4 114.9

4212.3

6184.6

0126.3

1 184.6

0 233.1

9145.7

4

It tosrion (t=constant) m4 11.63 21.24 57.02 39.62 57.02 69.00 43.12

2*t*Enclosed area m2 3.68 7.36 10.17 6.78 10.17 13.56 8.48

Section modules

Weak axis in top plate m3 2.37 3.89 6.27 4.46 6.76 7.74 4.52

Weak axis in bottom plate m3 1.60 3.14 4.99 3.51 5.62 6.54 3.70

Strong axis in top plate m3 8.33 15.39 13.88 9.50 13.88 17.53 10.96

Strong axis in bottom plate m3 13.93 25.74 22.38 15.31 22.38 28.27 17.67

Weight Steel skin (including longitudinal stiffeners) tons/m 11.1 20.0 17.4 12.2 21.5 25.0 13.1

Transverse stiffeneres tons/m 1.2 1.2 2 2 2.0 2.0 2.0

Total steel weight tons/m 12.3 21.2 19.4 14.2 23.5 27.0 15.1Table 5-2: Sectional properties of girder with updated plate thicknesses


37

Figure 5-2: Updated cross-sections of girder.


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5.2 Tower The reinforced concrete tower is an A-frame structure 215m high with 55m leg spacing at the base, as shown in Figure 5-3:

Figure 5-3: Tower front view (left) and transverse section (right)

The tower legs are 7m wide at the base which is linearly reduced to 5m at the top of the single legs below the stay cables. The length of the tower is 7m at the top, which is linearly increased to 12m at the base. All walls are 0.5m thick with local strengthening around the stay cable anchorages, which is not detailed at this stage. The tower is checked at 6 critical locations, which can be described as:

Below stay cables in level +170m (top of single leg)

Above bridge girder in level +55m

Below cross beam in level +45m

At base in level +5m

Cross beam at tower leg

Cross beam at CL-bridge


39

The examined cross sections are shown in Figure 5-4 to Figure 5-9:

Figure 5-4: Tower cross section below stay cables in level +170m (65kg/m³ reinforcement)


40

Figure 5-5: Tower cross section above and below bridge girder in level +55m and +45m, (140 kg/m³ reinforcement)


41

Figure 5-6: Tower cross section below cross beam in level +45m, (210 kg/m³ reinforcement)


42

Figure 5-7: Tower cross section at base in level +5m (220 kg/m³ reinforcement)


43

Figure 5-8: Cross beam at tower leg (210 kg/m³ reinforcement)

Figure 5-9: Cross at CL-Bridge between bearings (160 kg/m³ reinforcement)


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Reinforcement

The vertical reinforcement is from base to girder level comprised of ø32 c/c150 at the inner and outer face. Above the girder in level 55m the vertical reinforcement is ø25 c/c 150mm, which is gradually reduced to ø16 c/c 200mm at the top of the single tower legs. The horizontal reinforcement is limited and typically assumed as ø16 c/c 200mm at the inner and outer face. The total amount of reinforcement in the tower leg cross sections are from the top 65 kg/m³, 180 kg/m³, 210 kg/m³ and 220 kg/m³.

The main reinforcement in the cross beams is ø32 bars c/c 200mm, which is increased in the top layer close to the tower leg due to the large negative moments at these locations. The shear reinforcement is limited except vertically from the bearings to the tower leg. The total reinforcement amount in the cross beam sections is 210 kg/m³ at the tower leg and 160 kg/m³ centrally.

The average reinforcement amount of the tower structure is estimated to 160 kg/m³, which also account for the heavily reinforced stay cable anchorages in the top of the tower, which is not yet designed. The total amount of concrete B45 is 13000 m³ including the foundation with an approximate 50/50 share between sub- and superstructure.


45

5.3 Stay Cables The effective E-modulus (E-eff) is the tangent stiffness and calculated according to the following formulae.

Table 5-3: Effective E-modulus of stay cables

Effective E-modulus for the cable-stay ∙ ∙

∙

Tangent modulus 12 ∙

∙ ∙ 10 0.682 1

E-modulus of the steel 195

Density of the steel 77

Stress from permanent state (choose 28% of capacity)

520.8

The longest stays will have a reduction of stiffness of approximately 8 %.

The distributed vertical load to all cables is 175kN/m.

The vertical force components of stay cables are calculated from the total distributed load given above. The breaking stress of stays are 1860 MPa. The required area is determined assuming that the permanent load is utilizing the steel stress to 28% of breaking stress which gives each cable an deadweight stress of 520MPa.


46

.

Table 5-5 Cable Properties side span Table 5-4 Cable Properties Main span


47

5.4 Columns The columns are placed centrically on the pontoons and the column neutral axis intersects the bridge neutral axis. The column lengths vary along the bridge according to Table 5-6.

Table 5-6: Column lengths at each axis

Axis 3 Axis 4 Axis 5 Axis 6 Axis 7 Axis 8 Axis 9‐20

Column lengths 43.270 38.370 31.970 23.850 15.730 8.590 7.557

The column cross-sectional properties are listed in Table 5-7.

Table 5-7: Column properties

Column cross‐sections Axis Axis

3‐6 7‐20

Dimensions

Diameter m 10.0 10.0

Plate thickness m 0.050 0.040

Effective thickness vertical m 0.067 0.051

Effective thickness total m 0.077 0.058

Properties

Area m2 2.10 1.60

I (bending) m4 26.31 20.03

It (torsion) m4 52.62 40.06

Sectional modulus

Bending m3 5.26 4.01

Torsion m3 10.52 8.01

Weight tonne/m 19.0 14.3


48

Figure 5-10: Column dimensions, axis 3-6


49

Figure 5-11: Column dimension, axis 7-21


50

5.5 Abutment South In the south end of the bridge the cable stayed bridge girder is anchored in a 40m x 31m x 16m (L x W x H) caisson structure, which is filled with saturated sand ballast. The south abutment is shown in the figures below.

Figure 5-12: Abutment south section

Figure 5-13: Abutment south elevation

The caisson structure has 0.5 m outer walls, top- and bottom slab. The inner walls are 0.3m thick with varying spacing, thus uniform backfilling of the caisson shall be ensured. The transverse inner walls are placed 10 m c/c underneath the stay anchorage, while the longitudinal inner walls are placed under the shear stud plinth and


51

centrally. The total amount of concrete for the caisson is 3300 m³ with an estimated average reinforcement amount of 150 kg/m³. The total area of form work is 11000 m².

The forces from the bridge girder are transferred to the caisson through a shear stud connection, as shown in the illustration of plan in Figure 5-14.

Figure 5-14: Shear stud plan at abutment south

The total number of longitudinal and transverse shear studs at the south abutment is:

2 ∙ 4 ∙40

0.1254010

1 ∙150.15

≅ 3000


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5.6 Abutment Flua In the north end, the bridge girder is anchored in a 48m x 28m x 50.5m (L x W x H) caisson structure, which is filled with saturated sand ballast (42000 m³). The abutment at Flua is shown in below figures.

Figure 5-15: Section at Flua (north end)

Figure 5-16: Elevation at Flua


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The caisson structure has 0.75m outer walls and bottom slab. The top slab is 0.5m thick with inner walls of 0.35m. The total amount of concrete is 12000 m³ with an estimated average reinforcement amount of 150 kg/m³. The total area of form work is 41000 m².

The bridge girder is able to move longitudinally and all other forces than Nx from the bridge girder is transferred to the caisson through vertical and horizontal bearings, as shown in Figure 5-17 (bearings marked with x).

Figure 5-17: Plan at Flua

The vertical bearings are positioned in the front and rear end of the caisson on top of the outer transverse wall and longitudinal inner wall. The bridge girder will be filled with 5000 m³ ballast above the abutment at Flua to avoid uplift bearings due to weak axis and torsional moments. The horizontal bearings are fixed to a steel bearing console, which transfer the bearing reactions to the caisson by prestressing cables. The horizontal bearings are spaced 44m longitudinally to restrain the bridge girder for strong axis moments.


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5.7 Pontoons

Figure 5-18: Main dimensions for the pontoon

Figure 5-19: Wall thickness, compartments and column attachments for the pontoon


55

Table 5-8: Pontoon main parameters Main pontoon parameters

Name 5_400280105 na

Displacement 18 300 te

Mass 11 300 te

Roll inertia 4 900 000 tem2

Pitch inertia 1 360 000 tem2

Yaw inertia 5 700 000 tem2

Roll water plane stiffness gI44 5700 MNm/rad

Pitch water plane stiffness gI55 1000 MNm/rad

Heave stiffness 17.5 MN/m

COGx 0 m

COGy 0 m

COGz ‐4.2* m

Height 14.5 m

Freeboard 4.0 m

Draft 10.5 m

Width 68.0 m

Length 28.0 m

* z=0 at free surface

For the final bridge with bridge girder the modified roll stiffness vary with the height of bridge girder. For high part of floating bridge the roll stiffness is 3300 MNm/rad and for the low part 4900 MNm/rad. All pontoons satisfy the minimum roll stiffness of 1100 MNm/rad.

The pontoon roll stiffness is much higher the requirement. This is because the pontoons for the straight bridge are the same as for the curved bridge and therefore optimized for the curved bridge design, which has a roll stiffness requirement or 2500MNm/rad. In addition the curved bridge is heavier, so that the displacement of the pontoons is larger than required. Therefore, there is room for optimization of the pontoons for the straight bridge.

Added Mass

Figure 5-20: Radiation added mass for the 5_400280105 pontoon


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Figure 5-21: Radiation added mass coefficients for the 5_400280105 pontoon

Radiation Damping

Figure 5-22: Radiation damping for the 5_4002580105 pontoon.

As a reference for the magnitude of heave and sway damping, the percentage of critical heave damping at 6s, 8s and 14s and critical sway damping at ~6s is indicated in the plot.


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First Order Excitation Plots

Figure 5-23: First order excitation coefficients for 45deg incident waves for the 5_400280105 pontoon

The first order excitation forces for each pontoon will give a rough estimate of the quasi-static forces going into the bridge structure due to waves. By quasi-static we mean neglecting any dynamic contribution from radiation added mass or damping. Short-term maxima for excitation forces integrated with the JONSWAP wave spectrum (given in Figure 3-6) are calculated according with the following formula (ref DNV-RP-c205).

2 ∗ ln10800

∗ | | ∆

Where is the mean zero-upcrossing period, F is the excitation force transfer function, S is the wave spectrum and is the frequency of oscillation.


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Figure 5-24: Short term maxima of excitation forces per pontoon integrated with the JONSWAP spectra in Figure 6 for all Tp/Hs in the scatter diagram, see Table 3-7.

Drag Factors

Figure 5-25: Drag factors applied for the selected pontoon


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5.8 Mooring Lines

5.8.1 Mooring Line Component Data The mooring line component properties are presented in Table 5-9. These properties are approximate and subjected to changes, pending choice of supplier, final anchor locations and optimization of mooring system. If possible, the top chain will be substituted with a chain of grade R4 at a later stage. Applied component lengths and weights are given in


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Table 5-10 and Table 5-11.

Table 5-9: Mooring line component properties

Bottom chain Wire Top chain General data: Type R4 studless R5 studless Nominal diameter 175mm 175mm 175mm Axial stiffness, EA 2.41E6 kN* 1.59E6 kN 2.61E6kN* Initial data: Minimum breaking load 25 200 kN 24 300 kN 27 900 kN Weight in air 613 kg/m 144 kg/m 613kg/m Normal drag coefficient** 2.4 1.8 2.4 Axial drag coefficient** 1.15 0.01 1.15 Environmental conditions: Marine growth*** 40 mm 60 mm 80 mm Applied data (with growth): Weight in air 685 kg/m 203 kg/m 783 kg/m Normal drag coefficient 3.5 3.0 4.6 Axial drag coefficient 1.7 0.01 2.2 * Young’s modulus calculated according to DNVGL-OS-E301, 2.1.8 ** Recommended values from DNVGL-OS-E301, Section 2.7.1 *** Recommended values from DNVGL-OS-E301, Section 2.8. The bridge is located at approximately 60° north. Calculation of Young’s modulus for studless chain according to DNVGL-OS-E301, 2.1.8 (d = chain diameter in mm):

5.45 0.0025 ⋅ 10 / 6.00 0.0033 ⋅ 10 /


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Table 5-10: Line component lengths for each mooring line.

No Bottom chain Wire Top

chain 1 100m 641m 20m 2 100m 641m 20m 3 100m 641m 20m 4 100m 641m 20m 5 100m 641m 20m 6 100m 641m 20m 7 100m 641m 20m 8 100m 641m 20m 9 100m 641m 20m 10 100m 641m 20m 11 100m 641m 20m 12 100m 641m 20m 13 100m 920m 20m 14 100m 920m 20m 15 100m 920m 20m 16 100m 920m 20m 17 100m 920m 20m 18 100m 920m 20m Table 5-11: Steel weight of mooring lines components

Line

Steel Weight Bottom chain Wire Top Chain Line Total Weight

1-6 61 300 kg 92 300 kg 12 260 kg 165 860 kg 7-12 61 300 kg 92 300 kg 12 260 kg 165 860 kg 13-18 61 300 kg 132 500 kg 12 260 kg 206 060 kg

5.8.2 Fairlead Positions The fairlead positions on each pontoon are presented in the figure below.

Figure 5-26: Fairlead Positions


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5.8.3 Anchor Locations For the purpose of the analyses presented in this report, the anchors are assumed to be fixed. Data on soil-conditions are currently of a high degree of uncertainty and anchor locations are expected to change. The applied coordinates for the anchor locations are given in Table 5-12. Table 5-12: Line components and anchor locations for each line for mooring system at present stage. No Pontoon X* Y* Northing** Easting** 1 3 1153.7 -597.7 6 669 772.2 297 218.3 2 3 1206.0 -600.0 6 669 859.4 297 219.1 3 3 1258.3 -597.7 6 669 946.2 297 227.5 4 3 1258.3 597.7 6 669 841.0 299 217.1 5 3 1206.0 600.0 6 669 753.7 299 216.3 6 3 1153.7 597.7 6 669 666.9 299 207.9 7 9 2371.7 -597.7 6 668 569.6 297 553.7 8 9 2424.0 -600.0 6 668 622.0 297 554.2 9 9 2476.3 -597.7 6 668 674.1 297 559.2 10 9 2476.3 597.7 6 668 610.9 298 753.0 11 9 2424.0 600.0 6 668 558.6 298 752.5 12 9 2371.7 597.7 6 668 506.5 298 747.5 13 15 3554.8 -996.2 6 667 353.3 297 489.4 14 15 3642.0 -1000.0 6 667 405.7 297 489.8 15 15 3729.2 -996.2 6 667 457.8 297 494.9 16 15 3729.2 996.2 6 667 394.6 298 688.6 17 15 3642.0 1000.0 6 667 342.3 298 688.2 18 15 3554.8 996.2 6 667 290.2 298 683.1 * Coordinate system with origin at Axis 1, X along bridge north-south axis, Y along bridge east/west axis ** UTM32 coordinate system

The mooring spread and anchor coordinates are illustrated in the Figure 5-27 below.

Figure 5-27: Map – Bridge with Mooring Lines


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6 Wave and Wind Response

Wave loads induce large moments about bridge weak axis. Wind loads induce moments about bridge weak axis with roughly half the magnitude. About bridge strong axis the wave and wind induced moments are of similar magnitude, but are induced by different modes. Torque and axial load are of less importance for the ULS combination.

6.1 Eigenmodes Dominant modes for moments about bridge girder strong axis.

Eigenmodes important for response from wind.


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Figure 6-1: From top 78.3s, 71.2s, 40.8s and 32.5s. Modes dominating wind response about strong axis


65

Eigenmodes important for response in wind driven waves.

Figure 6-2: Top: 6.5s, bottom: 5.7s. Strong axis modes in the domain of wind driven waves


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Eigenmodes important for response in swell waves.

Figure 6-3: Top: 17.7s, middle: 14.1s, bottom: 11.3s. Strong axis modes in the domain of swell waves. The 11.3s mode is a coupled strong axis/pontoon roll mode


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Dominant Modes for Moments about Bridge Girder Weak Axis Wind driven seas dominate the response about bridge girder weak axis. Surge (pendulum) and heave motion of pontoons are mainly contributing to the induced moments.

In Figure 6-4 the lowest and highest eigenmode for heave response in wind driven waves are plotted.

Figure 6-4: Left: 7.6s, the shortest heave mode about bridge weak axis. Right: 10.9s, the longest heave mode about bridge weak axis

Figure 6-5: The range of eigen periods in heave with 5m flange. From hand calculations we predict a range from 7.8s to 10.8s, very near the actual range of 7.5s to 10.95s, seen in the global model in Figure 6-4.


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In Figure 6-6 important eigenmodes for surge (pendulum) response in wind driven waves are plotted.

Figure 6-6: Top: 4.7s, surge (pendulum) mode. Bottom: 6.4s, surge (pendulum) mode. Closely resembling mode 2 and mode 3 in hand calculations shown earlier

The range of modes seen in the global model match the simplified hand calculated range of modes. Thus, the simplified model represents the global bridge structure and screening of design parameters, especially for moments about weak axis, using the simplified model is robust.

6.2 Wave Response The objective of the wave response analyses has been to evaluate the maximum global response of the bridge structure subjected to the wave conditions given in section 3.3.5. To select the wave conditions to be used for load combination for ULS, iterations have been made to evaluate the most important characteristic responses. Through these iterations, it has been seen that the most important characteristic responses are the moment about bridge strong axis and moment about bridge weak axis. These characteristic responses have been used to select relevant wave conditions for the two load combinations presented in the table below.

Table 6-1: Wave conditions for waves to be used for load combinations (ULS)

Load Combination 1 (max

moment about bridge strong

axis)

Load Combination 2 (max

moment about bridge weak

axis)

Unit

Wind-driven wave, Hs 3 3 m

Wind-driven wave, Tp 6 6 s

Wind-driven wave, gamma 3.3 3.3 -

Swell-driven wave, Hs 0.4 0.4 m

Swell-driven wave, Tp 14 14 s

Swell-driven wave, gamma 7 7 -

Heading From West From Northwest


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6.2.1 Screening Due to the long simulation time involved in the final run, it is decided to choose one combination of sea states for moments about bridge girder strong axis and one for moments about bridge girder weak axis. The focus has been to find the worst case with respect to moments in the bridge girder. From the plots below it is clear that what is dimensioning for the bridge girder is not necessarily dimensioning for other main components. In a more thorough and detailed design, more wave load combinations should therefore be assessed.

It has been decided that wind and wind driven waves should have the same heading. Wind loads are always largest from West and are a factor when selecting the load case heading for moments about bridge strong axis.


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Moment about Bridge Girder Strong Axis

Figure 6-7: Bending moment about bridge girder strong axis. Screening of directions (left) and wave states (right) for swell seas during

one 1hour simulation. Waves from 270deg, North-West, with Hs=0.4m and Tp=14s give the largest moments.

Figure 6-8: Bending moment about bridge girder strong axis. Screening of directions (left) and wave states (right) for wind seas during

one 1/2hour simulation. Waves from 270deg, with Hs=3m and Tp=6s give the largest moments.


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Moment about Bridge Girder Weak Axis

Figure 6-9: Bending moment about bridge girder weak axis. Screening of directions (left) and wave states (right) for wind seas during

one 1/2hour simulation. Waves from 225deg, North-West, with Hs=3m and Tp=6s give the largest moments.

Figure 6-10: Bending moment about bridge girder weak axis. Screening of directions (left) and wave states (right) for swell seas during

one 1hour simulation. Waves from 225deg, North-West, with Hs=0.4m and Tp=12s give the largest moments.


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6.2.2 Discussion of Screening Results Moment about Bridge Strong Axis

In the period range of wind-driven and swell waves there are several sway and roll induced modes which govern the response for moments about bridge strong axis.

Swell

The screening of strong axis moments for swell waves show that the response is not very dependent on the peak period of the sea state. Part of the explanation is that for all sea states there are sway or roll induced eigen modes more or less near the peak period, see Figure 6-3. At 17.7s there is an eigen mode that is 98% sway induced, at 14.1s there is an eigen mode that is 82% sway induced and at 10.9s there is an eigen mode that is 90% sway induced. Integrated excitation in sway and roll, Figure 6-12, does not alone explain the responses seen in the screening. In order to fully understand response from waves about bridge strong axis, both the effect of triggered eigen modes and excitation forces must be seen considered.

Any of the swell sea states could have been selected for the final load combination. The reason for selecting Tp 14s is for comparison with results from the curved bridge analysis.

Wind seas

From Figure 6-8 it is clear that the largest moments appear at connections between bridge and columns. Mid-section (in girder between columns) moments are significantly lower. For this to be the case the mode of transverse bridge motion should be very near the stiffest mode, where every pontoon is out of phase with the neighbouring pontoons, see Figure 6-11. This is confirmed by the eigen modes around ~6s, see Figure 6-2.

Figure 6-11: Pontoon motion out of phase and simplified moment diagram. The stiffest eigen mode.

Direction

As expected from the position of the straight bridge, waves from west induce the largest moments about bridge girder strong axis.

Moment about Bridge Weak Axis

Looking at the plot of integrated excitation for each sea state in Figure 3-6 it is not intuitive that swell seas give small moments about the bridge girder weak axis. However, when we look at the range of eigen modes in heave and surge we see that there are no eigen modes above 11s for response about weak axis. Therefore we expect low dynamic amplification for swell waves.


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For wind driven seas it is different, especially for surge (pendulum) response where there are eigen modes around 6s. Here we get a significant dynamic amplification. This is also the case for heave response where the tail of the JONSWAP spectrum for wind driven seas give some energy at the lowest heave mode. It is therefore reasonable that the sea state giving the maximum moments about weak axis should be the wind driven sea state with maximum Hs and maximum Tp.

Figure 6-12: Short term maxima of excitation forces per pontoon integrated with the JONSWAP spectra in Figure 6 for all Tp/Hs in the scatter diagram, see Table 3-7.

Comparing the curved and straight bridge concepts, moments about bridge weak axis are slightly lower for the straight bridge. This is the case both for the high part and the low part of the floating bridge. The pontoon design is equal and have the same global orientation, the bridge girder weak axis stiffness is very similar. However, two things differ.

There is a difference in the mass distribution, more ballast for the straight bridge and more self weight in the bridge girder for the curved bridge

The global orientation of the bridge girder differ between the concepts At this point this difference has not been analysed sufficiently to conclude. More work should be performed to study the difference between the two bridge concepts.


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6.2.3 Second Order Load Effects from Waves The importance of second order effects from waves on the structure response is covered for the curved bridge report, ref /8/ NOT-KTEKA-021 Curved bridge South – Summary of analysis. The effect of these loads for the straight bridge has not been investigated. Viscous effects are expected to be of similar importance, while the effect of second order slowly varying drift must be looked at due to the difference between the straight and curved bridge with respect to response about bridge girder strong axis.

6.2.4 Damaged Condition – Two Compartments Filled An analysis of the bridge response in damaged condition, where one pontoon has two compartments filled, is analysed in the curved bridge report, ref /8/ NOT-KTEKA-021 Curved bridge South – Summary of analysis.

6.3 Wind Response Moment about Bridge Strong Axis

The dynamic effects that result in bending moments about strong axis and lateral deformations are dominated by the four fundamental modes having natural periods between 78.3 s and 32.5 s:

a) b)

c) d)

Figure 6-13: a) 78.3s b) 71.2s c) 40.8s d) 32.5s. Modes dominating wind response about strong axis

The maximum dynamic value appears at the fixed end in north. The dominating modes contributing to the total bending moment is given in the following table:

Mode Contribution [%] 1 14.5 2 22.0 3 19.6 4 25.9


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A major peak bending moment also occurs at x=3000m. Here only the two fundamental modes dominate the response with 32.9 and 56.8 % respectively.

In the following plot the total bending moment about strong axis from the total 75 modes is compared with the response from the two and four fundamental modes.

Even though some pontoon motion is induced, hydrodynamic analysis shows that the damping is negligible at these frequencies. Therefore, no hydrodynamic damping is included in the wind analysis.

It should be noted that the high degree of non-linearity in the mooring system will affect the wind-induced moments about bridge strong axis. The frequency analyses must rely on some sort of linearization of the mooring system. Depending upon the linearization procedure, the conservatism of the frequency analysis may be discussed. In general a linearization procedure here have been chosen that will give conservative results.

In the time domain analysis of wind in Orcaflex, the wind-induced moments about bridge strong axis are studied for the equivalent linear system and compared to the non-linear mooring system, see section 7.2.5, and the linear analysis is found to be conservative.

Moment about Bridge Weak Axis

The dynamic effects that result in bending moments about weak axis has a significant peak in axis 3. This peak is dominated by the pendulum modes 10, 36 and 42.


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a)

b)

c)

Figure 6-14: a) 11.5s b) 6.4s c) 4.7s. Modes dominating wind response about weak axis


77

The contributions from the dominating modes are given in the following table:

Mode Contribution [%] 10 22.9 36 38.9 42 12.8

The remaining contribution mainly occurs from the modes with about 8 to 10s periods.

The modal masses of these modes indicate the following motion of the pontoons:

Mode Modal mass X-translation [%]

Modal mass Z-translation [%]

Pontoon motion

10 35 63 Heave (+surge) 36 66 27 Surge (+heave) 42 75 14 Surge

Figure 5-22 shows that radiation damping may have a significant impact for the modes with periods 3-13s when it comes to surge motion of the pontoons. The damping actually almost peaks for the most important mode 36 (6.7s). The effect of hydrodynamic damping is not taken into account in the NovaFrame analyses, and the bending moments about weak axis will therefore be very conservative.

Hand calculations based on maximum accelerations gives the following damping forces taken into account pontoon velocity in surge is approximately 0.1m/s:

Mode Period [s] Surge Damping from Figure 5-22 Damping moment weak axis (50m height) 10 11.5 9 MN/m/s 9MN/m/s x 0.1m/s x 50m = 45 MNm 36 6.4 12 MN/m/s 60 MNm 42 4.7 9 MN/m/s 45 MNm

By comparing wind analyses in NovaFrame and OrcaFlex it is seen that including hydrodynamic damping may reduce the peak bending moments by 25-40%, se the following figure:


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6.4 Movements and Accelerations Table 6-2: Selected motion criteria compared with actual motions seen in analysis assuming a combination factor of 0.6

Motion Criterion From analysis

Rotation about bridge axis (roll) due to environmental loads (static + dynamic)

1.5 deg 1.1 deg

Vertical acceleration 0.5 m/s2 0.7 m/s2 (high bridge)

0.3 m/s2 (floating bridge)

Horizontal acceleration 0.3 m/s2 0.44 m/s2

The characteristic vertical accelerations from 1 year wind and wave are above the criterion, see Table 6-2. From Figure 6-17 it can be seen that the main contribution is from wind. This can be explained by the relatively high lift forces. The cross-section optimization has been focused on drag, and by further optimizing the cross-section taking into account lift forces the vertical acceleration will possibly be lower. In addition, the bending stiffness about bridge weak axis is considerably lower than for the curved bridge, where the vertical acceleration from wind was no issue. The high bridge can become stiffer about weak axis with one additional support in the back span.

The characteristic horizontal accelerations from 1 year wind and wave are also above the criterion. However, there is a great uncertainty related to the project-defined criteria. The main focus has been to design for characteristic response, not horizontal accelerations.


79

Figure 6-15: Characteristic rotation about bridge axis for 1year wind and wave

Figure 6-16: Characteristic acceleration transverse to bridge axis for 1year wind and wave


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Figure 6-17: Characteristic vertical acceleration for 1year wind and wave

Figure 6-18: Characteristic displacement west-east for 1year wind and wave. NOTE: Wind analysis is run with the initial mooring

stiffness. For the large displacements seen here, the stiffness increases significantly, and consequently the displacement shown is exaggerated.


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Figure 6-19: Characteristic vertical displacement for 1year wind and wave


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7 Mooring System

7.1 General The mooring system consists of 18 mooring lines. Six mooring lines are connected to pontoons 3, 9 and 15 (axis 5, 11 and 17). The mooring lines consist of 100m bottom chain, 641m / 641m / 920m wire and 20m top chain.

Data on soil-conditions are currently of a high degree of uncertainty. Since anchor locations are expected to change, the mooring system has not yet been optimized. The mooring is symmetric about both horizontal pontoon axes. Anchors for lines connected to pontoons 3 and 9 are located at a depth of 500m and anchors for lines connected to pontoon 15 are located at a depth of 350m.

7.2 Mooring Line Characteristics

7.2.1 Pretension Pretension for all lines are presented in the table below.

Table 7-1: Line Pretensions

Lines Axis Pontoon Pretension 1-6 5 3 3800kN 7-12 11 9 3800kN 13-18 17 15 4200kN

7.2.2 Catenaries The catenaries for different horizontal distances between fairlead and anchor are shown in Figure 7-1 and Figure 7-2.


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Figure 7-1: Catenaries for mooring lines 1-12

Figure 7-2: Catenaries for Mooring Lines 13-18


84

7.2.3 Individual Line Tension due to Pontoon Displacement The tension at the fairlead for each line when the pontoon is displaced in the east-west direction is shown in the figure below.

Figure 7-3: Individual mooring line tension due to east/west displacement of pontoon

7.2.4 Mooring System Stiffness Due to the catenary shape of the mooring lines, the mooring stiffness is not linear. The following figures show the combined load from the mooring lines on a given pontoon due to the pontoon’s displacement or rotation. The stiffness for 1m displacement /1 degree rotation have been applied for all NovaFrame analyses, unless stated otherwise.

Figure 7-4: Mooring stiffness – (east-west force/east-west displacement) and (moment about north-south axis due to east-west

displacement)


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Figure 7-5: Mooring stiffness – (moment about north-south/rotation about north-south) and (vertical force/vertical displacement)

7.2.5 Effects of Non-Linear Mooring System Stiffness Since NovaFrame is a frequency-domain program, it does not have the option of including non-linear stiffness. Different methods for linearization of equivalent mooring stiffness, to be implemented in NovaFrame for wind analysis, is presented in Figure 7-6.

Figure 7-6: Illustrations of non-linear mooring stiffness

The bridge strong axis eigen modes are highly dependent on the mooring stiffness. The first mode for initial stiffness and stiffness corresponding to the largest translations for the 100 year storm is shown in Figure 7-9.

The offset will vary over the range presented in Figure 7-6 during a 100 year storm. The stiffness from the mooring system will vary accordingly and higher-order effects will be introduced. As shown in Section 6.1, the mode shapes are of significant importance for the motions of the bridge. This will affect the response about bridge strong axis and discrepancies between a simulation with linearized stiffness and a simulation with non-linear stiffness are therefore to be expected. Thus conservative assumptions have been selected for the linearization when producing load effects that are used in the design: For comparison of results between non-linear and linear calculations other assumptions have been used. This must be taken into account when evaluating the procedure.

As can be seen from Figure 7-7, the strong axis bending moments calculated in NovaFrame are significantly higher than the moments calculated with OrcaFlex. Please see Section 10 for benchmarking of the OrcaFlex wind module.


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Figure 7-8 shows the an extract of the time-series of the moment about the bridge girder strong axis for the OrcaFlex model with linearized mooring system described in Section 11.1 as well as the actual, non-linear mooring system. These time-series show that the system with the linearized stiffness experience resonant motions, whereas the system with the catenary, non-linear mooring system does not see this behavior.

Figure 7-7: Comparison of bending about bridge girder strong axis for dynamic wind analyses with NovaFrame with linearized stiffness

and OrcaFlex with actual, non-linear mooring system.

Figure 7-8: Moment about the bridge girder strong axis for mooring system with linearized stiffness as well as the actual, non-linear

mooring system.

Figure 7-9: Plot of mode 1 for different mooring stiffnesses


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7.3 Capacity Check

7.3.1 Environment As the lines are oriented in the east-west direction, wind and waves coming from the west will result in the highest line loads. Hence, only weather coming from west (270 degrees) have been analysed for the mooring capacity check. The same weather condition was applied for both ULS (Ultimate Limit State) and ALS (Accidental Limit State).

7.3.2 Marine Growth Increased weight and drag coefficients due to marine growth have been calculated according to the guidance note for DNVGL-OS-E301, Section 2.8. The bridge is located at approximately 60 degrees north. The results are presented in Table 5-9. Marine growth was applied for both ULS and ALS analyses.

7.3.3 Material Factor, Load Factors and Load Combination Factor The applied factors are presented in Table 7-2.

Table 7-2: Applied factors for mooring lines Factor Symbol Value Condition To be applied for Material Factor γm 1.5 ULS & ALS MBL Static Safety Factor γSFstat 1.1 ULS Pretension

Dynamic Safety Factor γSFdyn 1.6 ULS Dynamic and static wind loads and wave loads

Static Safety Factor γSFstat 1.0 ALS Pretension

Dynamic Safety Factor γSFdyn 1.0 ALS Dynamic and static wind loads and wave loads

Wind/Wave Combination Factor γloadComb 0.7

ULS (& ALS) Applied for the minor response of dynamic wind and waves

Wave Load Statistical Factor γwaveLoad 1.25 ULS & ALS Wave loads *Dynamic wave loads are also multiplied by 1.25 to reach the 95 percentile used for other main structural components, see

Section 3.5.2.

** The wind/wave combination factor is higher than the bridge girder. This is because the combination factor for wind and wave

loads have not been studied explicitly for the mooring lines, and is increased for conservativism.

7.3.4 ULS - Calculation of Maximum Line Tension Of the different components, the wire has the smallest minimum breaking load of 24 300 kN. The line tension limit for ULS is given below.

243001.5

16200

The following two methods were applied for calculation of the maximum line tension.

Method 1

Wave loads are calculated using time-domain simulations in OrcaFlex and wind loads are calculated using frequency-domain simulation in NovaFrame. The maximum line tensions were calculated as follows.

1. Calculate line tensions for all lines for different east/west displacements of the pontoons, T(∆Y).


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2. Obtain the maximum horizontal displacement from ten 3 hour wave simulations in OrcaFlex with mooring lines treated properly as catenaries. Maximum displacement due to waves is ∆Ywa = 2.37m.

3. Obtain the maximum horizontal displacement from wind simulation in NovaFrame, with mooring lines modelled as springs (defined below). The horizontal stiffness is the secant stiffness for a pontoon east-west displacement of 8m.

Degree of freedom Pontoons 3 & 9 Pontoon 15East-west force due to east-west pontoon displacement 1637 kN/m 989 kN/m Moment about north-south due to east-west pontoon displacement 25799 kN/m 8685 kN/m Moment about north-south due to pontoon rotation about north-south 12152 kN/m 2040 kN/m Vertical force due to vertical pontoon displacement 827 kN/m 133 kN/m

Maximum displacement due to static and dynamic wind is:

Δ Δ Δ 3.56 3.76 7.32

4. Find the line tension corresponding to the total maximum horizontal displacement. The total maximum horizontal displacement is:

Δ Δ Δ 2.37 7.32 9.69

This gives a maximum line tension of:

_ Δ 9.69 10720

5. Calculate the maximum dynamic load by subtracting the pretension:

10720 3800 6920

6. Calculate the combined load with load factors (see Table 7-2). The contributions from wind and wave loads are weighted based on horizontal displacement.

max ⋅ ⋅ΔΔ

⋅ ⋅ΔΔ

⋅ ,

⋅ ⋅ΔΔ

⋅ΔΔ

⋅ ⋅

max 3800 ⋅ 1.1 6920 ⋅2.379.69

⋅ 1.25 ⋅ 0.77.329.69

⋅ 1.6,

3800 ⋅ 1.1 6920 ⋅2.379.69

⋅ 1.257.329.69

⋅ 0.7 ⋅ 1.6 max 14914 , 13418

Procedure overestimate some of the contributions and is as such conservative. Effect of current is neglected.


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Method 2 – Simultaneous Wind and Wave Analysis with OrcaFlex

The method for calculation of the maximum line load with OrcaFlex is described below. The results are presented in Table 7-3.

1. Extract the maximum line tension from a 1-hour wind, wave and current simulation in OrcaFlex for one seed, Twawicu_1hr_1seed.

2. Extract the maximum line tension from a 1-hour wave simulation in OrcaFlex for the same seed as in step 1, Twa_1hr_1seed.

3. Extract the mean of the maximum mooring line load from ten 3-hour wave simulations in OrcaFlex, Twa_3hr_10seeds.

4. Calculate the maximum total line tension as follows:

_ _ _ _ _ _


6. Calculate the combined load with load factors (see Table 7-2) as follows

⋅ ⋅ ⋅

This is extra conservative as the wind load is also multiplied with γwaveLoad. This because it is difficult to separate the wave and wind load in the time-domain simulation.

The highest loaded line has a tension of 11763 kN, which is well below the limit of 16200 kN.

Table 7-3: ULS – Maximum mooring line tension at fairlead – Method 2

Line No

Line Tension [kN]

Static (Pretension)

Total minus static Characteristic Load

With Load Factors

Twawicu_1hr_1seed Twa_1hr_1seed Twa_3hr_10seeds _

1 3796 -287 415 514

2 3800 -290 414 518

3 3803 -293 408 515

4 3803 2843 775 793 2862 9907

5 3800 2850 772 799 2877 9933

6 3796 2821 765 789 2845 9866

7 3796 -368 336 409

8 3799 -366 335 414

9 3803 -367 334 411

10 3803 3660 821 938 3777 11738

11 3799 3675 824 941 3792 11763

12 3796 3638 816 933 3755 11685

13 4196 37 427 431

14 4199 40 429 434

15 4201 41 425 432

16 4201 1466 570 588 1484 7589

17 4199 1466 571 591 1487 7592

18 4197 1455 568 590 1476 7569


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7.3.5 ALS - Calculation of Maximum Line Tension Single line failure is to be evaluated with safety-factors equal to 1.0. The line tension limit for ULS is given below.

243001.5

16200

Single line failure is the evaluated accidental condition for the mooring system. This is performed for the three lines upwind of the pontoon with the worst loaded lines in the ULS condition, pontoon 9. Since the results show that the ALS maximum tension is well within the limit, the results from a single time-domain simulation were directly applied using the following method.

1. Extract the maximum line tension from a 1-hour wind, wave and current simulation in OrcaFlex for one seed, Twawicu_1hr_1seed.

2. Calculate the maximum total line tension as follows:

_ _


4. Calculate the combined load with load factors (see Table 7-2) as follows

⋅

This is includes some extra conservative as the wind load is also multiplied with γwaveLoad. This because it is difficult to separate the wave and wind load in the time-domain simulation.

As can be seen from Table 7-3, lines 10, 11 and 12, connected to pontoon 9, are the most loaded lines. Three separate simulations were performed without lines 10, 11 and 12 in OrcaFlex and the maximum line tensions were extracted using the method described in Section 7.3.5. The highest loaded line has a tension of 12143 kN, which is well below the limit of 16 200 kN.

Table 7-4: ALS - Maximum mooring line tension at fairlead

Broken Line

Line

Line Tension [kN]

Static Total-static Characteristic Load With Load Factors

10 11 3799 6566 12007

10 12 3796 6497 11917

11 10 3803 6558 12001

11 12 3796 6522 11948

12 10 3803 6508 11938

12 11 3799 6542 11976

7.4 Anchor Loads The anchor loads were calculated using Method 2, presented in Section 7.3.4, and are presented in Table 7-5.


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Table 7-5: ULS – Maximum mooring line tension at anchor – Calculated with Method 2

Line No

Line Tension [kN]

Static (Pretension)

Total-static Characteristic Load

With Load Factors

Twawicu_1hr_1seed Twa_1hr_1seed Twa_3hr_10seeds _

1 2605 -289 415 526

2 2608 -291 418 531

3 2612 -290 413 527

4 2612 2833 769 799 2863 8598

5 2608 2839 773 803 2869 8608

6 2605 2813 764 795 2843 8552

7 2605 -359 347 413

8 2608 -357 347 417

9 2611 -357 344 415

10 2611 3651 820 941 3772 10416

11 2608 3666 823 944 3787 10443 12 2605 3627 817 937 3747 10358

13 3474 38 435 439

14 3477 41 437 440

15 3479 42 433 439

16 3479 1482 578 593 1498 6822

17 3476 1486 578 597 1505 6833

18 3474 1471 574 596 1492 6806

7.5 Angle with Vertical The static as well as minimum and maximum angles with vertical from the 1-hour simulation in OrcaFlex with simulteaneous wind, waves and current is given in Table 7-6 below.

Table 7-6: ULS – Line angles with vertical. See Figure 7-10 for definition of angle.

Line LineEnd

Angle with Vertical

Static Angle*

Dynamic

Min Angle Max angle

[deg] [deg] [deg]

1-3 Top end 141 142 144

4-6 Top end 141 137 140

7-9 Top end 141 142 144

10-12 Top end 141 136 139

13-15 Top end 124 124 127

16-18 Top end 124 121 123

1-3 Bottom end 114 107 112

4-6 Bottom end 114 117 122

7-9 Bottom end 114 106 111

10-12 Bottom end 114 118 124

13-15 Bottom end 90 89 90

16-18 Bottom end 90 90 95

* No environmental loads


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Figure 7-10: Definition of line end angle with vertical

7.6 Further Work Data on soil-conditions are currently of a high degree of uncertainty. Since anchor locations are expected to change, the mooring system has not yet been optimized. However, some further investigation can be performed with no additional soil-condition data, especially regarding the effect that the non-linear stiffness has on the eigen modes and therefore the response about strong axis.

7.7 Gravity Anchor For the current stage all anchors are taken as gravity anchors. At a later stage, anchors can be optimized for the actual seabed conditions. Candidate anchor types are suction achors, gravity anchors, drag embedded anchors (able to take uplift forces) and piled anchors.

An initial arrangement for the gravity anchors have been developed. The anchor is a steel structure with overall dimensions 20x20x6 meters. See Figure 7-11 and Figure 7-12 below. The anchor shall be ballasted with crushed rock as shown in Figure 7-13. The installation weight is estimated to approximately 500 tonnes and installation will be carried out by a heavy lift vessel. After installation the anchors will be ballasted with crushed rock using a special purpose vessel with a “fall pipe” solution. These vessels are capable of dropping rocks down to 2000 m depths with sufficient precision. Approximately 2160 m2 of rock will be placed in each anchor.


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Figure 7-11 Basic design for gravity anchor – Plan view


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Figure 7-12 Basic Design for gravity anchor – Section of side wall


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Figure 7-13 Basic design for gravity anchor – Section through anchor showing the crushed rock ballast


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8 Design

8.1 Girder

8.1.1 ULS Forces and Moments In this section, ULS response in the girder are shown with plots. The combinations are defined in section 3.5.2. There is in total three different ULS combinations:

ULS 1: Combination with dominant permanent load.

ULS 2: Combination with dominant traffic load.

ULS 3: Combination with dominant environmental loading (wave and wind forces).

In these plots all force components are fully correlated.


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ULS 3:

Environmental load direction=225

Figure 8-1 Combined normal force ULS 3 225

Figure 8-2 Combined torque ULS 3 225


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Figure 8-3 Strong axis bending moment ULS 3 225

Figure 8-4 Week axis bending moment ULS 3 225


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ULS3


Figure 8-5 Combined normal force ULS3 270

Figure 8-6 Combined torsion ULS3 270


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Figure 8-7 Combined strong axis bending moment ULS3 270

Figure 8-8 Combined week axis bending moment ULS3 270


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ULS 2:



Figure 8-10 Combined torque ULS2 225


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Figure 8-11Combined strong axis moment ULS2 225

Figure 8-12 Combined week axis moment ULS2 225


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ULS2



Figure 8-14Combined torque ULS2 270


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Figure 8-15Combined strong axis moment ULS2 270

Figure 8-16Combined week axis moment ULS2 270


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8.1.2 Stress Control in ULS – Cross-Sections used in Analyses

In this section, ULS stresses in girder are evaluated in two points along bridge girder as shown in figure below. The cross-section is according to the original analysis (H1, H2, S1 and F1) for the whole floating bridge.

The combination factor of 0.4 is used for non- dominant force components and a combination factor of 0.6 is used for the dominant wind force component when combined with the governing wave load.

The objective of the wave response analyses has been to evaluate the maximum global response of the bridge structure subjected to the wave conditions given in section 3.3.5. To select the wave conditions to be used for load combination for ULS, iterations have been made to evaluate the most important characteristic responses, see Table 6-1. Three load combinations are considered with dominant action of permanent loads, traffic load and environmental loads respectively. The utilization is limited to 418MPa (460MPa/1.10), according to Eurocode.

The point marked whit a circle in the top plate, is from now referred to as “stress point 1”.

The points marked whit a circle in the bottom plate is from now referred to as “stress point 2”.

Figure 8-17: Illustration of where in the cross-section stresses are calculated. Von Mises stress plots from environmental load direction=225, whit dominant wave Mz bending moment and environmental load direction=270,whit dominant wind My bending moment is showed.

ULS1

Figure 8-18: Von-Mises stresses, ULS1, environmental load direction=225, dominant wave Mz

050

100150200250300350400450500550600650700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stress ULS 1, environmental load direction=225, dominant wave Mz

Stress point 1

Stress point 2

Axis

S460/1.10


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Figure 8-19 ULS1, environmental load direction=270, dominant wind My

ULS2

Figure 8-20: Von-Mises stresses, ULS2, environmental load direction=225, dominant wave Mz.

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stress, environemtanl load direction=270, dominant wind My

Stress point 1

Stress point 2

Axis

S460/1.10

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stress, environmental load direction=225, dominant wave Mz

Stress point 1

Stress point 2

Axis

S460/1.10


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Figure 8-21: Von-Mises stresses, ULS2 – environmental load direction=270, dominant wind My. ULS3

Figure 8-22: Von-Mises stresses, ULS3, environmental load direction=225, dominant wave Mz.

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stress, environmental load direction=270, dominant wind My

Stress point 1

Stress point 2

Axis

S460/1.10

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stress, environmental load direction=225, dominant wave Mz

Stress point 1

Stress point 2

Axis

S460/1.10


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Figure 8-23: Von-Mises stresses, ULS3 – environmental load direction=270, dominant wind My.

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stress, environmental load direction=270, dominant wind My.

Stress point 1

Stress point 2

Axis

S460/1.10


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8.1.3 Stresses – Updated Cross-Sections Since the originally choice of section shows too high stresses in some parts of the bridge in ULS 3, the plate thicknesses are increased according to the plots given in Table 5-2. The girder above the two first pontoons were additional reinforced to 40mm equivalent thickness (S2*). The spans between axis 7/8, 8/9, 13/14 and 14/15 are also reinforced to 25mm in the webs (F2).

As before, the von mises stresses for top and bottom plate is showed, but only for ULS 3, whit environmental direction 225 and 270.

It can be seen that dominating moment about weak axis gives the largest stress at supports, while dominating moment about strong axis gives the largest span stress.

The last field before Flua have high stresses. This is because of the assumption of pinned connection at Flua in the analysis for self weight, which gives a large field moment. The building method assumes a fixed connection for self-weight at the caisson, which will reduce the field moment to ql^2/24. The section therefore not reinforced, since the analysis has to be re-run.

ULS3

Figure 8-24: Von-Mises stresses, ULS3 – Updated cross section, environmental load=225, dominant wave Mz.

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stres Updated crossection, enviroenmtenal load 225, dominant wave Mz

Stress point 1

Stress point 2

Axis

S460/1.10


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Figure 8-25: Von-Mises stresses, ULS3 – updated crossection, environmental load=270, dominant wind My.

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 500 1000 1500 2000 2500 3000 3500 4000 4500

MPa

Bridge Length [m]

Von Mises stress, updated crossection,environmental load=270, dominant wind My

Stress point 1

Stress point 2

Axis

S460/1.10


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8.1.4 Comparison of Stresses Extracted by Combination Factors vs Directly Extraction from Time-Series in OrcaFlex

Stresses from Method using Combination Factors

As explained earlier the stress control is performed using combination factors to cater for the correlation between force components from wave loading. In this chapter combination factor of 0.4 on the adjoining force components is compared with direct extraction of stresses from time domain simulations. For this test only permanent load combined with wave loading is considered. The maximum responses along the bridge girder are extracted from a 1-hour wave analysis and combined using factors. For comparison a direct von Mises stress calculation is performed of the same 1-hour wave analysis.

The study has not yet been completed for the straight bridge, and for now it is assumed that the compliance for the curved bridge concept also applies for the this concept.


112

8.2 Tower The tower cross sections are checked in the reinforced concrete program FAGUS for the ultimate limit state combinations with leading traffic (TRF), environmental loads with open bridge (TRF + ENV) and environmental loads with closed bridge (ENV). The design loads are for 225° and 270° wind and waves with correlated longitudinal and transverse bending for waves (My and Mz), see sequence and designations below:

ENV (Mz, 225°)

ENV (Mz, 270°)

ENV (My, 225°)

ENV (My, 270°)

TRF + ENV (Mz, 225°)

TRF + ENV (Mz, 270°)

TRF + ENV (My, 225°)

TRF + ENV (My, 270°)

TRF (Mz, 225°)

TRF (Mz, 270°)

TRF (My, 225°)

TRF (My, 270°)

The design check of bending and axial force eff(M,N) as well as torsion and shear eff(V,T) is shown below: Table 8-1: Design check of tower top cross section, level +170m

The maximum utilization vertically (M,N) is 0.65 and horizontally (V,T) 0.74, which is acceptable. Table 8-2: Design check of tower cross section above bridge girder, level +55m


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The maximum utilization vertically is 0.74 and horizontally 0.93, which is acceptable. Table 8-3: Design check of tower cross section below cross beam, level +45m

The maximum utilization vertically is 0.71 and horizontally 0.82, which is acceptable. Table 8-4: Design check of tower cross section at base, level +5m

The maximum utilization vertically is 0.77 and horizontally 0.96, which is acceptable. The tower legs have conservatively been designed assuming a full correlation between dynamic wind and wave forces, hence a future optimization is possible, as the true correlation is in the order of 0.6-0.8.

8.2.1 Tower cross beam The cross beam supports the bridge girder and secure the frame action of the tower structure. The maximum loads occur at the connection to the tower leg, which is based on a simple frame of 43m height and length as illustrated below:


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Figure 8-26: Idealized cross beam frame

The vertical bearing loads for governing wind and waves are:

, 1.2 ∙802

∙ 300 14.4

The negative bending moment at the cross beam to tower connection when assuming equal stiffness is calculated:

, 0.5 ∙ 28.7 ∙ 43 ∙3

6 1264.45

, 14.4 ∙13.75 ∙ 29.25

2 ∙ 43

13 4 213.7543 1 2

1 2 6 1

13 4 229.2543 1 2

1 2 6 189.8

, 264,45 89.8 354.3

The shear force is equal to the bearing reaction load and axial tension half the horizontal bearing reaction. The load is applied to the established FAGUS model:

Figure 8-27: Design check of cross beam at tower connection


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The axial utilization is 0.90 (M,N) and the vertical shear utilization is 0.74 (V,T), which is acceptable. The central part of the cross beam is assumed to be subjected to 60% of the maximum negative bending moment:

, 0.6 ∙ , 0.6 ∙ 354.3 212.8

The load is applied to the established FAGUS model:

Figure 8-28: Design check of cross beam, central part

The axial utilization is 0.91 (M,N), which is acceptable. The shear forces are insignificant at this location.

8.2.2 Tower Foundation The design loads at the foundation soffit in level 0 is presented in Table 8-5:

Table 8-5: Tower foundation, design loads

N Mz My Qz Qy Mx

ENV (Mz, 225°) ‐512.0 1590.1 1441.9 23.3 10.1 4.7

ENV (Mz, 270°) ‐506.0 1215.4 2056.4 31.3 8.0 4.7

ENV (My, 225°) ‐500.0 1055.4 2149.0 29.8 7.0 5.5

ENV (My, 270°) ‐501.7 1032.1 2860.1 38.1 7.0 5.5

TRF + ENV (Mz, 225°) ‐540.7 1706.2 778.4 15.7 11.2 28.9

TRF + ENV (Mz, 270°) ‐537.7 1518.8 1085.6 19.7 10.2 29.0

TRF + ENV (My, 225°) ‐534.6 1438.8 1131.9 19.0 9.7 29.3

TRF + ENV (My, 270°) ‐535.5 1427.2 1487.4 23.1 9.7 29.3

TRF (Mz, 225°) ‐554.7 1850.7 581.6 13.5 12.3 39.4

TRF (Mz, 270°) ‐552.6 1719.5 796.6 16.3 11.6 39.5

TRF (My, 225°) ‐550.4 1663.5 829.1 15.8 11.2 39.7

TRF (My, 270°) ‐551.0 1655.4 1078.0 18.7 11.2 39.7

The tower foundation is checked for maximum contact stress and friction between concrete cast on rock:


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Table 8-6: Tower foundation, design check

ex ey leff beff Aeff σeff Zr τ μEd

[m] [m] [m] [m] [m²] [MPa] [m³] [MPa] [‐]

ENV (Mz, 225°) 2.4 2.3 15.1 60.4 914 0.74 6338.0 0.03 0.04

ENV (Mz, 270°) 1.9 3.3 16.2 58.4 948 0.70 6987.9 0.03 0.05

ENV (My, 225°) 1.6 3.5 16.7 58.1 970 0.68 7327.6 0.03 0.05

ENV (My, 270°) 1.6 4.6 16.8 55.8 937 0.71 7075.4 0.04 0.06

TRF + ENV (Mz, 225°) 2.5 1.2 15.0 62.6 938 0.75 6465.5 0.03 0.03

TRF + ENV (Mz, 270°) 2.2 1.7 15.5 61.6 956 0.73 6794.7 0.03 0.04

TRF + ENV (My, 225°) 2.1 1.8 15.7 61.5 967 0.72 6960.7 0.03 0.04

TRF + ENV (My, 270°) 2.1 2.3 15.8 60.4 953 0.73 6859.4 0.03 0.04

TRF (Mz, 225°) 2.7 0.9 14.7 63.2 927 0.77 6271.0 0.03 0.03

TRF (Mz, 270°) 2.5 1.2 15.0 62.5 940 0.76 6497.3 0.03 0.04

TRF (My, 225°) 2.4 1.3 15.2 62.5 948 0.75 6609.3 0.03 0.04

TRF (My, 270°) 2.4 1.6 15.2 61.7 938 0.76 6546.4 0.03 0.04

The minimum friction required is 0.06, which is acceptable for concrete cast on rock. The maximum effective stress is 0.76MPa, which is acceptable. The future ground investigations at Svarvahelleholmen shall verify a sufficient strength of the rock material at the foundation position, which is likely to be in the order of 6-10MPa.

8.2.3 Bearings The bridge girder is vertically and laterally restrained by bearings, as shown in below figure.

Figure 8-29: Bearings at tower

The vertical bearings are governed by dead- and traffic loads, which in ultimate limit state is conservatively estimated to:

, 1.2 ∙ 1.35 ∙ ∙802

1.2 ∙ 300 1.35 ∙ 70 ∙802

18.2 20 ,

The horizontal bearings are governed by wind and wave loads, which in ultimate limit state can be calculated as:

, 1.6 ∙ 5.5 0.6 ∙ 5.5 1.6 ∙ 1.25 ∙ 7.3 28.7 30 ,


117

When using a correlation coefficient between dynamic wind and waves of 0.6. The maximum bearing reactions can be accommodated by a standard elastomeric pot bearing, e.g. Mageba type TA 9.5 og TA 12 as principally illustrated below:

Figure 8-30: Schematic view of elastomeric pot bearing (Mageba)

The bearings have a load capacity of NRd,TA 9.5 = 18.8MN and NRd,TA 12 = 29.2MN and can facilitate movements in every direction and rotations about every axis. No vertical or longitudinal forces are transmitted between the bridge girder and tower except friction, which is insignificant (guide bars no. 6 in Figure 8-30 is not included for TA bearings). The bearings are connected to the tower by threaded sleeves or anchor plates with shear studs. The bridge girder features a sliding plate (no. 5 in Figure 8-30) which shall allow the longitudinal and limited vertical movements. The bridge girder shall be able to transfer the bearing load, which requires some local detailing. The bearings shall be positioned at a transverse diaphragm when the bridge is in neutral position at reference temperature. The tower and cross beam shall likewise be modified locally at the bearing location in order to transfer the bearing load to the transverse shear walls and full tower cross section.

8.2.4 Construction Stages The free standing tower and the completed cable stayed bridge (CSB) is checked, due to the fact that these structures can be finished before the connection to the floating bridge is established at the anchor pier in axis 3. As the construction time for the cable stayed bridge is significant the tower and cable stayed bridge connected to the abutment south shall be able to withstand a 100 year storm event. The following load cases is checked with 0 degrees being wind parallel to the bridge:

Free standing tower 0 degr.



Completed CSB 0 degr.



Completed CSB 0 degr. w/column




118

It is checked whether a column in the side span is necessary during construction (w/column). The 4 tower leg cross sections is checked:

Table 8-7: Construction design check of tower cross section below stay cable, level +170m

The maximum utilization vertically (M,N) is 0.74 and horizontally (V,T) 0.73, which is acceptable.

Table 8-8: Construction design check of tower cross section above bridge girder, level +55m

The maximum utilization vertically is 0.98 and horizontally 0.61, which is acceptable.

Table 8-9: Construction design check of tower cross section below cross beam, level +45m

The maximum utilization vertically is 0.90 and horizontally 0.90, which is acceptable.


119

Table 8-10: Construction design check of tower cross section at base, level +5m

The maximum utilization vertically is 0.99 and horizontally 0.98, which is acceptable. The influence of the side span column is identified as being insignificant, hence not required for the construction stages.

The tower foundation is also checked for construction loads:

MRd,z/MEd,z MRd,y/MEd,y ez ey UR σeff μ

[‐] [‐] [m] [m] [‐] [MPa] [‐]

1.38 31.64 3.6 0.5 0.39 0.99 0.03

1.82 10.16 2.7 1.4 0.30 0.65 0.03

5.37 7.53 0.9 1.9 0.12 0.38 0.02

8.36 31.49 0.6 0.5 0.07 0.40 0.01

5.53 11.37 0.9 1.3 0.11 0.45 0.02

4.76 8.67 1.0 1.7 0.13 0.49 0.02

11.41 28.74 0.4 0.5 0.05 0.39 0.01

7.09 10.73 0.7 1.4 0.09 0.44 0.02

5.96 8.20 0.8 1.8 0.11 0.46 0.03

The table documents the safety against overturning, MRd/MEd with a minimum of 1.38, which is acceptable. Following handbook N400, clause 11.2.2 the eccentricity is checked for the rarely occurring SLS load combination.

Furthermore the effective stress below the foundation and the necessary friction below concrete and rock is checked following handbook N400, clause 11.2.3 and 11.2.5. The maximum stress is below 1 MPa, which is small and acceptable, but must be documented by future ground investigations at Svarvahelleholmen. The required friction is very small, hence sliding will not be a problem.


120

8.3 Stay Cables

8.3.1 Stay Cable Forces In table below characteristic loads are given for the stay cables. The loads are combined into 3 ULS load combinations with dominating permanent load, traffic load and environmental loads. Wind and waves are combined assuming full correlation. Stays are mainly governed by dominating permanent load in ULS1 (load factor 1.35 on permanent load).

Table 8-11: Characteristic loads and ULS-combinations, Cable-stays

Characteristic loads ULS combination

Cable id Perm Traffic Tidal Wave Wind Wind ULS 1 ULS 2 ULS 3 Max ULS kN kN kN 100year 100year Static 100year Dynamic

1101 5055 1603 260 579 -186 365 9023 8914 7537 90231102 4850 1573 253 569 -182 358 8704 8613 7264 87041103 4645 1540 245 549 -178 351 8374 8301 6969 83741104 4540 1504 236 534 -174 343 8178 8106 6804 81781105 4334 1465 227 516 -169 333 7841 7784 6510 78411106 4451 1385 211 492 -171 316 7884 7777 6566 78841107 4059 1240 175 414 -159 259 7114 7007 5867 71141108 3670 1159 134 315 -141 189 6389 6308 5124 63891109 3580 1167 94 213 -121 135 6156 6092 4750 61561110 3392 1185 58 122 -102 126 5828 5799 4330 58281111 3105 1189 30 63 -84 154 5394 5410 3895 54101112 3017 1173 10 55 -69 183 5253 5275 3806 52751113 2729 1155 -3 73 -57 196 4858 4916 3515 49161114 2535 1154 -10 83 -47 192 4599 4687 3308 46871115 2430 1113 -12 81 -38 172 4413 4500 3170 45001116 2216 1043 -11 69 -30 142 4046 4136 2875 41361117 2182 945 -9 53 -21 108 3891 3947 2785 39471118 2423 799 -6 36 -12 75 4064 4024 3026 40641201 5055 1603 260 579 53 365 9157 9048 7919 91571202 4850 1573 253 569 30 352 8820 8730 7597 88201203 4645 1540 245 549 6 332 8471 8398 7247 84711204 4540 1505 236 534 -16 318 8260 8188 7033 82601205 4334 1466 227 516 -34 315 7912 7855 6709 79121206 4451 1385 211 492 -48 321 7954 7847 6767 79541207 4059 1239 175 414 -58 326 7193 7086 6095 71931208 3670 1169 134 315 -63 325 6488 6411 5379 64881209 3580 1181 94 214 -64 312 6262 6203 5014 62621210 3392 1201 58 123 -62 288 5920 5898 4551 59201211 3105 1208 30 63 -57 255 5461 5485 4036 54851212 3017 1194 10 62 -51 219 5300 5331 3883 53311213 2729 1177 -3 81 -43 183 4888 4955 3542 49551214 2535 1176 -10 92 -34 151 4620 4716 3307 47161215 2430 1136 -12 89 -26 125 4432 4527 3160 45271216 2216 1067 -11 75 -17 103 4067 4166 2870 41661217 2182 968 -9 57 -9 84 3914 3979 2789 39791218 2423 819 -6 37 -2 64 4085 4054 3034 40851301 5178 1031 660 719 44 365 9275 8916 8732 92751302 4948 1112 537 760 24 352 8931 8639 8371 89311303 4621 1234 410 751 2 332 8453 8260 7781 8453


121

1304 4597 1364 291 695 -17 318 8370 8233 7476 83701305 4377 1476 188 616 -34 315 8010 7951 6920 80101306 4061 1554 104 532 -48 321 7508 7528 6272 75281307 3947 1593 41 447 -58 326 7265 7318 5893 73181308 3838 1599 -2 375 -64 325 7026 7098 5563 70981309 3537 1577 -28 314 -67 312 6525 6633 5038 66331310 3546 1527 -40 264 -67 288 6434 6520 4911 65201311 3069 1458 -41 224 -66 255 5685 5815 4228 58151312 2799 1379 -37 191 -64 219 5216 5355 3811 53551313 2935 1298 -29 160 -61 183 5299 5385 3891 53851314 2591 1221 -20 131 -58 151 4742 4848 3403 48481315 2268 1145 -11 106 -54 125 4218 4342 2955 43421316 2263 1066 -5 85 -49 103 4124 4216 2900 42161317 2293 970 -1 66 -42 84 4062 4111 2897 41111318 2379 824 1 50 -31 64 4030 4007 2967 40301401 5178 1053 660 654 -182 365 9124 8774 8242 91241402 4948 1136 537 712 -178 358 8809 8527 7958 88091403 4621 1257 410 715 -174 351 8357 8173 7444 83571404 4597 1387 291 678 -170 343 8303 8175 7221 83031405 4377 1499 188 606 -165 333 7957 7908 6709 79571406 4061 1579 104 522 -156 316 7463 7493 6075 74931407 3947 1618 41 442 -136 259 7219 7282 5692 72821408 3838 1627 -2 368 -112 189 6976 7059 5343 70591409 3537 1606 -28 306 -87 135 6475 6595 4817 65951410 3546 1557 -40 262 -65 126 6408 6507 4757 65071411 3069 1489 -41 228 -47 154 5695 5837 4171 58371412 2799 1411 -37 200 -33 183 5258 5409 3844 54091413 2935 1331 -29 174 -24 196 5365 5464 3990 54641414 2591 1254 -20 149 -20 192 4820 4940 3539 49401415 2268 1178 -11 123 -18 172 4298 4434 3092 44341416 2263 1099 -5 99 -18 142 4196 4301 3016 43011417 2293 1000 -1 76 -16 108 4120 4181 2981 41811418 2379 848 1 54 -12 75 4070 4057 3016 4070


122

8.3.2 Design of Cables In ULS, stays can be utilized to 1/1.8 = 0.56 of the breaking strength. This gives allowable stress in ULS of 0.56 x 1860 = 1042 MPa.

The analyses are not re-run due to these changes in stiffness.

The total weight steel in stay cables is approximately 1000 tons.

Table 8-12: Design-check, cables - ULS

Current crossection Updated crossection

Cable id

Max ULS

No of strands

Cable area

Stress

Stress limit

Stress/Stress limit

No of strands

Cable area

Stress

Stress/stress limit Length

Weight

kN mm^2 Mpa Mpa 0.56*GUTS Mpa m ton

1101 9023 59 8790 1027 1042 0.99 58 8700 1037 1.00 385.0 26.31102 8704 57 8494 1025 1042 0.98 56 8400 1036 0.99 374.8 24.71103 8374 55 8187 1023 1042 0.98 54 8100 1034 0.99 364.8 23.21104 8178 52 7869 1039 1042 1.00 53 7950 1029 0.99 354.7 22.11105 7841 50 7539 1040 1042 1.00 51 7650 1025 0.98 344.6 20.71106 7884 49 7389 1067 1042 1.02 51 7650 1031 0.99 325.6 19.61107 7114 47 7076 1005 1042 0.97 46 6900 1031 0.99 306.8 16.61108 6389 45 6758 945 1042 0.91 41 6150 1039 1.00 288.1 13.91109 6156 43 6433 957 1042 0.92 40 6000 1026 0.99 269.7 12.71110 5828 41 6104 955 1042 0.92 38 5700 1022 0.98 251.5 11.31111 5410 38 5771 937 1042 0.90 35 5250 1030 0.99 233.7 9.61112 5275 36 5436 970 1042 0.93 34 5100 1034 0.99 216.3 8.71113 4916 34 5102 964 1042 0.93 32 4800 1024 0.98 199.3 7.51114 4687 32 4773 982 1042 0.94 30 4500 1041 1.00 183.1 6.51115 4500 30 4453 1010 1042 0.97 29 4350 1034 0.99 167.6 5.71116 4136 28 4151 996 1042 0.96 27 4050 1021 0.98 153.3 4.91117 3947 26 3877 1018 1042 0.98 26 3900 1012 0.97 140.4 4.31118 4064 24 3643 1115 1042 1.07 27 4050 1003 0.96 129.3 4.11201 9157 59 8790 1042 1042 1.00 59 8850 1035 0.99 385.0 26.71202 8820 57 8494 1038 1042 1.00 57 8550 1032 0.99 374.8 25.21203 8471 55 8187 1035 1042 0.99 55 8250 1027 0.99 364.8 23.61204 8260 52 7869 1050 1042 1.01 53 7950 1039 1.00 354.7 22.11205 7912 50 7539 1049 1042 1.01 51 7650 1034 0.99 344.6 20.71206 7954 49 7389 1076 1042 1.03 51 7650 1040 1.00 325.6 19.61207 7193 47 7076 1016 1042 0.98 47 7050 1020 0.98 306.8 17.01208 6488 45 6758 960 1042 0.92 42 6300 1030 0.99 288.1 14.31209 6262 43 6433 973 1042 0.93 41 6150 1018 0.98 269.7 13.01210 5920 41 6104 970 1042 0.93 38 5700 1039 1.00 251.5 11.31211 5485 38 5771 950 1042 0.91 36 5400 1016 0.98 233.7 9.91212 5331 36 5436 981 1042 0.94 35 5250 1015 0.97 216.3 8.91213 4955 34 5102 971 1042 0.93 32 4800 1032 0.99 199.3 7.51214 4716 32 4773 988 1042 0.95 31 4650 1014 0.97 183.1 6.71215 4527 30 4453 1017 1042 0.98 29 4350 1041 1.00 167.6 5.71216 4166 28 4151 1004 1042 0.96 27 4050 1029 0.99 153.3 4.91217 3979 26 3877 1026 1042 0.99 26 3900 1020 0.98 140.4 4.31218 4085 24 3643 1121 1042 1.08 27 4050 1009 0.97 129.3 4.1


123

1301 9275 58 8669 1070 1042 1.03 60 9000 1031 0.99 423.1 29.91302 8931 56 8405 1063 1042 1.02 58 8700 1027 0.99 403.7 27.61303 8453 54 8133 1039 1042 1.00 55 8250 1025 0.98 384.3 24.91304 8370 52 7855 1066 1042 1.02 54 8100 1033 0.99 365.1 23.21305 8010 50 7569 1058 1042 1.02 52 7800 1027 0.99 346.0 21.21306 7528 49 7277 1035 1042 0.99 49 7350 1024 0.98 326.9 18.91307 7318 47 6977 1049 1042 1.01 47 7050 1038 1.00 308.1 17.11308 7098 44 6671 1064 1042 1.02 46 6900 1029 0.99 289.4 15.71309 6633 42 6358 1043 1042 1.00 43 6450 1028 0.99 270.9 13.71310 6520 40 6040 1079 1042 1.04 42 6300 1035 0.99 252.7 12.51311 5815 38 5718 1017 1042 0.98 38 5700 1020 0.98 234.8 10.51312 5355 36 5394 993 1042 0.95 35 5250 1020 0.98 217.3 9.01313 5385 34 5070 1062 1042 1.02 35 5250 1026 0.98 200.3 8.31314 4848 32 4749 1021 1042 0.98 32 4800 1010 0.97 184.0 6.91315 4342 30 4437 979 1042 0.94 28 4200 1034 0.99 168.5 5.61316 4216 28 4141 1018 1042 0.98 27 4050 1041 1.00 154.0 4.91317 4111 26 3871 1062 1042 1.02 27 4050 1015 0.97 141.0 4.51318 4030 24 3641 1107 1042 1.06 26 3900 1033 0.99 129.8 4.01401 9124 58 8669 1052 1042 1.01 59 8850 1031 0.99 423.1 29.41402 8809 56 8405 1048 1042 1.01 57 8550 1030 0.99 403.7 27.11403 8357 54 8133 1028 1042 0.99 54 8100 1032 0.99 384.3 24.41404 8303 52 7855 1057 1042 1.01 54 8100 1025 0.98 365.1 23.21405 7957 50 7569 1051 1042 1.01 51 7650 1040 1.00 346.0 20.81406 7493 49 7277 1030 1042 0.99 48 7200 1041 1.00 326.9 18.51407 7282 47 6977 1044 1042 1.00 47 7050 1033 0.99 308.1 17.11408 7059 44 6671 1058 1042 1.02 46 6900 1023 0.98 289.4 15.71409 6595 42 6358 1037 1042 1.00 43 6450 1022 0.98 270.9 13.71410 6507 40 6040 1077 1042 1.03 42 6300 1033 0.99 252.7 12.51411 5837 38 5718 1021 1042 0.98 38 5700 1024 0.98 234.8 10.51412 5409 36 5394 1003 1042 0.96 35 5250 1030 0.99 217.3 9.01413 5464 34 5070 1078 1042 1.03 35 5250 1041 1.00 200.3 8.31414 4940 32 4749 1040 1042 1.00 32 4800 1029 0.99 184.0 6.91415 4434 30 4437 999 1042 0.96 29 4350 1019 0.98 168.5 5.81416 4301 28 4141 1039 1042 1.00 28 4200 1024 0.98 154.0 5.11417 4181 26 3871 1080 1042 1.04 27 4050 1032 0.99 141.0 4.51418 4070 24 3641 1118 1042 1.07 27 4050 1005 0.96 129.8 4.1

Sum 18977.01002.3


124

8.4 Columns The ULS loads on the columns are dominated by bending moments about north/south and east/west axis from wave response, see Table 8-13. As a result only ULS 3 have been used for design check, meaning permanent loads are multiplied by a factor of 1.2, characteristic static and dynamic wind loads by a factor of 1.6, and characteristic wave loads by a factor of 2. The von Mises float criterion have been used to evaluate capacity. The combination factor for wind and waves has been set to 0.6, and is applied on the wind forces which are smaller in magnitude. For wave loads, the stress calculation is based on actual stress time series, which ensures full correlation between load components. For wind, the combination factors between the load components have been set to 1.0, which is conservative. The characteristic wave loads are larger at the top of columns than the bottom, and are listed in Table 8-13 for axes 3 to 7 (transition to low part of bridge) and axis 18 (most utilized column in low part of bridge). Total Von Mises stress at bottom and top of the columns are given in Figure 8-31. For axes 3 to 6 a cross-section with approximately 25% higher bending stiffness is used in order to get below the allowable stress level. The highest stress is observed at axis 3, where the utilization is 0.97. Axes 3, 4 and 5 are governed by waves from north-west direction. Here, both bending components contribute significantly. For the remaining axes (6 to 20), waves from west are governing and bending about the north/south axis is dominating. Table 8-13: Characteristic wave loads for top of columns in axis 3 to 7 and axis 18

Axis 3 Axis 4 Axis 5 Axis 6 Axis 7 Axis 18

Wave Heading (from) NW NW NW W W W

Axial force (vertical) [MN] 6.0 8.8 7.2 2.3 2.3 2.0

Shear force east/west axis [MN] 4.8 9.6 12.6 15.5 16.3 15.1

Shear force north/south axis [MN] 16.0 17.5 17.3 4.7 4.4 4.0

Bending moment about east/west axis [MNm] 904.3 907.8 786.0 174.7 125.5 78.4

Bending moment about north/south axis [MNm] 327.6 587.8 740.4 783.0 687.0 577.3

Torque [MNm] 255.8 232.7 223.0 152.2 144.6 147.7


125

Figure 8-31 Max Von Mises stress at top and bottom of columns for ULS 3


126

8.5 Abutment South The abutment in the south end of the bridge is checked at the joint between the bridge girder and the caisson, as well as between the caisson and the fjell/rock.

8.5.1 Bridge Girder Connection The south bridge abutment is designed for the following loads:

Table 8-14: Design loads at south abutment

ULS G‐EQ Q‐Trf Q‐Temp Q‐Trf/Env Q‐Env

N [MN] 75 80 72 91 113

Mz [MNm] 287 367 287 342 249

My [MNm] 565 574 565 867 1416

Qz [MN] 8 8 8 11 16

Qy [MN] 9 12 9 10 8

Mx [MNm] 44 59 44 49 19

The governing load combination is with leading environmental loads, Q-Env. The strong axis moment (My) is transferred to the caisson by two longitudinal shear connections, which is subjected to an axial force equal to:

2 16113

21416

16145

The number of shear studs at one girder and maximum shear force in one stud is:

4 ∙40

0.1251280

145 ∙ 101200

113

The design capacity of a ø22 shear stud is:

0.8 ∙ ∙ 0.8 ∙ 500 ∙ 380 ∙ 101.25

122 113 ,

The connection shall be able to submit tension due to the uplift forces from the stay cables and the weak axis bending and torsional moment. The tension in the shear studs will be more than 0.1PRd, hence elongated anchor dowels placed centrally in the connection are used to transmit the required force. The maximum allowable tension stress in the long studs are taken equal to the reinforcement stress:

5001.15

435

The tension transmitting studs are positioned with 250mm spacing along the total length of the abutment (2 x 160 nos) and along the front and end diaphragm. To evaluate the maximum stress in a stud an equivalent reinforced concrete model is established in FAGUS. The model is 40m long and 16.65m wide with ø22 bars placed as studs. The design loads to be applied is:

2 ∙ 5 ∙ 91 ∙ 150 ∙ 1860 ∙ 0.35 ∙ sin 24° ∙ 10 8 44

113 ∙ 1.75 249 447

19 16 ∙ 1.75 47


127

The design forces are applied to the model with the below result:

Figure 8-32: Stud tension connection at south abutment

The utilization of the connection is 0.89, which is acceptable. To prevent longitudinal shear failure and uplift of tension dowels two ø25 reinforcement hoops are placed at each transverse row of shear studs.

The maximum stress in a reinforcement bar is:

435 ∙ 224 ∙ 25

84

4 ∙ 113 ∙ 10

4 ∙ 25 ∙ 4230

84 3 ∙ 230 407 435 ,

The maximum stress caused by shear and tension is below the allowable yield strength in the reinforcement bar ø25, hence the shear stud connection has an sufficient capacity to transfer the loads from the bridge girder to the caisson.

8.5.2 Foundation on Rock The caisson is placed on solid rock with the following transformed design loads from the bridge girder connection:

Table 8-15: Design loads on south abutment foundation

N Mz My Qz Qy Mx

[MN] [MNm] [MNm] [MN] [MN] [MNm]

G‐EQ 380 1708 150 8 75 565

Q‐Trf 382 1883 145 8 80 574

Q‐Temp 380 1651 145 8 72 565

Q‐Env 381 2077 200 11 91 867

Q‐Env 378 2388 303 16 113 1416


128

The caisson structure is made of 3300 m³ concrete and filled with 16500 m³ saturated sand ballast, which increase the axial load with 400MN. The effective design stress and friction between concrete and rock is calculated based on effective area:

Table 8-16: Effective design stress and friction

ez ey leff beff Aeff σeff Zr τ μEd

[m] [m] [m] [m] [m²] [MPa] [m³] [MPa] [‐]

G‐EQ 4.5 0.4 31.0 30.2 937 0.41 9551 0.14 0.34

Q‐Trf 4.9 0.4 30.2 30.2 912 0.42 9179 0.15 0.36

Q‐Temp 4.3 0.4 31.3 30.2 947 0.40 9703 0.13 0.34

Q‐Trf/Env 5.5 0.5 29.1 30.0 871 0.44 8571 0.21 0.47

Q‐Env 6.3 0.8 27.4 29.4 805 0.47 7593 0.33 0.70

The governing load combination is with leading environmental loads, Q-Env, which include a maximum effective stress of 0.47MPa. A typical design resistance of 5MPa for solid rock is assumed, hence the maximum 0.47MPa is acceptable.

The maximum friction coefficient between concrete and rock is 0.70. The characteristic friction coefficient is 1.0 and in-lieu of more precise data a partial factor for friction is assumed equal to 1.3, hence a design value can be calculated:

1.311.3

0.77 0.70,

The abutment caisson is able to withstand the induced load by vertical contact stress and friction.

8.5.3 Caisson The caisson outer walls and bottom slab is verified for the induced pressures in SLS and ULS. For the outer walls the transverse pressure in SLS and ULS is calculated assuming an earth pressure coefficient of 0.5 at rest:

, 15 ∙ 0.01 15 ∙ 0.01 ∙ 0.5 0.225

The bending moment is based on an upper bound solution for a plate spanning in two directions subjected to a triangular load distribution:

9.7 , 15

2

1 , 1 ,

2 ∙ 9.7

√2 √26.9

2

1 , 1 ,

2 ∙ 15

√2 √210.6

16 1

0.225 ∙ 6.9 ∙ 10.6

16 16.910.6

10.66.9

0.32

1.35 ∙ 0.32 0.432


129

A FAGUS model of a 5m wall section is used to check the reinforcement stress in SLS and the capacity in ULS:

Figure 8-33: South abutment outer wall, SLS check

The wall is reinforced with ø25 bars c/c 150mm (average), which in SLS are utilized to 171MPa, which is acceptable to limit the crack widths to 0.19mm.

Figure 8-34: South abutment outer wall, ULS check

The utilization ratio in ULS is 0.53, which is acceptable.

The bottom plate will during SLS load combinations not be fully loaded from only one side, but assumed as a triangular distribution with full unloading at one side and 0 effective stress at the inner wall:

15 ∙ 0.02 0.3


7.7 , 9.35

2

1 , 1 ,

2 ∙ 7.7

√2 √25.4

2

1 , 1 ,

2 ∙ 9.35

√2 √26.6

16 1

0.3 ∙ 5.4 ∙ 6.6

16 15.46.6

6.65.4

0.222

At ultimate limit state the minimum effective length of the caisson is 27.3m (Q-Env), thus the front or rear row of cells will be unloaded from the ground and the bottom plate shall be able to carry the vertical load from the ballast:

1.2 ∙ 15 ∙ 0.02 0.36

The bending moment is based on an upper bound solution for a plate spanning in two directions subjected to a uniform load distribution:


130

7.7 , 9.35

2

1 , 1 ,

2 ∙ 7.7

√2 √25.4

2

1 , 1 ,

2 ∙ 9.35

√2 √26.6

8 1

0.36 ∙ 5.4 ∙ 6.6

8 15.46.6

6.65.4

0.533

A FAGUS model of a 5m bottom slab section is used to check the reinforcement stress in SLS and the capacity in ULS:

Figure 8-35: South abutment bottom slab, SLS check

The bottom slab is like the outer wall reinforced with ø25 bars c/c 150mm, which in SLS are utilized to 172MPa, which is acceptable to limit the crack widths to 0.2mm.

Figure 8-36: South abutment bottom slab, ULS check



131

8.6 Abutment North (Flua) The abutment at Flua is checked at the joint between the bridge girder and the caisson, as well as between the caisson and seabed.

8.6.1 Bridge Girder Connection at Flua The north bridge abutment at Flua is designed for the following loads:

Table 8-17: Design loads at abutment Flua

ULS G‐EQ Q‐Trf Q‐Temp Q‐Trf/Env Q‐Env

N [MN] 0 0 0 0 0

Mz [MNm] 2091 2136 1956 2195 2252

My [MNm] 2076 2083 2076 3358 5615

Qz [MN] 12 12 12 19 35

Qy [MN] 46 46 43 45 41

Mx [MNm] 356 400 356 533 795

The governing load combination is with leading environmental loads, Q-Env, which is examined in detail next. The strong axis moment (My) will be restrained by horizontal bearings, which are subjected to a reaction force in the front and rear end of the abutment:

, 48 85615

4035 175 2 90

, 48 85615

40140 2 70

Two bearings are positioned on each side of the bridge girder in each end of the abutment (total of 8), which all are assumed to be elastomeric pot bearings of 90MN (front end) and 70MN (rear end). The bearing force is transferred to the caisson by a steel bearing console, as illustrated below:

Figure 8-37: Steel bearing console, front end loading


132

In the design drawing, K82406, 3 x 16 nos. prestressing cables with 31 strands has been shown in each end of the abutment. The distribution between the front and rear end should rather be 3 x 14 cables in the rear end and 3 x 18 cables in the front, which will still total 96 cables (96 x 31 x 150mm² x 28m x 7.85 t/m³ = 100 ton). The design force, prestressing force and capacity is in the front of the abutment:

, 2 ∙ 175 350

, 3 ∙ 18 ∙ 31 ∙ 150 ∙ 1860 ∙ 0.75 ∙ 10 350

, 3 ∙ 18 ∙ 31 ∙ 150 ∙1860

1.1∙ 10 425 350 ,

And in the rear end:

, 2 ∙ 140 280

, 3 ∙ 14 ∙ 31 ∙ 150 ∙ 1860 ∙ 0.75 ∙ 10 272

, 3 ∙ 14 ∙ 31 ∙ 150 ∙1860

1.1∙ 10 330 280 ,

The capacity of the prestressing is sufficient, however uplift will occur in ultimate limit state as the design force in the rear end is slightly larger than the prestressing force:

∆280 272

2 ∙ 3 ∙ 16 ∙ 31 ∙ 150 ∙ 10∙28000190000

6 ,

The uplift is insignificant and acceptable to maintain the integrity and restrain of the structure. The contact stress between the caisson and the lower part of the steel bearing plinth is:

,1758 ∙ 0.6

36.5

The contact stress at the console-caisson interface exceeds the design concrete compression strength;

0.85 ∙ 451.5

25.5 36.5

Which is acceptable for concentrated loads, where the design resistance can be up to 3 x fcd (actual 1.43 x fcd). The steel bearing console shall be able to transfer the full bearing reaction as shear together with a maximum moment in the central part. The vertical and horizontal structural steel S460N is calculated based on these sectional forces:

175

460 1.1⁄ √3⁄0.725

2 ∙175 ∙ 6 5⁄

460 1.1⁄1

To account for local detailing around bearings and prestressing the total weight of each bearing console is calculated as 2 m² x 13m x 7.85 t/m³ = 200 ton (800 ton for 4 consoles).

The weak axis moment and torsion (Mz and Mx) are restrained by 5000 m³ ballast inside the bridge girder. The bearing reactions in the front and rear end of the abutment will then be:

,

5000 ∙ 0.02 ∙ 0.4

2352

37.5 75


133

,

5000 ∙ 0.02 ∙ 0.6

230 50

Standard elastomeric pot bearing of 75MN and 50MN is choosen, e.g. Mageba type TA 16 and TA 20. The design resistance against weak axis and torsional moment is:

, 2 ∙ 30 ∙ 40 2400 2252 ,

, 75 37.5 ∙ 15.5 50 30 ∙ 15.5 891 795 ,

The ballasted bridge girder is able to withstand the induced moments without any uplift bearings or bearings positioned on top of the bridge girder. The total volume inside the bridge girder is 7000 m³ above the abutment (40m length), hence it is possible to place 5000 m³. The horizontal and vertical bearings together with ballast will restrain the bridge girder for all sectional forces except normal force, as the bridge is free to move longitudinally.

8.6.2 Foundation on Seabed at Flua The Flua caisson is placed on 40m water depth with the following transformed design loads from the bridge girder connection:

Table 8-18: Design loads for foundation on seabed at Flua

N Mz My Qz Qy Mx

[MN] [MNm] [MNm] [MN] [MN] [MNm]

G‐EQ 925 2091 640 12 0 2076

Q‐Trf 925 2136 640 12 0 2083

Q‐Temp 921 1956 640 12 0 2076

Q‐Trf/Env 924 2196 1072 19 0 3358

Q‐Env 920 2253 1921 35 0 5615

The caisson structure is made of 12000 m³ concrete and filled with 56000 saturated sand ballast (42000 m³ dry sand and water), which increase the axial load with 1400MN. The total uplift force is 538MN (28m x 48m x 40m x 0.01MN/m³). The effective design stress and friction between concrete and rock is calculated based on effective area:

ez ey leff beff Aeff σeff Zr τ μEd

[m] [m] [m] [m] [m²] [MPa] [m³] [MPa] [‐]

G‐EQ 2.3 0.7 43.5 26.6 1157 0.80 12259 0.18 0.22

Q‐Trf 2.3 0.7 43.4 26.6 1155 0.80 12224 0.18 0.23

Q‐Temp 2.1 0.7 43.8 26.6 1164 0.79 12352 0.18 0.22

Q‐Trf/Env 2.4 1.2 43.2 25.7 1110 0.83 11435 0.31 0.37

Q‐Env 2.4 2.1 43.1 23.8 1027 0.90 9976 0.60 0.67

The governing load combination is with leading environmental loads, Q-Env, which include a maximum effective stress of 0.90 MPa. A typical design resistance of 5MPa for rock is assumed, hence the maximum 0.90 MPa is acceptable.

The maximum friction coefficient between concrete and rock is 0.67, which is below the design value of 0.77, hence acceptable.


134

8.6.3 Caisson at Flua The caisson outer walls and bottom slab is verified for the induced pressures in SLS and ULS. For the outer walls the transverse pressure in SLS and ULS is calculated assuming an earth pressure coefficient of 0.5 at rest:

, 49.25 ∙ 0.01 49.25 ∙ 0.01 ∙ 0.5 39.25 ∙ 0.01 0.35


7.65 , 49.25

2

1 , 1 ,

2 ∙ 7.65

√2 √25.4

2

1 , 1 ,

2 ∙ 49.25

√2 √234.8

16 1

0.35 ∙ 5.4 ∙ 34.8

16 15.434.8

34.85.4

0.54

1.35 ∙ 054 0.69

A FAGUS model of a 5m wall section is used to check the reinforcement stress in SLS and the capacity in ULS:

Figure 8-38: Flua abutment outer wall, SLS check

The outer wall is reinforced with ø25 bars c/c 150mm, which in SLS are utilized to 182MPa, which is acceptable and to limit the crack width to 0.25mm.

Figure 8-39: Flua abutment outer wall, ULS check


The bottom plate is checked for the differential pressure between the ballast force and the bouyancy force:


135

, 49.25 ∙ 0.020 40 ∙ 0.010 0.585

The bending moment is based on an upper bound solution for a plate spanning in two directions subjected to a uniform load distribution:

7.65 , 7.4

2

1 , 1 ,

2 ∙ 7.65

√2 √25.4

2

1 , 1 ,

2 ∙ 7.4

√2 √25.2

8 1

0.585 ∙ 5.4 ∙ 5.2

8 15.45.2

5.25.4

0.69

1.2 ∙ 0.69 0.83

A FAGUS model of a 5m bottom slab section is used to check the reinforcement stress in SLS and the capacity in ULS:

Figure 8-40: Flua abutment bottom slab, SLS check

The bottom slab is reinforced with ø25 bars c/c 150mm, which in SLS are utilized to 230MPa, which is acceptable to limit the crack width to 0.29mm.

Figure 8-41: Flua abutment bottom slab, ULS check



136

8.7 Pontoon The concrete design are governed by two major issues:

- Concrete surfaces exposed to permanent water pressure.

- Shear capacity of walls exposed to ship impact loads. Addressed in section 9.2.

The submerged boundaries of pontoons shall be watertight, according to NS3473. To ensure this the bottom slab is prestressed in both directions, the outer walls are prestressed vertically and the upper part of outer walls is prestressed horizontally. In order to get the best effect, the prestress is applied before top slab is casted.

Design requirements to ensure watertight external surfaces according to NS3473 tabell A.9 is as follows:

- Bottom plate: Zero membrane force in both directions (tendons in both directions) - Walls (vertical): Zero membrane force (vertical tendons in walls) - Walls (horizontal): Zero membrane force or pressure zone at 0.25h (min. 100mm)

In addition decompression criterion in Eurocode must be fulfilled for prestressed elements. The corresponding load combination is rarely occurring according to NS-EN 1990.

Decompression of tendons is the critical design issue. In Figure 8-42 and Figure 8-43 small areas with decompression are illustrated. With some small adjustment of the cable geometry the requirements will be satisfied.

X

YZ

1.301.201.101.000.9000.8000.7000.6000.5000.4000.322

0.3000.2000.100

0.0739

0.0387

0.0301

0.0221

0.0179

0.0034

0.0030

0.0027

0.0

0.0

-0.0018

-0.0057

-0.0061

-0.0064

-0.0070

-0.0101

-0.0136

-0.0146 -0.0170

-0.0224

-0.0224-0.0288

-0.0292

-0.0295-0.0312

-0.0322

-0.0326

-0.0339-0.0356-0.0362

-0.0411

-0.0424

-0.0447

-0.0450 -0.0498

-0.0529

-0.0538

-0.0557-0.0557

-0.0570

-0.0571

-0.0574

-0.0576

-0.0580

-0.0588

-0.0597

-0.0600

-0.0606

-0.0626 -0.0648

-0.0648

-0.0651

-0.0654 -0.066

-0.0681

-0.0688

-0.0698-0.0706

-0.0713

-0.0746

-0.0757

-0.0763

-0.0781

-0.0785

-0.0800

-0-0.0803

-0.0804

-0.0816

-0.0818-0.0819

-0.0828

-0.0833 -0.0836

-0.0846

-0.0848

-0.0869

-0.0871

-0.0887

-0.0887

-0.0889

-0.0906

-0.0906

-0.0908

-0.0923

-0.0924

-0.0929

-0.0945

-0.0946 -0.0952

-0.0955

-0.0959

-0.0963

-0.0966

-0.0970

-0.0973

-0.0974

-0.0979

-0.0995

-0.100

-0.112

-0.115

-0.118

-0.118

-0.118

-0.120

-0.131

-0.145

-0.149

-0.188

1.46

Sector of system Group 1

Maximum decompression strain in the direction of tendons in Node , Design Case 3 SLS design

50.00 60.00 70.00 80.00

12


137

Figure 8-42: Decompression strain (0/00) in bottom slab

Figure 8-43: Decompression strain (0/00) in vertical walls Crack requirements are according to Eurocode table NA.7.lN with exposure class XS3 (splash zone), with w = 0.3 mm for combination “rarely occurring”. Interior walls are in intact situation not exposed to water pressure. In temporary phase some cells are used for water ballast.

In an accident situation it is assumed that two chambers can be filled with water. In this situation the structure must limit water penetration into intact cells order to avoid progressive collapse. For the Okanagan floating bridge a limiting criteria on reinforcement stresses of 120 MPA for water filling of the cells up to the external water levels without combination with other loads except own weight was used. Alternatively a pressure zone at 0.25h ( min 100mm) combined with crack width requirements equal 0.3mm should be used.

For combined loads in intact situation the combination rarely occurring is used with crack width equal 0.3mm.

XYZ

2.802.602.402.20

2.04

2.001.801.601.401.201.00

0.800

0.600

0.5240.452

0.400

0.276

0.200

0.175

0.120

0.0991

0.0832

0.0442

0.0190

0.0125

0.0108

0.00960.0079

0.0

-0.0024

-0.0066

-0.0121-0.0134

-0.0184

-0.0203

-0.0210

-0.0279

-0.0301

-0.0308

-0.0330

-0.0333

-0.0355

-0.0365

-0.0379

-0.0385

-0.0391

-0.0392

-0.0400

-0.0425

-0.0429

-0.0436

-0.0440

-0.0440

-0.0448

-0.0452

-0.0455

-0.0464

-0.0465-0.0466

-0.0469

-0.0486

-0.0487

-0.0500

-0.0503

-0.0506

-0.0506-0.0507

-0.0511

-0.0512

-0.0513

-0.0520

-0.0520

-0.0521

-0.0529

-0.0532

-0.0534

-0.0534

-0.0536

-0.0544

-0.0549

-0.0551

-0.0555

-0.0557

-0.0558-0.0558

-0.0561

-0.0563

-0.0575

-0.0576-0.0584

-0.0590

-0.0602

-0.0608

-0.0610

-0.0619 -0.0619

-0.0626

-0.0627

-0.0634

-0.0640

-0.0644

-0.0662

-0.0665

-0.0673

-0.0677

-0.0678

-0.0683

-0.0691

-0.0695

-0.0699

-0.0702

-0.0704

-0.0710

-0.0710

-0.0732

-0.0735

-0.0758-0.0761

-0.0763

-0.0764

-0.0765

-0.0767

-0.0770

-0.0771

-0.0771

-0.0772

-0.0774

-0.0776

-0.0777

-0.0777

-0.0777

-0.0777

-0.0777

-0.0778

-0.0779

-0.0780

-0.0780-0.0780

-0.0780

-0.0781

-0.0784

-0.0786

-0.0786

-0.0786

-0.0791

-0.0791

-0.0794

-0.0797

-0.0799

-0.0802

-0.0804

-0.0807-0.0810

-0.0821

-0.0822

-0.0824 -0.0825-0.0827

-0.0831

-0.0834

-0.0847

-0.0854

-0.0855

-0.

-0.0871

-0.0876

-0.0892

-0.0896

-0.0897

-0.0898

-0.0902

-0.0963

-0.0

-0.0974-0.0990

-0.100

-0.101 -0.101-0.102-0.137 2.90

Sector of system Quadrilateral Elements Group 2 3

Maximum decompression strain in the direction of tendons in Node, Design Case 3 SLS design , from -0.257 to 2.90

60.00 70.00 80.00 90.00

2


138

Figure 9-1: Illustration of simplified head on bow impact model in USFOS

9 Ship Impact From the ship collision risk analysis, 3 events have been identified as potential risks for the concept:

‐ Head-on-bow collisions with bridge pontoons ‐ Deckhouse collision with bridge girder ‐ Head-on-bow collisions with bridge girder

Head-on-bow collisions with bridge girder event is mitigated by ensuring that the bridge girder is placed high enough to avoid such collisions. For all ship impact events the load and material factor is set to 1.0.

9.1 Head-on-Bow Collisions with Bridge Pontoons The main concern for ship impact has been related to the global response from head-on-bow collisions with bridge pontoons. The methodology can be summarized by the following two steps:

‐ Impulse loads from the striking ship is estimated from local dynamic analyses of the hit pontoon using USFOS. The pontoon characteristics are idealized from the global model using non-linear springs and point masses. The striking ship is modelled by a mass with initial velocity. The connection between the striking ship and the hit pontoon is modelled with a non-linear spring characterized by an indentation curve. See Figure 9-1 for illustration.

‐ The global dynamic response is analysed in OrcaFlex by applying the impulse loads from USFOS, and analysing the response in time domain. Structural capacity of main structural components is evaluated by simultaneous/direct design checks using von Mises float criterion.

The stiffness characteristics of the deformed ship follows a simplified indentation curve, interpolated from the indentation curve in Figure 3-7 and multiplying by a factor of 2, see red curve in Figure 9-2. The stiffness is defined by using an elasto-plastic spring.


139

Figure 9-3 Center of attack for centric and eccentric impacts

Figure 9-2: Simplified indentation curve used in dynamic analysis, HoB impact on bridge pontoons

To account for dynamic effects during impact, the most important bridge and pontoon characteristics have been included in the analyses, see Figure 9-1. The added mass of the pontoon cannot be defined as frequency dependent in USFOS and therefore taken as the value of infinite frequency. The bridge weak axis and torsional stiffness have been estimated based on representative eigen modes for each degree of freedom, other bridge stiffnesses have been extracted from static analyses in OrcaFlex. Sensitivity analysis has shown that the mooring stiffness is not of significance in the generation of impulse curves, corresponding stiffness of 1MN/m. Vertical position of attack have been roughly estimated to 6 meter below the waterline, based on evaluation of design ship and pontoon freeboard of 4 meters. Centric and eccentric impacts are considered for each axis. To account for the effect of off-sliding, and pontoon/ship interaction, the eccentric impacts have been reduced according to Figure 9-4, illustrating reduced energy for eccentric impact (analysis conducted by SSPA). The different evaluated impacts are shown in Figure 9-3. Eccentric impact 1 is not reduced as the point of attack is normal to the pontoon wall (the impact is analysed in USFOS), Eccentric impact 3 is reduced by 10 %, and eccentric impact 2 and 4 is reduced by 50 %.


140

Figure 9-5: Centric Impact Axis 3 Figure 9-6: Centric Impact Axis 4 Figure 9-7: Centric Impact Other Axes

. The eccentric impacts 2-4, see Figure 9-3, have been analysed, but are not dimensioning for any of the structural components, and the remainder of this section concerns the other impacts. The resulting impulse loads are simulated in time domain using Orcaflex, where the floating bridge is modelled with beams with hydrodynamic parameters describing the behaviour of the pontoons.

Figure 9-4: Reduction factor for an impact between a 160 m container ship and a cylindrical structure for different energy levels. The eccentric impacts have been reduced accordingly with respect to diameter of pontoon for the floating bridge.


141

Figure 9-10: Eccentric Impact Axis 3Figure 9-9: Eccentric Impact Axis 3Figure 9-8: Eccentric Impact Axis 3

Figure 9-11: Overview of energy levels, impacts and time domain Orcaflex model used for analysis of ship impact

The centric and eccentric impacts have been analysed for every axis along the bridge from only the east direction of bridge. The energy levels and analysis model is illustrated in Figure 9-11.

The most critical is the eccentric and centric impact on axis 3. The resulting maximum dynamic moments and axial force from this impact is shown in Figure 9-12, Figure 9-13, Figure 9-14 and Figure 9-15.


142

Figure 9-12: Dynamic axial force in bridge girder resulting from centric and eccentric ship impact at axis 3.

Figure 9-13: Dynamic moment about bridge strong axis in bridge girder resulting from centric and eccentric ship impact at axis 3.


143

Figure 9-14: Dynamic torque in bridge girder resulting from centric and eccentric ship impact at axis 3.

Figure 9-15: Dynamic moment about bridge weak axis in bridge girder resulting from centric and eccentric ship impact at axis 3.

For each considered impact a direct design check is done for main structural components, based on von Mises yield criterion. This captures the simultaneity of loads. The resulting utilization of the bridge girders and columns is shown in Figure 9-16, Figure 9-17 and Figure 9-18. The evaluated points in bridge girder and columns is as described in section 8.1. The eccentric impact on axis 3 is the only impact resulting in a utilization above capacity (utilization 1.1). In Figure 9-19 a stress plot along bridge for the most critical point critical point is shown. The exceedance is assumed tolerable as the energy input will be reduced according to client. The most critical impacts for the columns are eccentric impact in axis 3 and 4, however the exceedance is less than 2 % above capacity, and is not accounted for in design at this stage as the energy levels will be reduced according to client.


144

Figure 9-16: Utilization in bridge girder for centric and eccentric impacts axes 3-9, without second update of cross section

Figure 9-17: Utilization in bridge girder for centric and eccentric impacts axes 10-21 without second update of cross section


145

Figure 9-18: Utilization of columns for centric and eccentric impacts axes 3-9 without second update of cross section

Figure 9-19: Utilization of most critical point in west girder for an eccentric impact at axis 3, utilization 10 % above capacity. See design of bridge girder chapter for definition of critical points for design check.


146

9.2 Head on Bow Collision with Bridge Pontoon, Local Design To sustain loads from ship impact the following pressure/area relationship is used for local design of pontoon walls on the east/west side:

2 ∗ 18 .

The relationship was evaluated at Marine Technology NTNU /6/, where a containership impact with a rigid wall was analysed in a non-linear explicit software. The factor of 2 is used to account for ice-reinforcement of ships, as proposed by client. The maximum force is 80 MN which give a maximum area of 5m2. The force corresponds to the peak force in the impulse curve for axis 3, see Figure 9-5. The contact area is assumed circular, in accordance to results from analysis at NTNU.

To determine the local loads for the concrete and reinforcement, a FEM model has been analysed in FEM Design. The model is simplified as a 13 m wide and 8 m high straight wall, with a web spacing of 2 m. Three loads have been analysed using the pressure/area relationship above, with contact areas of 1m2, 3m2 and 5m2. The largest area and force have been found as dimensioning for the pontoon walls.

Figure 9-20: Illustration of simplified FEM model (right), and strengthened pontoon walls

(left).

For the design check Eurocode 2 (NS-EN 1992-1-1) have been used. The dynamic shear capacity of the concrete has been increased by a factor of 1.8. The impact loads require a wall thickness of 1100 mm with concrete stiffeners to strengthen the pontoon for local bending and shear.

The north/south walls are dimensioned for a contact area of 5m2 with an area load 2000 kN/m2 (total 10MN), significantly lower than the east/west walls.

9.3 Deckhouse Collision - Local Design of Bridge Girder The local design of bridge girder against deckhouse impact has not yet been conducted. The results for the curved bridge concept are assumed to be in the same order of magnitude, see main report /8/.

9.4 Deckhouse Collision – Global Response The global response analysis has not yet been conducted for the straight bridge concept. The results for the curved bridge concept are assumed to be in the same order of magnitude, see main report /8/.


147

10 Correlation between Wind and Wave Response

For the 100 year environmental loads, the 100 year wind- and 100 year wave conditions act simultaneously. In the wind and wave analyses, the responses are simulated separately and in the design process combined using combination factors. This chapter covers the analyses performed to estimate these combination factors by simultaneous simulation of wind and wave in the time domain.

The proposed method for combination of wind and wave response is novel for floating bridge structures. However, the method is more or less in accordance with the recommendation in DNV-OS-J101 for direct simulation of combined load effect of simultaneous load processes; a recommended practice for design of offshore wind turbine structures:

“Whendynamicsimulationsutilisingastructuraldynamicsmodelareusedtocalculateloadeffects,thetotalperiodofloadeffectdatasimulatedshallbelongenoughtoensurestatisticalreliabilityoftheestimateofthesought‐aftermaximumloadeffect.Atleastsixten‐minutestochasticrealisations(oracontinuous60‐minuteperiod)shallberequiredforeach10‐minutemean,hubheightwindspeedconsideredinthesimulations.Sincetheinitialconditionsusedforthedynamicsimulationstypicallyhaveaneffectontheloadstatisticsduringthebeginningofthesimulationperiod,thefirst5secondsofdata(orlongerifnecessary)shallbeeliminatedfromconsiderationinanyanalysisintervalinvolvingturbulentwindinput.”

It should be noted that offshore wind turbines deviate significantly from floating bridges with regards to eigen periods and dynamic behavior, and therefore the analysis procedure from the recommended practice do not directly validate the procedure for wind and wave analysis of floating bridges. Assumptions and limitations in study:

‐ The focus during the study has been on the moment about bridge strong axis as it is the only critical characteristic response for wind analysis.

‐ In the analyses used to evaluate combination factors the wind has only been applied to the bridge girder. In the verification between NovaFrame and OrcaFlex wind is applied on all relevant elements. The deviation in response for the floating part of bridge is little when comparing wind on only bridge girder and on all relevant elements.

10.1 Method and Results for Combination Factors Simultaneous wind and wave response is analysed in OrcaFlex. These analyses are performed solely to find combination factors and not to calculate the simultaneous characteristic wind and wave loads because of the following:

‐ The wind characteristic loads have a short term statistical description, that fundamentally differ from the description of wave characteristic loads, with a most probable maximum from 10 minute stochastic realisations for wind, and a 95 % maximum from 3 hours stochastic realizations for waves. A framework needs to be established that unites short term characteristic wave and wind loads.

‐ In order to obtain the 95% maximum form the 3 hours stochastic realizations for waves, the mean of the maxima from the 10 realization needs to be multiplied by 1.25 (see Section 3.5.2). In the simultaneous wave and wind analyses it is not possible to know how much of the response stems from the wave loads alone.

‐ The time domain simulations in OrcaFlex have been compared to results in Novaframe, and even though the overall compliance is good, some discrepancies still exists and further testing and benchmarking must be conducted.

Especially for the design of bridge girder it is critical to determine the wind combination factor, defined in the equation below.


148

Figure 10-1: Dynamic axial force combination factors for wind in bridge girder. Green, combination factors for positive forces. Red, combination factors for negative forces.

Figure 10-2: Dynamic strong axis combination factors for wind in bridge girder. Green, combination factors for positive forces. Red, combination factors for negative forces.

The combination factors for axial force, moment about bridge strong axis, torque and moment about bridge weak axis are presented in Figure 10-1 - Figure 10-4 . The maximum responses are presented in Figure 10-5 - Figure 10-8. The axial force and torque are not important, as the wind loads induce very low response for these load components.


149

Figure 10-3: Dynamic torque combination factors for wind in bridge girder. Green, combination factors for positive forces. Red, combination factors for negative forces.

Figure 10-4: Dynamic weak axis combination factors for wind in bridge girder (positive and absolute of negative values). Green, combination factors for positive forces. Red, combination factors for negative forces.


150

Figure 10-5: Dynamic axial forces in bridge girder from wind and wave simulations. Mean denotes the average max from 3 realizations.

Figure 10-6: Dynamic strong axis moment in bridge girder from wind and wave simulations. Mean denotes the average max from 3 realizations.


151

Figure 10-8: Dynamic weak axis moment in bridge girder from wind and wave simulations. Mean denotes the average max from 3 realizations.

Figure 10-7: Dynamic torque in bridge girder from wind and wave simulations. Mean denotes the average max from 3 realizations.

For the moments about bridge strong axis and moments about bridge weak axis, there is an overall compliance with the wind combination factor 0.6, used for the ULS combinations. However, there are some areas where this factor is exceeded. It is assumed that the factors will be more even if more realizations were run. For the curved bridge concept, the average maximum from three realizations was used to find the wind combination factor, resulting in a more even factor along the bridge, see chapter 10 in report /8/.

There is a high wind combination factor for moments about bridge weak axis at the high bridge. However, the wave loads are negligible at this part of the bridge, and therefore the combination factor is not important.

The wind combination factor for moments about bridge strong axis are in some areas negative, which is due to wave response alone is higher than the response from wave and wind. Again it must be emphasized that it is assumed that the factors will be more even if more realizations were run.


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Figure 10-10: Ramping function Figure 10-9: Wind speed sample, illustrating crossfading of 10 minute time series

10.2 Description of Analyses The simultaneous wind and wave maximum response is found by simulating a one-hour realization of wind and waves and calculate the maximum response along the bridge. The wind only maximum response has been found by simulation of the same wind realization without waves. The wave only maximum response has been found by simulating the same one-hour realizations of waves without wind.

The built in wind simulation tool in OrcaFlex is not able to represent spatial wind coherence, which is essential for the analysis of long slender structures. This shortcoming has been addressed by developing an external python function to calculate the wind forces and moments based on wind speed time series from WindSim (time domain wind load simulation tool developed by Ketil Aas-Jakobsen).

In WindSim, the mean wind speed and gust wind speed time series are calculated at points distributed along the bridge span based on gust spectrums and coherence functions, in accordance with the frequency domain analyses in Novaframe. By using the external function in OrcaFlex one can access the instantaneous positions of objects and velocities of the structure and account for relative velocity and instantaneous drag and lift coefficients of a cross section relative to mean wind direction when applying forces.

Six ten-minute stochastic realisations have been generated separately and joined together by cross-fading. The cross-fading have been performed by down- and up-ramping of connected series using 5th order polynomial with a duration of 10 seconds, see Figure 10-10 and Figure 10-9 for illustrations. In Figure 10-9. In Figure 10-9 a close-in on the combined series at a crossfading is shown. The blue series is the first time series and the green series the second time series.

The results from the time domain analysis of wind only in OrcaFlex have been compared to the frequency domain analysis in Novaframe with good overall compliance. The dynamic results from OrcaFlex are somewhat higher, as a result of extracting the maximum response from 6 stochastic 10 minute series, which statistically should be higher than the most probable maximum determined in Novaframe. This comparison is presented in Chapter 11.

As the analysis is in time domain, the convergence for the wind response have been studied, and it seems that a simulation of 10 minute is sufficient.


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11 Benchmarking – OrcaFlex Wind Module

11.1 Description of Models In general the time domain analyses in Orcaflex, calculate the response of the bridge using a system with the catenary, non-linear moorings. In order to compare the results from NovaFrame and OrcaFlex, in this section the mooring system is modelled as horizontal springs in the bridge east-west direction, both in NovaFrame and OrcaFlex. The springs for pontoon 3 and pontoon 9 have a stiffness of 1637 kN/m and the spring for pontoon 15 has a stiffness of 989 kN/m. Results in this section is used only for benchmarking the calculations and are not used as basis for the design.

Note: Unfortunately, the OrcaFlex model was run without re-ballasting pontoons 3, 9 and 15, which induced additional forces. Re-ballasting is necessary for this comparison due to the purely horizontal stiffness applied, as opposed to the analysis shown in the rest of the document, where the weight and pretension of the actual mooring system pulls the pontoons down. Due to the deadline, there was not enough time to re-run the dynamic analysis. However, it is seen from the comparison of static results with a model with correct ballasting that this mainly affected the bending moment about weak axis and shear force vertical. Dynamic results for model with correct ballast will be prepared once the simulation is finished and will be made available upon request. The error mainly affects moments about bridge girder weak axis, as seen in Figure 11-2.

11.2 Comparison of Static Wind Results As can be seen from Figure 11-1, the static wind models in NovaFrame and OrcaFlex correspond very well. As NovaFrame does not include increase in axial forces from bending of the bridge, the axial forces in OrcaFlex are slightly higher.


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Figure 11-1: Comparison of bridge girder forces and moments from static wind calculated with NovaFrame and OrcaFlex

Figure 11-2 shows the static wind results for the OrcaFlex model with ballasting errors. This figure is only included as the dynamic results from OrcaFlex currently only exist for this model.


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Figure 11-2: Comparison of bridge girder forces and moments from static wind calculated with NovaFrame and OrcaFlex. Results from

OrcaFlex are for model with too little ballast in pontoons 3, 9 and 15, see Section 11.1. The error mainly affects the weak axis moments.

11.3 Comparison of Dynamic Wind Results A comparison of the loads from dynamic with the models in OrcaFlex (with ballasting error) and NovaFrame can be found in Figure 11-3. Please note the following:

The bending about bridge girder weak axis and shear force vertical were likely affected by the ballasting error described in Section 11.1.

The dynamic results from OrcaFlex are somewhat higher, as a result of extracting the maximum response from 6 stochastic 10 minute series, which statistically should be higher than the most probable maximum determined in Novaframe.

The OrcaFlex results are the maximum observed values from a single time-domain simulation, consisting of 6 stochastic 10 minute wind velocity series. Running several simulations would smooth the graphs.

Hydrodynamic damping is neglected in the NovaFrame model. Hydrodynamic damping will give a negligible effect to bending moment about strong axis from wind loading, which is dominated by first mode motion. The bending moments about weak axis will have a more significant reduction (but here wave loads are dominating).


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Figure 11-3 Comparison of bridge girder forces and moments from dynamic wind calculated with NovaFrame and OrcaFlex. Results

from OrcaFlex are for the model with too little ballast in pontoons 3, 9 and 15, see Section 11.1.


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12 Concluding Remarks

12.1 Key Challenges Avoid large induced moments from resonance in structure exposed to waves

o Heave motion of pontoons exposed to waves can potentially induce large moments about bridge girder weak axis.

o Surge motion (pendulum) of pontoons in high part of floating bridge can potentially induce large moments about bridge girder weak axis.

Avoid large induced moments about bridge strong axis from resonance in structure exposed to wind and waves

o Wind. Long eigen modes exist with virtually no damping, exposing the structure to large induced moments about bridge girder strong axis from slowly varying wind gusts and second order drift.

o Waves. Eigen modes at around 6s are triggered. These moments are in the same order of magnitude as wind induced moments around bridge strong axis.

o It is important to avoid a large increase in these moments, since designing for these will give added material quantity in main girder, tower and abutments.

Bridge exposed to large loads from head-on-bow collisions with pontoons

Design restriction on pontoon water plane area. During traffic it is not regarded feasible with more than 1m vertical displacement of bridge girder. This significantly limits the range of free parameters for pontoon design.

Designing a pontoon with low self-weight. Self-weight constitutes 2/3 of the pontoon displacement. This is due to the material used (concrete) and local pontoon design against ship impact loads, which requires a minimum wall thickness of 1.1m.

Simultaneous combination of wind and wave is not covered in Eurocode, making the combination of these loads challenging to assess. The wind characteristic loads have a short term statistical description, that fundamentally differ from the description of wave characteristic loads, with a most probable maximum from 10 minute stochastic realisations for wind, and a 95 % maximum from 3 hours stochastic realizations for waves. A framework needs to be established that unites short-term characteristic wave and wind loads.

Find an optimal span/girder height ratio for the floating bridge.

Due to the long natural vibration period of the structure, classical formulation for obtaining dynamic wind response due to buffeting load might not give accurate results, as wind statistics is normally based on 10 minute events. It is suggested that the effect of long natural vibration period in relation to the wind spectra and coherence function is studied in more detail at a later stage, and that the wind measurement at site is used to identify proper wind parameters.

12.2 Robustness In mooring design, moderate changes in anchor positions due to inadequate soil conditions can be

accounted for. Even if the inadequate soil conditions are discovered after bridge installation, modification of existing mooring design should be feasible.

The mooring system as proposed is robust against progressive collapse. See Section 7.3.5.

In order to avoid resonance about bridge weak axis:


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o Heave. Eigen periods of coupled pontoon and bridge structure are between 7.8 and 10.8s, above wind driven seas and below significant swell waves.

During design, if new information about the wave climate appears, the flange can be redesigned to ensure that the heave added mass is sufficient.

In-place, if the actual wave climate differs from the design wave climate, an additional heave plate can be attached to the structure, ensuring that the heave added mass is sufficient.

o Surge (pendulum)

1. A keel plate is applied that lifts the lowest eigen period above wind driven seas, from 2.6s to ~8s. The size of the plate will be in the order of 60m long and 50m deep.

2. An additonal connection between pontoons in axis 3 and 4 will make sure that the pendulum modes in the wind driven wave regime are eliminated.

3. Since these moments act locally and only in the high part of the floating bridge, an increase in moments can be designed for without adding much steel.

In order to ensure robustness against a change in loads from head-on-bow collisions with pontoons, due to changes in impact energies, two measures have been identified.

o Increasing pontoon displacement decreases the dynamic response in bridge during impact for axes 4-21. For axis 3, ship impact loads in bridge structure are not sensitive to pontoon displacement.

o A large fraction of the ship impact load acts in the connection between girder and column and reinforcement in this part will significantly increase robustness without much added steel.

Simulation of wind and wave simultaneously can be performed and correlation between loads can be assessed in detail. Results verify that applied combination factors are conservative.

Stability issues have been studied for the structure and it was found that for the current configuration it is not expected that vortex shedding will be a problem, mainly due to the mass of the structure. With respect to flutter onset velocity the study concludes that aerodynamic derivatives for the cross section are needed before any conclusion can be made. No problems in relation to galloping or divergence were identified. Thus, based on the current knowledge the structure is aerodynamically robust.

The solution with navigation channel in the south is more robust than the solution with navigation channel mid fjord mainly for two reasons; the tower supporting the cable-stayed high bridge is fixed on ground and a larger part of the floating bridge has a low profile line.

12.3 Improvements Further work should be performed to assess motion criteria for floating bridges.

It is seen that there is a large potential for reduced moments in bridge girder from pontoon optimization. Since these moments are driving the steel weight there is a potential for cost reduction.

Perform relevant measurements and evaluate these time series of wind at location to find more appropriate wind spectra, coherence along the bridge and duration for wind short-term statistics. The target is to reduce uncertainties related to wind loads relevant for the long eigen modes of the bridge structure.

Fatigue has been assessed at an early stage based on limited knowledge of the environment. With improved and more detailed environmental long term statistics fatigue can be evaluated in detail.

Vessel impact in pontoons – with accurate modelling of concrete crushing the wall thickness can possibly be lowered. As is, the wall thickness is such that the pontoons withstands all ship impact loads.


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It might be beneficial to decrease the span/girder height ratio because a large part of the utilization is from self-weight.

Interaction effect between wind and wave response should be assessed using model tests.

In order to reduce the total mooring line weight, measures for removal of marine growth should be evaluated.

The moments about bridge strong axis are affected by the non-linearities in the mooring system. To separate the wind and wave response in the analyses and increase validity of frequency domain analyses it may be a target to make the mooring system more linear. The non-linearity is caused of the high self-weight of the mooring lines and can be reduced by yearly removal of marine growth.

12.4 Uncertainties Motion criteria are defined within the project group. There are limited references on this topic for floating

bridges.

Limited information about wave and wind climate

Hydrodynamic properties of pontoons should be assessed in a tank test, especially 2nd order wave drift and viscous effects. It is especially critical to assess the flange.

Fatigue in structure not possible to assess accurately with available environmental data

The large mooring line self-weight has resulted in a non-linear mooring system, challenging the validity of the frequency domain analyses used for wind analyses (the study presented in 7.2.5 shows that the frequency domain analyses for wind are conservative). The large self-weight of mooring lines is a consequence of the high safety factors used for these structural elements (adding material and load factor for wave loads the safety factor is 3.0 for wave loads) and accounting for marine growth.

Novel application of analysis software. Consider more evaluation between independent software.

Future vessel impact loads are difficult to predict: ship indentation curve, impact energies and traffic frequency.

13 References /1/ RAP-GEN-001 Design basis

/2/ DNV-RP-C205 Environmental conditions and environmental loads

/3/ NOT-HYDA-014 Curved Bridge Fairway in South Stage 2 – Environmental Loading Analyses

/4/ NOT-SKST-006 Curved Bridge Final – Ship Impact Analyses

/5/ NOT-MO-003 Method Statement, Bridge with Navigational channel in South

/6/ Ship collision force for the pontoon of the Bjørnefjorden floating bridge, Yanyan Sha, Jørgen Amdahl - NTNU

/7/ Fergefri E39 Ship collision risk analysis for the Bjørnafjorden crossing, SSPA

/8/ NOT-KTEKA-021 Curved bridge South – Summary of analysis

/9/ NOT-GEN-004 Operation and maintenance - Moorings

Documents

COWI AS STRAIGHT BRIDGE – NAVIGATION CHANNEL IN · ADRESSE COWI AS Grensev. 88 Postboks 6412 Etterstad 0605 Oslo TLF +47 02694 WWW cowi.no OPPDRAGSNR. A058266 DOKUMENTNR. NOT-KTEKA-020