Final report Mega Floating Concrete

MEGA FLOATING CONCRETE

The final report

Master Thesis of Ali Halim Saleh

TU Delft 1 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

Content:

0.0 Introduction 0.1 Problem analysis 0.2 Problem definition 0.3 The objective of the thesis 0.4 Boundary conditions 0.5 The case study

1 Literature study for the floating bridges 1.1 Introduction 1.2 Conventional bridges 1.2.1 Types 1.2.2 Construction methods 1.2.3 The main constraints of the construction 1.3 Very large floating structure (VLFS) 1.3.1 VLFS types and definition 1.3.2 Comparison between VLFS and land-based structures 1.3.3 Structural behavior classification of VLFS 1.4 The floating bridges 1.4.1 The history of the floating bridges 1.4.2 The technical aspects of the floating bridge 1.4.3 Floating bridges classifications 1.5 The floating bridge around the world 1.6 Introduction to the hydro-static 1.6.1 Equilibrium and stability 1.6.2 Meta Centre Height 1.6.3 Rotation 1.7 Introduction to the hydro-dynamic 1.7.1 Dynamic motion definition 1.7.2 Basic Dynamic Analysis of continuous beam 1.8 Material specifications 1.9 Evaluation

2 Design principles 2.1 Argumentation of the choice (with pontoons and mooring cables) 2.2 Evaluation of the floating bridge layouts 2.2.1 The continuous pontoon floating bridge models 2.2.2 The separated pontoon floating bridge models 2.2.3 Comparison between the separated pontoon- and continuous pontoon floating bridge 2.3 The main structural elements of the floating bridge with alternatives 2.3.1 The pontoon 2.3.2 The access bridge 2.3.3 The pontoon connector 2.3.4 The mooring system 2.3.5 Additional members (abutment – stability pontoon – wave breaker) 2.4 The creation of different bridge alternatives 2.5 Mechanical modelling of the floating bridge 2.6 The construction procedure 2.6.1 The continuous pontoon floating bridge 2.7 Durability and concrete technology

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2.7.1 The situation analysis 2.7.2 Durability of marine concrete structures

3 The sea wave-wind load 3.1 The wind and wind classifications 3.1.1 Introduction 3.1.2 Wind classifications 3.1.3 The wind load 3.2 The ocean waves definition and characteristics 3.2.1 Introduction 3.2.2 The simple linear wave 3.2.2.1 Basic definitions 3.2.2.2 Basic relationships 3.2.2.3 Influence of water depth 3.2.2.4 Subsurface pressure 3.2.3 Wave energy principles 3.2.4 Wave breaking 3.3 Wave generation by wind 3.3.1 Bretschneider method 3.3.2 Monogram method 3.4 The float geometry effects 3.4.1 The wavelength 3.4.2 Lateral opening 3.4.3 Draft 3.5 The sea wave load 3.5.1 Linear theory 3.5.2 The wave force on the bottom slab 3.5.3 The wave force frequency 3.6 Evaluation

4 Structural analysis 4.1 Local design 4.1.1 The total bridge length 4.1.2 Pontoon dimensions (length-width- depth) 4.1.3 Pontoon compartmentalization 4.1.4 Pontoon slabs and walls design 4.1.5 Pontoon rigidity (flexural/ torsional stiffness) 4.1.6 Design and analysis of the mooring line 4.1.7 Loads determination and load combinations 4.2 Global design 4.2.1 Heaving and pitching motion (XZ-plane) 4.2.2 Swaying and Yawing (XY-plane) 4.2.3 Rolling (ZY-plane) 4.2.4 Hydro-static analysis 4.2.4.1 Pontoon length influence 4.2.4.2 Pontoon connector stiffness influence 4.2.4.3 Mooring system stiffness influence 4.2.5 Hydro-dynamic analysis 4.3 Prestressing design 4.3.1 The moment capacity of the pontoon 4.3.1.1 Serviceability limit state

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4.3.1.2 Ultimate limit state 4.3.2 The shear capacity of the pontoon 4.4 Evaluation

5 Case study 5.1 Dimensioning 5.1.1 Global dimensioning 5.1.2 Local dimensioning and load combinations 5.1.2.1 The bridge width 5.1.2.2 The bridge depth 5.1.2.3 Determination of the additional required coefficients 5.1.3 Pontoon rigidity 5.2 The hydrostatic analysis 5.2.1 The sea wave 5.2.2 The loading 5.2.3 Slabs and walls thicknesses verification 5.2.3.1 The design of the internal wall 5.2.3.2 The design of the External wall 5.2.3.3 Design of bottom slab 5.2.3.4 Design of top slab 5.2.4 The mooring system 5.3 The Global design 5.3.1 Individual pontoon response method 5.3.2 The total bridge static response 5.3.2.1 Heaving and pitching motion (XZ-plane) 5.3.2.2 Swaying and Yawing (XY-plane) 5.3.2.3 Rolling (ZY-plane) 5.3.3 The maximum moment capacity of the pontoon 5.3.3.1 The serviceability limit states 5.3.3.2 The ultimate limit states 5.3.3.3 The shear strength of the pontoon 5.3.3.4 Pontoon connector rigidity 5.3.3.5 Pontoon connector analysis 5.4 Evaluation

6.1 Summary 6.2 Conclusion 6.3 Recommendations

References Appendix A Appendix B

TU Delft 4 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge Acknowledgment

This research is the outcome of much effort and encouragement from many interested parties. Many significant contributions made in this thesis for Master of Science degree at TU Delft, The Nederland.

To begin with I would like to thank gratefully Professor J.C. Walraven, Head of Concrete Structure Department at TU Delft for his support throughout the study period. I am also grateful to all commission members for their support, ideas, flexibility, knowledge, enthusiasm, and especially for my supervisor’s dr.ir.C.R. Braam and dr.ir. P. Hoogenboom for their patience, encouragement with close guidance and continuous assistance during entire thesis period.

Similarly, I am grateful to other persons who helped and support me includes my friends and colleagues in TU Delft.

I do not like to forget the close guidance of the study adviser Mrs. Karel Karsen during the entire study period and I would to thank him gratefully.

Last of all, a special thank to my parents, brothers, and sisters in and all my thanks to my wife and children for their patience, care, and optimism in difficult times. I hope that you are proud of me. Thanks for their continuous motivations, prayers, and moral support during academic period.

COMMISSION MEMBERS:

Prof. Dr. Ir. J.C. Walraven Head of Concrete Structure Department Dr. Ir. C. van der Veen Concrete Structure Dr. Ir. C.R. Braam Concrete Structure Dr. Ir. P.C.J. Hoogenboom Structure Mechanics Ir. Dil Tirimanna FDN Engineering Company

A.H. Saleh 23 Augustus 2010

TU Delft 5 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

0.0 Introduction

This graduation project has been initiated to research the technical feasibility of floating bridges. The project has been done in co-operation with the FDN engineering company and Delft technical university. A design is made of a continuous pontoon floating bridge, which connects a mainland to an island.

0.1 Problem analysis

Floating bridges can be constructed where conventional bridges are impractical (under the conditions that are described in section 1.4.2). The buoyancy forces support the bridge in the vertical direction and the mooring system in the horizontal direction.

Environmental loads are the main loading on the floating bridge. Because of the random form of the sea wave forces and the wind force, it is difficult to expect the precise value and direction of loading on the bridge. The environmental loads twist the bridge and excite it in the horizontal and in the vertical direction. When it is possible to construct a sliding pile mooring system to introduce the wind and wave load in the horizontal direction, the floating bridge will have a satisfactory stability. In most cases, it is impossible to construct the sliding piles due to the large water depth or the seabed soil weakness; therefore, the mooring system should be replaced by chains/cables mooring system to maintain the lateral supporting. The efficiency of the mooring cable is lower than the sliding pile due to the relatively large compliance range. That is valid also for the vertical displacement; the bridge response will be introduced by the bridge flexural rigidity, the bridge mass, the water spring, the water damping and the pontoon connector stiffness when discrete pontoons are used. In this case, the floating bridge deflections, internal forces and stresses will be relatively large and unexpected.

The linear theory is applied to determine the sea wave load. The hydro-static and the hydro- dynamic analysis of a multi-body slender structure consisting of rigidly or flexibly connected elements will be made. The behavior of the continuous pontoon floating bridge under the wave and wind load and the connections between the elements are examined. The design procedure of the mooring cables of the offshore structure is applied to design the mooring system.

The construction of a slender structure on an unlimited flexible foundation such as water has a certain risk. Material fatigue is another important issue that should be discussed. Fatigue depends on the range of the stress variation and the loading recurrence which they should be also controlled to ensure the service life of the structure. Because of dealing with a hydraulic structure, an additional relevant condition will be the concrete crack width. Water leakage in the pontoon should be prevented totally in all loading cases.

0.2 Problem definition

Which design limitations and structural parameters can ensure stability of the continuous pontoon floating bridge under wind and wave load?

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0.3 The objective of the thesis

The objective of this thesis is to understand the response of the continuous pontoon floating bridges under wind-wave load and traffic load that is described in the euro code which enables us to optimize the structural design procedure. That can be accomplished by studying the influence of the pontoon dimensions and the pontoon connector rotational rigidity on the global stability of the bridge. Determination the principles of response reduction and converting the displacement into internal forces are a relevant part of this thesis as well as the mitigating of the local environmental loads to be redistributed along larger parts of the bridge.

0.4 Boundary conditions

The scope of the graduation project is very wide. It contains an overview of floating bridges; its hydrodynamic behaviour will be defined and due to the limited period of time will be not analyzed. The hydrostatic behaviour and analysis of continuous pontoon floating bridges will be researched as a multi-body slender structure with flexible connections. Also the conceptual design of the pontoons and the connections and the shape effects were researched. Detailed design calculations for the case study are included in this thesis.

0.5 The case study

A continuous pontoon floating bridge connects a mainland to an island at a distance of 2km. The sea bed under the centre line of the bridge is flat sand soil. The average water depth is about 25m. The average speed of the water current in both direction is 0.5m/s. The maximum tidal range does not exceed 2m.

The climatological registrations of the bridge site are described in table (5-3):

Table (5-3) the design wind speeds Unit value Beaufort scale The extreme recurrent wind storm 100-year [km/h] 180 12 (knots) The extreme recurrent wind storm 20-year [km/h] 74 8 (knots) The normal recurrent wind storm 1-year [km/h] 39 5 (knots) The monthly average tide variation [m] 2

TU Delft 7 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge Chapter I: Literature study on floating bridges .

1.1 Introduction

Figure (1-1) Homer M. Hadley Memorial Bridge to the left And the Lacey V. Murrow Memorial Bridge to the right

Bridges are constructed to cross obstacles. The obstacles can be water, infrastructures or elevation difference. A floating bridge can be used doubtlessly to cross a water obstacle when it is impossible to construct a conventional bridge. The construction difficulties of the conventional bridges involve the several factors such as a high water depth, a seabed soil weakness, the occurrence of sever earthquake etc.

The human necessity to cross the obstacles is existed since the times. Although of using many type of structures for this purpose such as the conventional bridges, floating bridges, tunnels and tubes, civil engineers still face many difficulties to find the suitable alternatives to cross the unusual obstacles. All the mentioned conventional structures have design and construction limitations which make them inappropriate for all situations. In spite of the broad variations in the types of those structures, there is still lack to cover all cases.

For instance, in the city of in , the floating bridge is constructed on 500m water depth for which it is impossible to construct any pillars. The technical restrictions are not the only factors influencing the choice of a floating bridge; the economical factor plays also an important role. A floating bridge is a cost-effective solution when the cost of conventional bridge construction is too high. The bridge foundations are the most costly structural element.

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The design of a floating bridge is still most challenging to civil engineers. The design procedure depends on analytical and experimental methods. Many researches are made in this field to understand the behaviour of floating bridges under wind and wave load. The cyclic characteristic of the loading whether the environmental or the traffic loads adds extra design requirements. Fatigue needs to be considered within the entire design life.

The conceptual design of the very large floating structures (VLFS) is studied to understand the differences with the conceptual design of the floating bridges. Comparison between the VLFS and the land-base structures will enable us to understand the general hydro-elastic behaviour and the design and construction requirements of the floating structure.

Demonstrating of the technical specifications of the most important floating bridges in the world gives the reader an indication about design and construction requirements that need be taken.

1.2 Conventional bridges

In this section, conventional bridges will be discussed, in relation to floating bridges.

1.2.1 Conventional bridge types

The bridges have many design and construction requirements and those requirements vary the bridges in different types and different construction methods. The most famous bridge types can be summarized as follows:

1. Simple supported beam: is where a bridge or beam spans a single length without or assumed to be without fixity at the support. 2. Continuous beam: is a beam which extends beyond two supports, usually to at least one further support. 3. : an arch bridge is a bridge with abutments at each end shaped as a curved arch. Arch bridges work by transferring the weight of the bridge and its loads partially into a horizontal thrust restrained by the abutments at either side. 4. Box Culvert Bridge: is a rectangular section concrete box. They can be in situ or precast in construction, but precast is the most common due to the speed and ease of construction. 5. Cable Stay Bridge: is the type of the bridge the main structural members of which are beams supported by one or more straight inclined cables supported by a tower. 6. : is a form of bridge where the main suspension elements are cables from which the deck is suspended.

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Suspension Bridge Cable Stay

Simple supported beam Arch Bridge

Continuous Bridge

Box Culvert Bridge

Figure (1-2) the types of the conventional bridges

1.2.2 Construction methods

The bridges can be constructed in different method according to the feasibility of the bridge the site facilities, the bridge type and function, soil condition, the financial support, ect. The most used construction methods are:

 Segmental: is a form of bridge construction in which the bridge is constructed in pieces of various configurations and then connected together.  In-situ: is a form of construction where the structural elements of the bridge are formed on site. Formwork is used to shape a structural member, reinforcement is placed and concrete is poured. In-situ construction ranges reinforced concrete, post- tensioned and prestressed members and in some instances precast members which are too large for factory controlled condition.  Precast: is a form of concrete construction where the structural members are cast under factory-controlled conditions and not erected on sited until fully hardened. Just like in situ concrete, precast concrete can be plain reinforced and prestressed.  Span-by-span construction: is a convenient method of erecting medium simply supported and continuous box girder bridges. Launching gantries are placed to span between adjacent piers. Precast or in-situ segments can then be placed and stressed together. The gantry is then moved to the next span.

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1.2.3 The main constraints of the construction

The construction of a conventional bridge includes many aspects which can be important in the final choice of the bridge type and construction methods. We can summarize them briefly:

 The function of the bridge: the reasons of its existence. Generally, bridges are required to carry pedestrian, rail and vehicular traffic across the roads, railways, gorges and open water. Width, loading and bridge dimensions are influenced by the function of the bridge.  The road designation whether motorway or another road designation which includes the loading limitation and the number and width of the lanes.  When considering the conceptual design of an aqueduct, the engineer must concentrate on the following specific points: the size of the stream or the river the aqueduct must cross the depth of the water body, the water quality and current velocity.  The economic factor is always existed in all projects and its influence is very wide.  The soil condition, either inside or outside the water, determines the foundation sort that should be applied for the pillars. The suspension bridge can not be constructed on the very weak soil because it can not carry the high tension force of the cables.  The environment has also a portion in the restrictions of the bridge construction and design.  The fatigue due to the stress ranges and stress reversals need to be considered in the railways.  The chosen construction material whether concrete, steel or composite from both of them dictates the cross section form of the bridge.  The location of the bridge: the site configuration indicates the bridge type and construction methods. The arch bridge is used when the obstacle has a large elevation difference.  Ecological restrictions: the construction of a large project like a bridge requires intervention in nature. The design of the bridge should comply with nature conservation requirements.  Maintenance methods, durability and life time of the bridge are additional restriction in the design of the conventional bridges.  Earthquake: in some locations the design or the construction of the conventional bridges are impossible due to the fluctuated seismic load where the foundation can’t support any bridge.  The bridge length: the required length is an additional restriction. The table (1-1) below shows the length limitation for each kind of the bridge. The choice of the bridge type is determined by its length.

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Figure (1-3) the acceptable span range of the bridge.

1.3 Very large floating structure (VLFS) (1)

A Very Large Floating Structure is a unique concept of ocean structures primarily because of its unprecedented length, displacement and associated hydro-elastic response, analysis and design. Very large floating structures are considered as an alternative of such land-based large facilities as, for example, airport. A proposed design of floating airport has a thin plate configuration of large horizontal extend. Bending rigidity of such a floating plate is small, and wave-induced motion of the plate is significantly affected by its elastic deflection.

1.3.1 VLFS types and definition

There are basically two types of very large floating structures (VLFSs), namely the semisubmersible-type and the pontoon-type. Semi-submersible type floating structures are raised above the sea level using column tubes or ballast structural elements to minimize the effects of waves while maintaining a constant buoyancy force. Thus they can reduce the wave induced motions and are therefore suitably deployed in high seas with large waves. In contrast, pontoon-type floating structures lie on the sea level like a giant plate floating on water.

Pontoon-type floating structures are suitable for use in only calm waters, often inside a cove or a lagoon and near the shoreline. Large pontoon-type floating structures have been termed Mega-Floats by Japanese engineers. As a general rule of thumb, Mega-Floats are floating structures with at least one of its length dimensions greater than 60 m.

One of the important characters of the VLFS that the wavelengths are very small compared to horizontal size of typical VLFS λ/L =1/50~1/100[Ref.22].

(1) VLFS is the abbreviation of the Very Large Floating Structure

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1.3.2 Comparison between VLFS and land-based structures

Figure (1-4) Components of a Mega-Float System [ref.24]

The analysis and design of floating structures need to account for some special characteristics when compared to land-based structures; namely:

• Horizontal forces due to waves are in general several times greater than the (non-seismic) horizontal loads on land-based structures and the effect of such loads depends upon how the structure is connected to the seafloor. It is distinguished between a rigid and compliant connection. A rigid connection virtually prevents the horizontal motion while a compliant mooring will allow maximum horizontal motions of a floating structure of the order of the wave amplitude.

• In framed, tower-like structures which are piled to the seafloor, the horizontal wave forces produce extreme bending and overturning moments as the wave forces act near the water surface. In this case the structure and the pile system need to carry virtually all the vertical loads due to self weight and payload as well as the wave, wind and current loads.

• In a floating structure the static vertical self weight and payloads are carried by buoyancy. If a floating structure has got a compliant mooring system, consisting for instance of catenary chain mooring lines, the horizontal wave forces are balanced by inertia forces. Moreover, if the horizontal size of the structure is larger than the wavelength, the resultant horizontal forces will be reduced due to the fact that wave forces on different structural parts will have different phase (direction and size). The forces in the mooring system will then be small relative to the total wave forces. The main purpose of the mooring system is then to prevent drift-off due to steady current and wind forces as well as possible steady and slow-drift wave forces which are usually more than an order of magnitude less than the first order wave forces.

• A particular type of structural system, denoted tension-leg system, is achieved if a highly pre-tensioned mooring system is applied. Additional buoyancy is then required to ensure the pretension. If this mooring system consists of vertical lines the system is still horizontally compliant but is vertically quite stiff. Also, the mooring forces will increase due to the high pretension and the vertical wave loading. If the mooring lines form an angle with the vertical line, the horizontal stiffness and the forces increase. However, a main disadvantage with this system is that it will be difficult to design the system such that slack of leeward mooring lines are avoided. A possible slack could be followed by a sudden increase in tension that involves

TU Delft 13 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge dynamic amplification and possible failure. For this reason such systems have never been implemented for offshore structures.

• Sizing of the floating structure and its mooring system depends on its function and also on the environmental conditions in terms of waves, current and wind. The design may be dominated either by peak loading due to permanent and variable loads or by fatigue strength due to cyclic wave loading. Moreover, it is important to consider possible accidental events such as ship impacts and ensure that the overall safety is not threatened by a possible progressive failure induced by such damage.

• Unlike land-based constructions with their associated foundations poured in place, very large floating structures are usually constructed at shore-based building sites remote from the deepwater installation area and without extensive preparation of the foundation. Each module must be capable of floating so that they can be floated to the site and assembled in the sea.

• Owing to the corrosive sea environment, floating structures have to be provided with a good corrosion protection system.

• Possible degradation due to corrosion or crack growth (fatigue) requires a proper system for inspection, monitoring, maintenance and repair during use.

1.3.3 Structural behavior classification of VLFS

Before starting to study the structural behavior of the floating bridge, it is necessary to study the structural design assumptions of the VLFS. The behavior of a floating bridge is entirely differing than the behavior of a VLFS. The VLFS’s are two-dimensional floating structures while floating bridges are one-dimensional slender floating structure. In order to summarizing the comparison aspects between the VLFS and the floating bridge, we will discuss the following:

 The bending stiffness: the flexure rigidity of the floating bridge is larger than of the VLFS.  The structure dimensions: the VLFS is a mat-like and extend on a large area in both horizontal dimensions while the floating bridges are longitudinal slender structure.  The functional requirements: floating bridge should be stable to carry a permanent traffic load while the VLFS is usually airport or floating city.  The draft: VLFS has a small draft to increase the transmitted wave portion while the floating bridge should be designed to reflect a large portion of the wave energy to reduce the drift-off forces.

VLFS analysis and basic assumptions:

In the hydro elastic analysis of the VLFSs of the mat-like type, usually the following assumptions are made [Ref. 11]:

 The VLFS is modeled as a thin elastic (isotropic/orthotropic) plate with free edges.  The fluid is ideal, incompressible, and in-viscid; the fluid motion is ir-rotational, so that the velocity potential exists.

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 The amplitude of the incident wave and the motions of the VLFS are both small, and only the vertical motion of the structure is considered.  There is no gap between the VLFS and the free surface of the fluid.  The sea bottom is assumed to be flat.

Those assumptions are made to comply with the derivative mathematical analysis which describes approximately the motion of the VLFS.

Structural Classification:

The floating bridge can be designed in different manners depends, such as all other structures, on the design assumptions and structural type. With respect to the continuous pontoon floating bridge, there are four main behaviour types according to the longitudinal bending stiffness of the pontoons and the connection type between them.

1. Rigid body: rigid pontoon connected rigidly together end-to-end which represents a rigid continuous beam. 2. Flexure elastic body: flexure elastic pontoon connected rigidly together end-to-end which represents a flexible continuous beam. 3. Multi-rigid body: rigid pontoons connected flexibly. This kind of structure represents a chain of connected discrete rigid body. 4. Multi-flexure elastic body: flexure elastic pontoon connected flexibly together. This kind of structure represents a chain of connected discrete elastic flexible body.

Table (1-1) the structural classification [Ref .19 p.8]. The pontoon bending stiffness (EI ) Body classification z Rigid elastic The connection Rigid 1 2 rotation stiffness flexible 3 4 (Kconnector)

1.4 The floating bridges

The function of the floating bridge is to carry vehicles, trains, bicycles and pedestrians across an obstacle (a body of water). Inasmuch as a floating bridge crosses an obstacle, it creates an obstacle for marine traffic. Navigational openings must be provided for the passage of pleasure , smaller water crafts, and large vessels. These openings may be provided at the end of the bridge.

However, large vessels may impose demands for excessive horizontal and vertical clearances. In such cases, movable spans will have to be provided to allow the passage of the large vessels. The Floating bridge in State has a pair of movable spans capable of providing a total of 183 m of horizontal clearance. Opening of the movable span for marine traffic will cause interruption to the vehicular traffic. If the frequency of opening is excessive, the concept of a floating bridge may not be appropriate for the site. Careful consideration should be given to the long term competing needs of vehicular traffic and marine traffic before the concept of a floating bridge is adopted.

The floating bridges typical of those used in Washington State consist of concrete pontoons bolted together end-to-end to form a continuous floating bridge, rectangular in cross section,

TU Delft 15 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge with the top surface of the closed pontoons serving as the road surface. This type of floating bridge is referred to as a longitudinal . Each of the pontoons is compartmentalized, as is common with many marine vessels and structures, to prevent flooding of an entire pontoon when the outside walls are damaged or punctured. In the transverse or horizontal direction, each of the pontoon sections are held in position through a system of mooring cables connecting the pontoons with anchors located on the lake or sea bottom. Significant efforts have been made to understand floating bridge behaviour, both experimentally and analytically.

The basic concept:

The concept of a floating bridge takes advantage of the natural law of buoyancy of water to support the dead and live loads. There is no need for the conventional piers or foundations. Continuous floating bridges essentially act as beams on elastic foundations in both the vertical and transverse directions. In the vertical direction, buoyancy provides the linear modulus of the vertical support, while the discrete mooring cables provide the nonlinear horizontal support for the bridge under transverse loading. The design of a floating bridge for traffic is fairly straightforward and typical beam-on-elastic foundation methods can be used. However, the stochastic structural loading generated by wind and wave action and the corresponding dynamic response of the floating bridge to this loading presents a very complicated system to be understood. The design of a floating bridge for the environmental loading becomes much more difficult than for traffic loading. Despite the complications, understanding must be achieved if an efficient and safe design for a floating bridge is to be obtained. Floating bridges are cost-effective solutions for crossing large bodies of water with unusual depth and very soft bottom where conventional piers are impractical.

1.4.1 The history of the floating bridges

Roman bridge of boats crossing the during the Figure (1-5) King Xerxes Floating Bridge across the [ref.24] [ref.24] Dacian Wars Hellespont

The history of floating bridges can be dated back to time immemorial 2000 BC. Floating bridges have been built since that time. Ancient floating bridge was generally built for military operations so troops and equipment can be deployed quickly. All of these bridges took the form of small vessels placed side by side with wooden planks used as a roadway; see the figure (1-2). Subsequently, designers added openings for the passage of small boats.

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Floating bridges have been used to cross bodies of water since the time of the Persian military escapades into southern Europe. However, throughout history, many of the floating bridges built were only temporary structures. Procedures for the design and maintenance of permanent floating bridges have lagged in comparison to the great length of time over which floating bridges have been used. Floating bridge behaviour has been a research interest only for the past 60 or so years, mostly in Washington State and in Scandinavia.

Modern floating bridges generally consist of concrete pontoons with or without an elevated superstructure of concrete or steel, movable span for the passage of the large ships, variable flotation to adjust for change in elevations, and so on.

As compared with land-based bridges, only limited fundamental information is available for floating bridges in many respects, such as past construction records, meteorological and durability conditions. In recent years floating bridges can be designed on more scientifically reliable basis by theoretical developments in the hydrodynamic interactions between fluid and floating structure. For a large, permanent bridge, the concept is scalable, but not easily. However, if you need to bridge a deep body of water that has a soft bed, a more conventional design might not be feasible.

1.4.2 The technical aspects of the floating bridge

The floating bridges have particular technical characteristics in comparison with the conventional bridges or other floating structures. Most of them can be briefly mentioned as follow:  Takes advantage of the natural law of water buoyancy.  There is no need for the conventional piers or foundations.  Anchoring or mooring structural system is needed to maintain transverse and longitudinal alignments of the bridge.  It creates an obstacle for marine traffic; therefore the navigational opening is required.  It need access bridge to connect the abutment because of the tide variation during the day and to reduce the undesirable cross sectional forces when it bases on the abutment directly.  Stability structural system at both ends of the bridge is required to reduce the amplified response of the free end wave’s reflection (that will be explained later).  Cost-effective solutions.  Multi-rigid body analysis has relatively advantage to be complied with the wave loads.

The reasons of selecting floating bridges must be investigated in economical and technical problems. Floating constructions are preferred to fix ones in the following conditions:

 In deep waters where making fixed foundation is very expensive or impossible.  In places with a very weak bed where making fixed foundations is impossible.  In remote places where it is difficult to build or perform a project. For this case the construction can be built in another place and then moved to the main location.  In those ports which have high tides, so there will be a large difference between the surface of the ship’s deck and the fixed jetty.  In military operations, in which there is time limitation for doing the project.  In seismic places where fixed foundations can be shaken severely.

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 In temporary projects and operations, after which the construction is not useful anymore.  In those projects in which environmental and biological conditions should not be changed a lot.  Smart solution when the conventional bridges are impossible.

1.4.3 Floating bridges classifications

Modern floating bridges generally consist of concrete pontoons with or without an elevated superstructure of concrete or steel. The pontoons may be reinforced concrete or prestressed concrete post-tensioned in one or more directions. According to the pontoon arrangements, the design and the construction requirements, the conditions of the land or the types of barriers to cross, the floating bridge can be classified into two types, namely, the continuous pontoon type and the separate pontoon type. Openings for the passage of small boats and movable span for large vessels can be incorporated into each of the two types of the modern floating bridges.

Figure (1-6) Nordhordland Floating Bridge in Norway [ref.21]

A separate pontoon floating bridge figure (1-6) consists of individual pontoon placed transversely to the structure and spanned by a superstructure of steel or concrete. The superstructure must be of sufficient strength and stiffness to maintain the relative position of the separated pontoons. The two floating bridges in Norway are of the separate pontoon floating bridge type. Both types of floating structures are technically feasible and relatively straightforward to analyze. They can be safely designed to withstand gravity loads, wind and wave forces and extreme events such as vessel collisions and major storms.

Figure (1-7) Hood Canal Floating Bridge in USA [Ref.21]

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A continuous pontoon floating bridge figure (1-7) consist of individual pontoons jointed together to form a continuous structure. The pontoon can be connected in the longitudinal and transversal direction. The size of each individual pontoon is based on the design requirements, the construction facilities and the constraints imposed by the transportation route. The top of the pontoons may be used as a roadway or a superstructure may be built on top of the pontoons. All the present floating bridges in Washington State are of the continuous pontoon floating bridge type.

They perform well as highway structures with a high-quality roadway surface for safe driving in most weather conditions. They are uniquely attractive and have low impact on the environment. They are very cost-effective bridge types for water crossing where the water is deep (say, over 30m) and wide (say, over 900m), but the current must not be very swift (say, over 6 knots), the winds not too strong (say, average wind speed over 160km/h), and the waves not too high (say, significant wave height over 3m).

1.5 Floating Bridges around the World

Less than a dozen operational pontoon bridges can be found worldwide. The United States has five pontoon bridges, four of them in Washington and the fifth in Hawaii. The other bridges are located throughout the world in Norway, Netherlands, Canada, Germany and Japan.

The bridges are as different as the countries where they can be found. The majority is made of concrete but one bridge is made mostly with fibreglass. A few bridges are still wood, and some are steel. They vary from several hundred meters in length to more than 2 kilometer long. Each bridge is uniquely designed to handle the specific elements and topography of the area.

The following demonstration deals with a number of concrete floating bridges which were built outside the United States:

• The Takahiko-Three County Golf Course Prestressed Concrete Floating Bridge was built in 1992 in Daigo Town, in the Ibaraki Prefecture in Japan. This 57 m long bridge is constructed of concrete and prestressed thread reinforced plastics and used for golf cart and maintenance vehicle traffic. • A 93 m railroad pontoon scow was used at Lake Champlain, N.Y., from 1851 to 1868. • A 305 m pontoon bridge had been maintained since 1819 that crossed the Rhine at Koblenz, Germany. • A 91.5 m highway and railroad pontoon bridge crossed the Panama Canal at Paraiso. • A 540 m highway bridge crossed the Dvina River at Riga, Russia. • A 467 m bridge was built across the at in 1911-1912. • In 1874, a pontoon bridge was built to cross the Hoogli River at Calcutta, India.

Several floating bridges were constructed of steel or wood around the time of the Lacey V. Murrow Bridge. Examples include the steel pontoon bridge built in 1912 in . The bridge was built with fifty steel pontoons connected by hinges. Other pontoon bridges include swing spans constructed in Curacao in 1923 and in Chicago in 1924.

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Examples of modern permanently floating concrete structures include:

• Heidrun Concrete Tension Leg Platform (60,000 m3 of concrete), in the North Sea. • Troll West Concrete Semisubmersible (46,000 m3 of concrete), in the North Sea. • N’Kossa Concrete Barge (26,400 m3 of concrete) off the West Coast of Africa. • Sakti Ardjuna Concrete LPG Terminal in Indonesia, (140.6 m x 41.5 m x 17.4 m).

The world map below; figure (1-8) shows the locations of some important bridges in the world.

NO.2, 6, 8 WESTINDIA NORDHORDLAND

GALATA ADMIRAL CLAREY

HOBART QUEEN EMMALT

Figure (1-8) Map of the major Floating Bridges around the world [ref.18]

The following briefly explanations focus only on the technical specifications of the floating bridges which enable us to get obvious idea about the design methods and requirements:

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1.5.1 Evergreen Point Floating Bridge

Figure (1-9a) Evergreen Point Floating Bridge Figure (1-9b) Evergreen Point Floating Bridge

The Evergreen Point Floating Bridge, now officially the Governor Albert D. Rossellini Bridge, is the longest floating bridge in the world at (2,310 meters). It carries State Route 520 across from Seattle to Medina and is often called the "520 bridge" by locals.

Starting in August 1960, construction crews ashore built 33 hollow, concrete boxes (pontoons), each (110X18X45) m length, width and high respectively. These huge pontoons were floated and then towed into position, where they were linked by thick steel cables to anchors to hold them in place. The 62 anchors, buried deep in the lake bed, weigh about 77 tons each. The bridge has a retractable draw span in the middle that is raised to protect the structure from strong winds. Designed of four lanes and to carry 65,000 vehicles a day, it now carries 115,000. That wear and tear, coupled with storm damage, has led to costly repairs. The bridge is exposed to tide swings of (1.2 m) and the design wind speed was 137 km/h. Building the bridge cost a relatively modest $21 million ($154 million in today's money) [Ref.21].

1.5.2 Hood Canal Floating Bridge

The Hood Canal Bridge is located in Washington State in the USA and connects the Olympic Peninsula and the Kitsap Peninsula across Hood Canal. It is (2,398 m) long, (The floating part is 1972 m) making it the longest floating bridge in the world located in a saltwater tidal basin, and the third longest floating bridge overall. It was the second concrete floating bridge constructed in Washington State and first opened in 1961. Since that time, it has become a vital link for local residents, freight haulers, commuters and recreational travelers. The convenience has had a major impact on economic development, especially in eastern Jefferson County. Some of technical aspects are listed below:

 It has a center draw span opening of (183 m) see figure (1-7).  The east approach span weighs more than 3,800 tons and the west approach span weighs more than 1,000 tons.  Average daily traffic across the Hood Canal Bridge is approximately 15,000 vehicles. Peak volumes reach 20,000 vehicles on summer weekends.  The water depth below the pontoons ranges from (24 to 104 m). In its marine environment, the bridge is exposed to tide swings of (5 m).

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 During inclement weather, the draw span is retracted (closing the bridge to vehicle traffic) when winds of (64 km/h) or more are sustained for 15 minutes although it is designed for maximum wind speed of 133km/h.

The design and planning process for the Hood Canal Bridge took nearly a decade amid criticism from some engineers throughout that time. Critics questioned the use of floating pontoons over salt water, especially at a location where tide fluctuations vary as much as five meters and the funneling effect of the Hood Canal might magnify the intensity of winds and tides. The depth of the water, however, made the construction of support columns for other bridge types prohibitively expensive.

1.5.3 Lacey V. Murrow floating Bridge

The Lacey V. Murrow Memorial Bridge is a floating bridge that carries the eastbound lanes of Interstate 90 across Lake Washington from Seattle to Mercer Island, Washington, the right side of figure (1-1). It is the second longest floating bridge in the world at (2,018 m), whereas the longest is the Evergreen Point Floating Bridge just a few miles to the north on the same lake, built 23 years later. The original two-way, four-lane bridge was designed by the engineer Homer Hadley (1885-1967) and constructed of reinforced concrete in 1940.

Since construction, the bridge has been part of the major trunk route crossing the state and accessing Seattle from the east. This pontoon bridge was of unprecedented scale and sophistication and the first constructed of concrete. The concept for its construction was originally proposed by Homer M. Hadley, and designed by the Washington Toll Bridge Authority. The bridge was removed from the National Register of Historic Places when it sank. A replacement, new concrete floating bridge with pontoon size of (107X18X4.5) m using the original approaches is under construction, a second parallel floating structure was completed in 1989 to accommodate increasing traffic. The water depth below the pontoons is (75 m). In its marine environment, the bridge is exposed to tide swings of (1.2 m) and it is designed for maximum wind speed of 100 km/h.

1.5.4 Third Lake Washington Bridge

The Third Lake Washington Bridge, officially the Homer M. Hadley Memorial Bridge, is the fifth longest floating bridge in the world at (1771 m), see figure (1-1). It carries the westbound and reversible express lanes of Interstate 90 across Lake Washington between Mercer Island, Washington and Seattle. Most local residents have never heard of the Hadley name and refer to both bridges together as "the Mercer Island Bridge". Some also refer to the "Old" and "New" Mercer Island Bridges, but these terms are ambiguous because the Murrow Bridge was rebuilt after the Hadley Bridge was completed. The water depth below the concrete pontoons of (108X23X5) m is (61 m). In its marine environment, which is similar to the previous bridge, the bridge is exposed to tide swings of (1.2 m) and it is designed for maximum wind speed of 100 km/h.

1.5.5 Galata Floating Bridge

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The is a bridge that spans the Golden Horn in Istanbul, . From the end of the 19th century in particular, the bridge has featured in Turkish literature, theater, poetry and novels. The 466 m floating bridge is completed in 1912 and now is out of use. Utilizing three well- known geometrical principles, the pressed-bow, parabolic curve and keystone arch, created an unprecedented single span 240 m long and 25 m wide bridge for the Golden Horn, which would become the longest bridge in the world of Figure (1-10) Galata Bridge [ref. 21] that period if constructed. The steel pontoon size was (25X9X3.5) m. The bridge is exposed to tide swings of (0.6 m) and it is designed for maximum flow speed of 3 m/sec. The bridge historically provides high demands for connecting Asia and Europe. Used until 1992 and then it is demolished and replaced by a non-floating bridge see figure (1-10).

1.5.6 Bergsoysund Floating Bridge

The 934m Bergsoysund Bridge floating section spans more than 845 m across. It was completed in 1992 and is located in Kristiansund, Norway. The bridge, which is the first of its type in the world, without stays or mooring lines (lateral support). It has a design life of at least 100 years. Both floating bridges in Norway (Bergsoysund Bridge & ) consist of a steel superstructure arch shaped in plan and placed on concrete pontoons.

Figure (1-11) Bergsoysund Floating Bridge [Ref.21]

Bergsoysund Bridge is constructed from pipe trusses, in a shape of an arch fixed on seven floating concrete pontoons of (34X20X9)m, with an 845 m span and the radius of the arch is 1300 m, see figure (1-11). In a vertical direction the structural system is a continuous arched beam on an elastic foundation. Elastic foundations are the pontoons of a floating bridge. The pontoons have been constructed from light concrete and it is divided into 9 watertight compartments. In its marine environment, the bridge is exposed to tide swings of (4 m) and it is designed for maximum wind speed of 135 km/h.

1.5.7 Nordhordland Floating Bridge

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The 1246m Nordhordland Bridge or Salhus Bridge was completed in 1994 in Bergen, Norway, with an 1159m floating bridge portion to cross the Salhus Fjord, figure (1-6). The span between the lightweight concrete pontoons is 113.25m. The steel deck width is 10m and the deck level above the water level is about 11m. The Nordhordland superstructure has the shape of an eight-corner box girder. The structural type and the design conditions of the Nordhordland floating bridge are similar to the previous bridge. The water depth below the pontoons is (500 m). In its marine environment, the bridge is exposed to tide swings similar to the previous one, of (4 m).

1.5.8 Yemenai Bridge

The 879 m Yemenai Bridge in the figure (1-12) includes a 366 m swinging outstanding float bridge section and was completed in 2000 in Osaka, Japan. The bridge is constructed across a water channel and it floats on two hollow steel pontoons each of dimensions (58 m x 58 m x 8 m). The bridge can be swung around a pivot axis near one end of the girder when a passage way for very large ships in the channel is needed.

Figure (1-12) Yumemai Floating Bridge [Ref.21]

1.5.9 West India Quay Foot Bridge

The bridge located in Docklands, Tower hamlets, Greater London, , United Kingdom and completed in 1996, see figure (1- 13). This is a gently curved, 94m arc aluminium deck supported on four sets of splayed tubular steel legs which rest on largely- submerged pontoons secured by light-tension piles. The bridge is a steel structure with 750x300 U - [ref.24] shaped spine beam. Tapered Figure (1-13) West India Quay footbridge, United Kingdom

TU Delft 24 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge angles, set diagonally to the spine beam, help to cross-brace it. The splayed legs are in 244.5 CHS and are bolted to the spine beam. They terminate in solid, cone-shaped connections welded to circular plates that are bolted to the pontoons. Only 500mm of the 2800mm diameter foam-filled pontoons are above the water surface. The deck is a 75mm deep aluminium box section with grooved pattern on the surface to give a non-slip surface. The bridge deck is divided into three, two gently inclined sections on each side of a central section, 6.6m long, which can be lifted hydraulically to allow boats to pass through. The opening action is by a simple cantilever counterbalance.

1.5.10 Hobart Floating Bridge

In 1943, the 956m Hobart Bridge in Tasmania, Australia, was completed with hollow concrete pontoons of (40X11X3.7) m crossing the Derwent River. This bridge has since been replaced. The water depth below the pontoons is (31 m). In its marine environment, the bridge is exposed to tide swings of (2.4 m) and it is designed for maximum wind speed of 198 km/h.

1.5.11 Kelowna Floating Bridge

The 640 m Kelowna Floating Bridge also known as the Okanagan Lake Bridge was completed in 1958 in Kelowna, British Columbia, Canada. The water depth below the pontoons is (49 m). In its marine environment, the bridge is exposed to tide swings of (1.5 m) and its pontoon size was (61X15X4.4) m.

Table (1-1) Major Floating Bridges around the World Translated from the guideline for design of floating brides Japan society of civil engineers, March 2006 p.8 [ref.18]

Deep- Leng Pontoon No est . Year Name Location -th dimension (m) (m) s (m) 1 1912 Galata Istanbul, Turkey(River mouth) 41 466 25x9x3.7 2 1940 Lacey V Murrow Washington State, USA(Lake) 75 2,018 107x18x4.4 3 1943 Hobart Tasmania, Australia(River mouth) 31 965 40x11x3.7 4 1957 Kelowna British Columbia, Canada (Lake) 49 640 61x15x4.6 5 1961 Hood Canal Old (east Washington State, USA(Lake) 104 1,972 110x15x4.4 side) 6 1963 Evergreen point Washington State, USA(Lake) 61 2,310 110x18x4.5 7 1983 Hood Canal new (west Washington State, USA(Lake) 104 1,972 110x18x5.5 side) 8 1989 Third Lake Washington Washington State, USA(Lake) 61 1,771 108x23x5.0 9 1992 Bergsoysund Kristiansund, Norway(Fjord) 300 934 34x20x6.0 10 1994 Nordhordland Bergen, Norway (Fjord) 500 1,246 42x12.5x6. 8 11 1996 West India Quay Foot London, England (River mouth) 94 Φ 2.8x10 Bridge 12 1996 Nagoya Fish Port Nagoya, Saga, Japan(Inner 10 110 110x15x3.0 Terminal Harbor) 13 1998 Admiral Clarey Hawaii, USA (Inner Harbor) 15 310 93x15x5.1 14 2000 Kujira Nishino Omote, Kagoshima(Lake) 180 15 2000 Mumai Oohashi Osaka (Inner Harbor) 10 410 58x58x8.0

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Natural Condition High Pontoon Wave Wind Methods of No. Water level wave Flow Lanes structure cycle speed(m/s restraint change(m) force (m/sec) material Ts(sec) ec) Hs(m) 1 0.6 3.0 4 Steel Chain/Anchor 2 1.2 2.4 4.0 28 4 Concrete Cable/Anchor 3 2.4 2.1 1.5 55 2 Concrete Fixed end 4 1.5 1.8 2 Concrete Chain/Anchor 5 5.0 3.3 1.5 37 2 Concrete Cable/Anchor 6 1.2 2.7 38 4 Concrete Cable/Anchor 7 5.0 3.3 1.5 37 2 Concrete Cable/Anchor 8 1.2 2.4 4.6 28 5 Concrete Cable/Anchor 9 4.0 1.4 4.5 1.3 37.5 2 Concrete Fixed end 10 3.0 1.7 5.1 27.1 2 Concrete Fixed end 11 Steel Cable/Anchor 12 2 PC Hybrid Jacket 13 2 Concrete Chain/Anchor 14 0.3 Aluminium 15 2.0 2.5 7.7 0.3 42 4 Steel Fender/Dolphin

No. Notes 1 Used until 1992, then demolished and new non-floating bridge 2 Replaced some pontoons in 1990 due to damage by disaster 3 Used until 1964, then non-floating bridge. Reusing the concrete pontoons as break-water 4 Rebuilding began in 2005, and estimated completion in 2008 5 Rebuilding began in 2003, and estimated completion in 2007 6 Rebuilding began in 2007 7 Due to damage by disaster, rebuilt the west side only in 1979 8 9 10 11 Foot bridge 12 Pier/ road dual use 13 Military only and not for public 14 15

1.6 Introduction to hydro-statics

When the inertial component of Newton equation of motion is neglected, we speak of a static analysis: ΣF = m*a, convert to ΣF = 0. In calm water, this simplification permitted. The hydrostatics can help to determine the depth and the rotation of a floating structure charged by static load. The next paragraphs deal with this concept with more details.

1.6.1 Equilibrium and stability

A standing body is in balance, this means that should apply: Σ Fhor = 0, Σ Fvert = 0 and Σ Tm = 0. When we have a balance in the body from achieving balance, there are three possible responses. The body will return to the equilibrium state (stable equilibrium), the body will not return to the equilibrium state (unstable equilibrium) or the body will find a new balance in the displaced state (neutral equilibrium), see the figure (1-14). In this case, the potential energy is constant.

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Stable Unstable Neutral Figure (1-14)

Stability can be defined as the extent to which an object to return to the stable equilibrium position. On the basis of the figure (1-15), we will dwell on the stability of a floating body.

Figure (1-15) floating object

The stability is calculated by first finding the centre of buoyancy (B) which is also the centre of the volume of the immersed part of the float. In figure (1-15), the buoyancy centre (B) represents the application point of the buoyancy force. That means that (B) is the gravity centre of the displaced mass of water. The (G) is the gravity centre of the total mass of the float, and the superstructure. When we tilt the float with an angle (α) the buoyancy centre (B) will move. The intersection of the buoyancy force acting line with the symmetry axis is called the Meta centre (M), see figure (1-16).

Figure (1-16) [ref.5]

Due to the angular rotation shift the buoyancy centre (B) and the centre of gravity (G) from the vertical, the acting line of the forces is no longer the same line by which a moment is created. The left side of figure (1-16) shows the righting moment with value (F x a). This moment try to return the float to the stable position. In the right figure, we see a heeling moment (F×b) which turns the float down. The figure (1-17) shows the curve of the relation

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Figure (1-17) Heeling – Righting moment curve

Clearly the Righting moment would be arose when the Metacentre (M) rise above the gravity centre (G) of the float. In other words, the structure is stable if the metacentre (M) above the centre of gravity (G). The degree of stability is reflected in the distance between (G) and (M). This distance is called the metacentre height (hm). By ensuring a high (M) and a low (G) meta centre height is promoted. These two parameters (G and M) are the basis of the distinction between form stability and weight stability.

Form Stability

The concept of form stability lies in shifting of the buoyancy centre (B). The extent to which the buoyancy centre (B) moves in a certain angle depends on the width of the float base. The wider the float base, the small the shifting distance of the buoyancy centre (B) will be from the centre. As we mentioned earlier, the shifting of the buoyancy centre (B) is in direct relation with the height of metacentre. The small shifting of the buoyancy centre (B), the higher the metacentre can be lie. So, the wider the float bases the more stabile structure.

The form has been stability in small angle distortions effective. This provides a comfortable structure: a form stable construction has a large initial stability. If the rotation is, however, increases the distance between G and M smaller, so that the righting moment smaller. The stability is inversely proportional to the angle of rotation.

Weight Stability

The lower centre of gravity, the greater the distance is between G and M. That leads to more stable structure. Weight stability will only be effective with a great angle of rotation. The distance between G and M increases with increasing of the angle: the larger the angle the greater the righting moment. The stability increases with the angle of rotation. The stability in a mass scale construction is very stable. This provides a secure mechanism.

1.6.2 Meta Centre Height

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A float in the equilibrium status has a characteristic that the moment as a result of acting eccentric loads equal to the righting moment. When an eccentric load is applied will therefore distort the construction until there is balance. When the righting moment as a function of the angle is known, we can balance the angle which is determined. Using the Meta Centre Height (hm), the righting moment in a certain angle determined. It is therefore important to first metacentre height to be determined. Scribanti has derived that the distance from the buoyancy centre to metacentre applies:

I BM  1(*  1 tg 2)  2

Where:

l *b3 I = : Moment of inertia of the water by cutting surface to the z-axis. 12 ∇ = l × b × d: Volume of the underwater body. α = angle of the float against the horizontal axis.

Figure (1-18) the definition of the Metacentre height [ref.5]

The above formula shows that the place of the metacentre depends on the angle of rotation. It appears, however, that small angle distortion, to around (10) degrees, the influence of the rotation is negligible. The formula then reduces to:

BM = I/∇

For a rectangular cross section is to write as: b 2 BM  12d b 2 The distance from Meta Centre to the bottom of the float (KM) is: KM   d 12d 2 b 2 Metacentre height (hm) can now be written as: h   d  KG m 12d 2 KG is the distance from the bottom of the float to the centre of gravity of the float. Like the other variables, this value is known. Metacentre height above formula is so easy to determine.

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1.6.3 Rotation

After the determination of the Metacentre height hm, it is simple now to calculate the arm of the righting moment. For the figure 1.6 we can find out the following relation: a = hm x sin (α)

Mrighting = F * hm * sin (α)

Where: a = the righting moment arm. hm = the metacentre height. α = the tilting angle. F = the force.

As discussed above, for the stable structure the metacentre must lie above the gravity centre, and the Righting moment should be equal to the imposed moment. Now we will consider the case where the angle of rotation is not imposed angle, but the float rotate due to the external eccentric load which is applied until a new equilibrium position is found. From the figure (1- 19) we can derive the following equations:

∑Tm = 0 → Mrighting = M external → M external = F * hm * sin (α)

-1 The critical angle of tilting (α) = sin (M external / (F * hm))

Figure (1-19) the arm of the righting moment [ref.5]

The maximum permissible rotation of a floating structure is an important design parameter. There are no standards set which limits on permissible rotations. Overall it can be stated that the rotation below (5) degrees should be maintained .

1.7 Introduction to hydro-dynamic analysis

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Floating structures are dynamically charged by waves. It is important to give attention to the dynamic loads due to waves, because in certain circumstances, the movements can take extreme forms, which can result a possible collapse of the structure.

1.7.1 Dynamic motions definition

Translation Rotation

 In the x –direction: Surge - In the x –direction: Roll  In the y –direction: Sway - In the y –direction: Pitch  In the z –direction: Heave - In the z –direction: Yaw

Figure (1-20) body motions [ref.4]

 Dynamic analysis (general)

Moving a floating body can be described by six coupled motion equations. A system with 6- linked movement leads to a stiffness matrix of (6 x 6). By using such a system to resolves it. There are several computer programs developed that specialize in determining the movements of floating bodies. To the TU-Delft developed Delfrac program is a good example. However, it is wise to check the software result through a few hand calculations.

1.7.2 Basic dynamic analysis of continuous beams

The basic approach to dynamic analysis is to solve the equation of motion:

MẌ + CẊ + KX = F (t) (1-1)

This equation is familiar to structural dynamic problems of land-based structures. However, in predicting the dynamic response of a floating bridge, the effects of water-structure interaction must be accounted for in the analysis. As a floating bridge responds to the incident waves, the motion (heave, swing, and roll) of the bridge produce hydrodynamic effects generally characterized in terms of added mass and damping coefficients. These hydrodynamic coefficients are frequency dependent. The equation of motion for a floating structure takes on the general form:

[M + A] Ẍ + [C1 + C2] Ẋ + [K + k] X = F (t) (1-2) [ref.3]

Where:

X, Ẋ, Ẍ = generalized displacement, velocity and acceleration at each degree of freedom.

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M = mass-inertia matrix of the structure. A = added mass matrix (direction, geometry, frequency dependent) (see section A.1.1). C1 = structural damping coefficient (see section A.1.1). C2 = hydrodynamic damping coefficient (frequency dependent). K = structural stiffness matrix (elastic properties, including effects of mooring lines when used) (see section A.1.1). k = hydrostatic stiffness (hydrostatic restoring forces) (see section A.1.1). F (t) = forces acting on the structure.

A substantial amount of experimental data has been obtained for the hydrodynamic coefficients for ships and barges. Based on these experimental data, numerical methods and computer programs have been developed for computing hydrodynamic coefficients of commonly used cross-sectional shapes, such as the rectangular shape.

For structural configurations for which no or limited data exist, physical model testing will be necessary to determine the basic sectional added mass, damping and wave excitation loads. Structural damping is an important source of damping in the structure. It significantly affects the responses. A structural damping coefficient of 2 to 5% of critical damping is generally assumed for the analysis. It is recommended that a better assessment of the damping coefficient be made to better represent the material and structural system used in the final design.

The significant wave height, period and central heading angle may be predicted using a program. The Joint North Sea wave Project (JONSWAP) spectrum is commonly used to represent the frequency distribution of the wave energy predicted by a program. This spectrum is considered to represent fetch limited site condition very well. A spreading function is used to distribute the energy over a range of angles of departure from the major storm heading to the total energy.

Frequency-Domain Analysis:

The frequency-domain analysis is based on the principle of naval architecture and the strip theory developed for use in predicting the response of ships to sea loads. The essence of this approach is the assumption that the flow at one section through the structure does not affect the flow at any other section. Additional assumptions are:

 The motion is relatively small.  The fluid is incompressible and in viscid.  The flow is ir-rotational.

By using the strip theory the problem of wave structure interaction can be solved applying the equation of motion may be expressed in terms of frequencies, ω, as follows:

2 {-ω [M + A] + i ω [C1+ C2] + [K + k]} = {F (ω)} (1-3) [ref.3]

This equation may be solved as a set of algebraic equations at each frequency and the responses determined. The maximum bending moments, shears, torsion, deflections and rotations can they be predicted using spectral analysis and probability distribution. The basic steps involved in a frequency-domain analysis are:

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1. Compute the physical properties of the bridge – geometry of the bridge elements, section properties, connections between bridge elements, mass-inertia, linearized spring constants, structural damping, etc. 2. Compute hydrodynamic coefficients-frequency dependent added mass and frequency dependent damping. 3. Compute hydrostatic stiffness’s. 4. Calculate wind, wave, and current loads and other loading terms. 5. Build a finite-element computer model of the bridge as a collection of nodes, beam elements and spring elements. The nodes form the joints connecting the beam elements and the spring elements and each node has six degree of freedom. 6. Solve the equation of motion in the frequency domain to obtain frequency responses amplitudes of which are referred to as response amplitude operators (RAOs). 7. Perform spectral analysis, using the RAOs and the input sea spectrum, to obtain the root mean square (RMS) of responses. 8. Perform probability analysis to obtain the maximum values of the responses with the desired probability of being exceeded. 9. Combine the maximum responses with other loadings, such as wind, current, etc. for final design.

1.8 Material specifications

The materials used for the floating body may be steel, or concrete or steel-concrete composite, plastic or synthetic material and the relevant specifications should be followed. Since water-tightness of concrete is important to avoid or limit corrosion of the reinforcement, either watertight concrete or offshore concrete should be used. High-performance concrete containing fly ash and silica fume is most suitable for floating structures. The high performance concrete has a high strength and low permeability. The effects of creep and shrinkage are considered only when the pontoon are dry and hence not considered once the pontoon are launched in the sea. Steel used for floating structures shall satisfy the appropriate standard specifications.

Table (1-3) the high-performance concrete technical properties Concrete f’ck f’b fb fbm E’b ’bu ’bpl grade (N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2) (10-3) (10-3) B65 65 39 2,15 4,3 38500 3,5 1,75 B75 75 45 2,25 4,5 38900 3,25 1,75 B85 85 50 2,35 4,7 39300 3,00 1,80 B95 95 55 2,45 4,9 39700 2,75 1,85 B105 105 60 2,55 5,1 40100 2,50 1,90

1.9 Evaluation

To perform a precise studying, the following questions should be answered: 1. For which wind speeds the floating bridge is designed? 2. Which sea wave form and direction create the maximum displacement? 3. In which way respond the floating bridge against the wind/wave loads? 4. In which parts and cases appear the large displacement? 5. How can this displacement be reduced or converted it into internal forces? 6. What is the effect of flexural stiffness continuity of the bridge on its response? 7. What is the effect of the pontoon length and the connector stiffness on the response reduction? What is the optimum design method that can meet the design requirements?

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2 Design principles

The strategy of the total design procedure involves the arrangement of the design activities into different levels. The level of the fundamental design procedure concerns the selection and creation of the floating bridge geometry and the selection of the suitable structural elements of the floating bridge, which fit in the design requirements, and the environmental circumstances of the bridge site. For instance, the choice of the mooring system should be a mooring cable/ anchor system when the water depth is larger than the distance that can be supported by a sliding pile or when the cost of a sliding pile mooring system is higher than of a mooring cable /anchor system. This step is a global view on design aspects, without intervention into the specified details that will be dealt with later at the design specification level. The design requirements of the floating bridge are very wide and depend on the site situations. Therefore, the availability of several structural element alternatives extends the design options and facilitates reaching the design target. The design requirements can be developed from the following parameters:

1. The seabed condition (soft - sand - rock). 2. The type of mooring system (slide pile - mooring cables) is according to the water depth. 3. The environmental loads determine the bridge type (continuous - separate pontoon bridge), the pontoon shape, and the connection type. 4. The traffic discharge determines the bridge width. 5. The marine traffic determines the size of the navigational opening (if required). 6. The tidal range determines the access bridge length and shape.

Different alternatives for different situations will be created and discussed for each of the mentioned parameters. That will be the base for the fundamental design level. In this chapter, we will deal with different floating bridge alternatives and structural elements alternatives and study the technical characteristics and field of application of each alternative. The combination of different structural elements, which can be complied with different situations, is made to specify the final choice.

This chapter illustrates in tables the alternatives for all structural elements of a floating bridge. Some of them are already applied in constructed floating bridges while the author collects others from literature and adds new ones. Each one has a symbol that consists of a letter to denote the structural element and a number to denote the sequence. Abbreviated description of the geometry and functionality of each alternative is mentioned with symbol reference.

The last two parts deal with a literature study on the mechanical modelling of the continuous pontoon floating bridge and the construction procedure of a floating bridge as an aspect that can determine the design procedure.

2.1 Argumentation of the choice

A floating bridge is constructed, in most cases, in impractical sites in deep water where it is impossible as too costly to construct a conventional foundation or sliding piles. The mooring cable/anchor system is a compliant system that can provide reliable supporting for an offshore structure, such as the floating bridge, which is exposed by the wind/wave loads.

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As mentioned before, floating bridges can be classified into two types: continuous- (CPFB) and separated pontoon floating bridges (SPFB). The latter type represents a continuous beam supported by series of individual floating foundations where the differential displacement between the individual pontoons as a result of the water motion, is a main loading type on the bridge. The first type (CPFB) has other structural characteristics. It represents a continuous beam supported uniformly by the water and the mooring system. The combination of more than one uniform supporting element in the structure can provide an ideal model for the slender floating structure which has exceptional stability and rigidity properties.

The (CPFB) is selected as an ideal option in most constructed floating bridges in the world which are mentioned in chapter one because of the large stability created by the continuity of flexural stiffness, the large contact area with the water which leads to a large supporting area and the uniform distribution of the mooring points.

2.2 Evaluation of floating bridge layouts

The symbols (A1-A7 & A14) represent the already used and suggested layouts of the (CPFB) while the symbols (A8-A13) show the proposed layouts of the (SPFB).

Table (2-1) floating bridge layout alternatives; left CPFB; right SPFB. A1 A8

Side view

A2 A9

Top view and side view Top view and side view A3 A10

Side view Side view A4 A11

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Side view Side view A5 A12

Side view

Side view A6 A13 Top view

A7 A14

Figuur 1 A15

Top view of two crossed floating bridge

2.2.1 The continuous pontoon floating bridge models

The (CPFB) consists of several hollow concrete boxes connected to each other at width- draft face in such a way to create the main part of the bridge body that behaves like the backbone. The width of these boxes is determined according to the traffic demand requirements and the

TU Delft 37 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge draft and length are determined according to the structural design and construction requirements. A1 The alternative (A1) is the simplest style of the continuous pontoon arrangement. This type is already used in the Hood Canal Floating Bridge as shown in the figure (1-7). This alternative is simple and easy in erection and construction. Therefore, it can be considered as the economic option. For instance, the same formwork can be used for all pontoons and the construction can be executed rapidly.

A2 The alternative (A2) represents a normal pontoon dimension with a variable width to increase the stiffness of the water spring (K). The width variability is created by connecting additional concrete wings from both sides. These wings increase the projected area of the pontoon, which increases the water pressure under the bridge during vertical motion. Therefore, it has to be braced to resist the water pressure and the effect of the dynamic amplification due to the bridge response by the sea wave excitation. The wings can be connected at different levels of draft, which will not only affect the water resistance but will increase the mass of the bridge by increasing the movable water mass, which concerns the motion (the added mass term).

A3/A4 The alternatives (A3 and A4) represent a pontoon bridge with a variable draft. This system provides a variable flexural stiffness that affects the characteristic length of the pontoon. It is used when a long pontoon is required. The connection should be located at the smallest draft. The variability of the draft can be linear as shown in (A3) or curved as shown in (A4). The water pressure under this bridge alternative is not uniform due to the variety of the draft and the maximum pressure is concentrated under the deepest part.

A5 Alternative (A5) is a large-scale arch bridge. Every strip represents a pontoon with a prismatic shape. The pontoons depth difference plays a main role in the structural behaviour of the bridge. When this difference is large enough, it may lead to a partial submergence that means that some of the pontoons are fixed above the water level. This type can therefore, provide a navigational opening.

A6 Alternative (A6) is based on the post and beam concept to connect the bridge deck with the pontoon. The method can be modified to be a double deck floating bridge if the pontoons remain partially submerged.

A7 The arch concept, alternative (A7), is another double deck floating bridge using the arch to transform the load from the deck to the pontoon. This system has a higher shear capacity, between the decks, than the post and beam concept.

A14 The tidal effects can be solved by using this alternative. The system works as follows: In the flood case, the ballast water will be taken into tanks inside the pontoon. In this way, the bridge will remain at the same level as where it is connected to land. In the ebb case, the water will be pumped out of the ballast tank to raise the bridge. This system consumes much energy but requires no access bridge (see [ref.32]).

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2.2.2 The separated pontoon floating bridge models The separated pontoon floating bridge consists of two main parts: individual pontoons and girders. The pontoons provide an elastic block foundation of the bridge, which is connected later by the girders to form the body of the bridge. The serious matter in this type of bridge is the differential vertical displacement between the pontoons, which leads to high internal forces in the girders. Flexible connections can solve the problem. The location of the connection at the midspan of the girder increases the rolling of the pontoon while the location of the connection above the pontoon keeps it stable with only the heave motion.

A8/A9 The normal simply separated pontoon bridge has pontoons and simply supported beams that connect the pontoons. It is convenient for normal light traffic. The elliptic shape of the pontoon of (A9) facilitates the water flow and reduces the lateral pressure of the water current.

A10/A11 For a heavy environmental load or for a large span, the application of an arch beam or a prismatic beam seems to be a suitable solution.

A12 For a very long bridge, a large span is required. Alternative (A12) is an exceptional solution. It consists of the very large pontoon, which can lift the total weight of a bridge unit, which consist of the pontoon and two prismatic cantilever beams built integrally with the pontoons to form one unit of the bridge. Pylons and tension cables can provide additional supports for additional length of the prismatic cantilever.

A13 The rotational stability (roll) of the separated pontoon floating bridge is very low due to the high position of the gravity centre and the relatively low position of the meta centre. The arc form of the floating bridge provides a sufficient support for the total structure. The base of the total structure can be considered as being the maximum distance between the arc and the chord. This distance determines the degree of curvature. Furthermore, the arc should be pointed to the opposite direction of the water stream.

A15 The top view of two crossed bridges: the crossing of two continuous pontoon bridges in the middle distance provides a lateral support. The efficiency of the entire geometrical shape depends on the inclination angle of the crossing leg with respect to the centre line of the crossing. The large inclination angles the large lateral support.

2.2.3 Comparison between separated- and continuous pontoon floating bridges

A floating bridge can be constructed in two types: a Continuous Pontoon Floating Bridge (CPFB) and a Separated Pontoon Floating Bridge (SPFB). The decision has to be taken according to the site situation and the functional and structural requirements. In order to reach a clear idea of these requirements, we will highlight the major differences between both types (More comparison aspects can be found in table (2-2)):

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 The CPFB requires a navigational opening while the SPFB creates no obstacle for the marine traffic when the girders have a sufficient clearance with the water surface.

 The rolling stability in the CPFB is higher than the SPFB (except the arc form) for two reasons, the first is that the foundation area of the CPFB is relatively larger than SPFB and the second is that the meta centre –gravity centre distance is larger.

 The heave stability of the CPFB is higher than of SPFB due to the large contact area with the water and the uniform mooring force distribution along the bridge. These are limited in the SPFB.

 The influence of the sea wave on the CPFB is larger than on the SPFB due to the large contact area with the water as well as the structural continuity hinders the water flow generally. In a storm case, the navigational opening is opened to release the lateral wave pressure on the bridge. In the SPFB, usually more (50-70) percentage of the water surface is open to a sea wave.

 The constructability of the CPFB is better than the SPFB. The CPFB is constructed by connecting several units with the same size. Those units are floated and towed in the sea to the bridge site and connected directly while the SPFB generally consists of two different units: the pontoons and the girders. The pontoons are towed to the site and connected by the girders, which are assembled above the pontoons. This process requires a floating crane. Therefore, the construction costs of the SPFB are higher. In some cases, it is necessary to divide the bridge in several uniform units, tow them to the site, and connect them there. Those units should be a series of structural elements (pontoon - girder - pontoon) in different numbers depending on the site possibilities. The unit has to start and end with a pontoon to avoid the using of the floating crane inside the water.

 The wind action on the CPFB is limited and directly proportional to the freeboard height. A compressive force on the side that faces the wind and a suction force on the opposite side as well as a frictional force on the bridge deck represent the wind forces on the CPFB. The influence of wind on the SPFB is very high due to the large contact area of the bridge with the wind because the girder is completely above the water and the wind acts on all sides. In addition to that, the wind speed increases with the elevation, which increases finally the wind force.

 The mooring system that is required for the pontoon of the SPFB should be relatively more intensive than for the CPFB because of the high wind force on the girders. These forces have to be taken by the pontoon mooring system. The forces of the mooring system are distributed in a limited area of the pontoon while the mooring system in the CPFB is distributed along the total bridge length.

Table (2-2) Comparison between SPFB and CPFB No. The parameter Separated Pontoon Continuous Pontoon Floating Bridge (SPFB) Floating Bridge (CPFB) 1 Navigational opening - + 2 Rolling stability - + 3 Heaving Stability + +/-

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4 Sea wave influence + - 5 Water current influence + - 6 Wind influence - + 7 Constructability - + 8 Mooring intensity + - 9 Horizontal arc form efficiency + -

2.3 The main structural elements of the floating bridge with alternatives

Figure (2-1) plan view of the floating bridge

2.3.1 The pontoon

A floating bridge consists of a series of pontoons in different sizes and shapes that are arranged in a different manner (continuous – discrete – longitudinal – transversal) to form different types of floating bridges. The pontoon can be concrete caisson, steel pipes or made of a composite material and it represents the foundation of the floating bridge. The pontoon is a flat-bottomed float used to support a structure on the water and it acts as an elastic foundation. It may be simply constructed from closed cylinders such as pipes or barrels or fabricated as boxes from metal or concrete. The tables (2-3) and (2-4) illustrate different alternatives for the pontoon shape with a functional description of each alternative. Different transversal and longitudinal sections affect the technical properties of the pontoons.

2.3.1.1 Pontoon transverse cross section alternatives

Table (2-3) the pontoons transverse cross section alternatives B1 B2

B3 B4

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B5 B6

B7 B8

B9 B10

B1 The first alternative (B1), of the concrete pontoon represents a cross section of a concrete box with a uniform wall and slab thickness. This type is used for small pontoon dimensions and light loading.

B2 Alternative (B2) shows two built integrally pontoons and provides a large pontoon width and it is used for light loading.

B3/B4 The additional wall thickness in (B3) and (B4) provides an additional longitudinal flexural stiffness as well as space for eventual post-tensioning prestressing. The behaviour of this pontoon in the longitudinal direction is a beam element when length/width (L/W) ratio is large.

B5/B6 The alternatives (B5) and (B6) represent a cross section of the pontoon, which can be considered in one or two direction of the pontoon. Those walls increase the flexural stiffness in both directions too. The behaviour of the pontoon under the loading is a two way ribbed element, which deflects in two directions. The L/W ratio plays an important role in that matter.

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|B7 The advantage of the alternative (B7) that it has an increment in the projected area which provides an increase of the water resistance (hydrostatic stiffness modulus (k)) and an increase of the added mass that increase the stability of the bridge.

B8 The keel under the section in the alternative (B8) increases the added mass and the stability of the bridge against rotational movement and lateral loading (wave forces).

B9 The FDN Company developed alternative (B9). It has two wings to increase the projected area leads to an increase of the hydrostatic stiffness (k). The lower position of the wings increases (in case of dynamic behaviour) the weight of the structure by an increment equal to the water mass above the wings, as well as an increment in the added mass in all directions. The second advantage of the low wings is an increase the draft of the pontoon, which leads to an increase of the reflected wave with respect to the transmitted wave.

B10 Alternative (B10), as it is shown, has a movable column in the transversal direction, which it is connected with a concrete or steel plate at both ends and connected with the bridge by a spring to turn it back to the first position after the movement. The column moves into a hollow concrete beam that connects the two external walls and provides a lateral bracing to them. The position of the column must be at the water level and the plate height must be equal to the significant wave height (Hs). The advantage of this alternative is to transfer the wave force from one side of the bridge to the other side to reduce the wave load on the bridge.

2.3.1.2 The pontoons layout alternatives

The concrete pontoon is generally made as a concrete box with different dimensions and wall thicknesses. The external walls must be thicker than the internal walls because they carry the water pressure. The internal walls are used to increase the flexural stiffness of the pontoon in one or two directions and to reduce the bending moments and the shear forces in the top and the bottom slabs. They also confine the leakage water.

Table (2-4) Pontoon layout and side view B11 B12

Horizontal cross section Horizontal cross section B13 B14a

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Horizontal cross section Horizontal cross section B15a B14b

Isometric Isometric B16a B15b

Horizontal cross section Horizontal cross section B16b B17a

Longitudinal side view Side view B17b B18

Longitudinal side view Longitudinal side view

B11/B12/B13/B14a

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The pontoon alternatives (B11), (B12), (B13), and (B14a) show the horizontal cross sections of different types of caissons that can be used for the pontoons of the CPFB and the SPFB.

B15/B16 The alternatives (B15a-b) and (B16a-b) are only in use for the SPFB. They are made from steel cylinders connected together at the top side by a concrete slab. Alternative (B16) allows the water to pass freely among the cylinders to reduce the current pressure and wave forces.

B17 The longitudinal side view of the pontoon has openings in the rectangular pipes that extend in the transversal direction. The openings are located at the water level. The opening dimensions depend on the design significant wave height. The system functions as a wave energy absorber. It reduces the sea wave pressure on the external wall of the pontoon and as a result, it mitigates the lateral wave load on the total bridge.

B18 The alternative (B18) is taken from the design of the Mobile Offshore Base (MOB). It consists of two parallel concrete slabs connected by steel pipes. The steel pipes spread between the two slabs at different distances depending on the vertical loading and the wave properties.

2.3.1.3 Evaluation

Table (2-5) B B B B B B B B B B B B B B B B B B 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8

Constructability + + + + + + - + - - + + + + + + - - Maintainability + + + + + + + + + + + + + + + + - - High wave load ------+ - + + - + - - - + + + Heavy traffic load - - - - - + + - - - - + + + - - - - High tide variation - - + + + + + + - - + + + + + + + + High current speed ------+ - + Vertical stability (Heave) - - - - + + + - + + + + + + + - + + Rotational stability (Roll) - - - - - + + + + - - + + + - - + -

2.3.2 The access bridge

An access bridge is the link between the pier and the shore or riverbank. For efficient dock operation, the means of access must provide effective circulation and the shortest possible distance from the pier to the floating bridge. This can be achieved in several ways, depending on local conditions. The variation of the bridge elevation due to the tide or the waves could be maintained by using the access bridge. The access bridge rescues the floating bridge from undesirable internal cross sectional forces. The length is the main property of the access bridge, which is determined according to the tidal range during the variation cycle. At high tidal range, a long access bridge is required to keep it within the maximum allowable slope for the traffic.

 Design requirement

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The access bridge must be designed as an inclined simply supported beam with two hinges, loaded by its self-weight and the traffic load. It must be capable to move/rotate in the vertical and horizontal direction as well as in the longitudinal direction. When the floating bridge lowers due to the tide, the access bridge must be elongated to keep the two ends of the floating bridge in the same vertical lines. This implies that an additional length is required. This problem can be solved by using a slide joint, which it will be illustrated later.

2.3.2.1 The access bridge alternatives

Table (2-6) the access bridge alternatives E1 E2

E3

E1 The access bridge (E1) has been used in the Hood Canal Bridge. The approach is extended to a distance where the seabed is shallow.

E2 The alternative (E2) has been used in some floating bridges where the elevation difference between the abutment and the water level is very high so that the suitable traffic slope required a very long access bridge. In this case, an elevated bridge deck for a distance can eliminate the length.

E3 The alternative (E3) is used when the rotation at the bridge end should be restricted.

2.3.2.2 Access bridge length

The connections of the access bridge should be complied with the vertical movement of the floating bridge due to the tide. The construction of sliding - or expansion joint at the abutment

TU Delft 46 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge is necessary to compensate for the variation of distance between the two connection points. Both joints are hinges in order to be able to rotate in the ZX- plane.

Figure (2-2) access bridge details The connections of the access bridge are not stiff enough to restrict the horizontal displacement of the floating bridge in the Y– direction (swaying). Therefore, dolphin – frame guide or sliding piles should be constructed at both bridge ends and sides to restrict the swaying motion.

Figure (2-3) the sliding joint (B) Figure (2-4) the hinge joint (A)

The access bridge length is designed according to the maximum elevation difference between the abutment and the bridge such that the slope does not exceed %15. The access bridge length can be calculated as follows:

LAccessbridge= (XAbutmentspacing + the maximum expected response at the end)/the maximum slope

As mentioned before, the access bridge should be hinged at the abutment while an expansion joint has to be used at the floating bridge to introduce the length difference (∆x) between the access bridge and the distance between the two connection points during the tide. That difference (∆x) can be determined as eq. (2-1), see figure (2-5):

2 2 x  LAccessbridge  habutment( flow)  X Abutmentspacing (2-1)

Where: LAccessbridge = the access bridge length.

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XAbutmentspacing = the spacing between the abutment and the floating bridge. habutment (flow) = the elevation difference between the abutment and the bridge at flow case.

Figure (2-5) the access bridge motion

An additional argument to place the expansion joint on the floating bridge is to enable the pontoon to rotate freely in the XY-plane. Moreover, it is not necessary to make the access bridge a stiff structure in the XY-plane to prevent these rotations to occur. 2.3.3 Pontoon connector

The pontoons on the water can be connected in several different ways according to the bridge design and functionality method. The connection can be rigid or flexible at one or two contact points.

2.3.3.1 The pontoon connector alternatives

Table (2-7) different alternatives of pontoon connectors illustrated in longitudinal section of the pontoon C1 C2

C3 C4

C5 C6

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C7 C8

C9 C10

C1 The alternative (C1) is a connection developed by the Canady Company (IFM) [ref.31]. It allows the horizontal movement in both directions by means of the pieces of rubber, which are present at three positions. The first one is confined between the elements and the other two are at the two ends of the steel bar and screw. This system provides the effect of a spring between the concrete elements and maintains free space between them.

C2 When the rolling motion of the pontoons is partially allowable, the alternative (C2) provides this possibility. The pontoons are connected at the upper edge using pivots and rubber rings in-betweens. This system provides a simple and economic connection method because of the lack of need for intervention by divers in the erection process. C3 When the rotational spacing between the pontoons is required to be moderate, the alternative (C3) provides the solution. It represents a series of three springs that maximize the total displacement. It is important to mention that the spring stiffness at the two ends is equal to summation of the two different parts, eq. (2-2), namely the stiffness of confined and unconfined rubber: 1 N 1   (2-2) k e i  1 k i

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1 1 1   kequivalent kconfinedrubber kunconfinedrubber

C4 This connection is the modified of the already used in the Hood Cannel Floating Bridge figure (1-7). The prestressing cable is used to connect the pontoons. A satisfactory rigid base has to be provided for the prestressing cables, which are distributed along the upper and the lower edges of the pontoons. A steel frame are fixed on both faces of the pontoons with a rubber layer in between and connected by a hard steel ball joint to allow the pontoon to rotate in both directions. The maximum allowable motion is confined by the steel edge as shown.

C5 An alternative (C5) is used to connect two pontoons with small depth and small relative rotation. It is similar to alternative (C7) but the connection is at two points of the depth. The stiffness of this alternative is small and larger than (C7).

C6 The alternative (C6) is made to connect two pontoons with a relatively high depth. The pontoon walls have to extend along the pontoon length with a half circle shape from one side and a wall thickening from the other side. The circle diameter equals to the clear height between the top and bottom slabs. Each pontoon will extend a half circle into the next one and exactly beside each other to form a whole circle contact area, figure (2-6). The first connection point is the steel pin at the center of the circle. The edge of the circular shape should be coated with a steel plate or elastic interface material to protect the concrete to be crushed during the rotation. The wall thickening at the connection zone has to be designed to provide spacing for the prestressing cables which are responsible for the stiffness of the connection. Those cables must be symmetrical in numbers and positions about the rotation center. The connector stiffness (Kconnector) is equal to (see chapter 4 for more details):

Kconnector = ΔM / θ (2-3) ΔM = ∑ [(Fi +ΔFi)* di - (Fi-ΔFi)*di]

Figure (2-6)

C7 The connection (7) is developed by FDN Company to connect wave breakers at one point of the depth, figure (2-7). This method does not provide moment transformation between the pontoons. It is made from steel ring coated by a high stiff rubber. These elements are placed between the pontoons and connected by steel cables. The concrete is not protected against crushing. It has the same technique of alternative (C2).

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Figure (2-7) FDN Company pontoon connector [ref.34]

C8 The alternative (C8) has the same principle of the alternative (C5) except that the rubber part is confined in two steel cylinders to protect it from the environmental effects and to optimize the compressive strength of the rubber by enforcing it to deform in only one direction. Another advantage of this system is that the maximum allowable displacement of the spring can be restricted by the length difference between the rubber and the steel case.

C9 The connector (C9) looks like the alternative (C10). The main difference is the position of the hinge (pivot). It can be applied when the pontoon connector should transform a large moment so that the large distance between the two points reduces the applied force on the pivot and the cables.

C10 The connector (C10) is used when the pontoons of the bridge have to be separated and closed from all sides. The pivot that is fixed at the water level makes the first connection. The prestressing cables make the second point connection. These cables take the shape of a non- closed circle. Each end of the cable is anchored at one pontoon so that when the pontoons try to rotate and the walls try to approach each other, the prestressing cable will prevent that. The two circles in figure of (C10) represent two pulleys, which assist cable elongation. Another straight-line cable is anchored at the same place to prevent the rotation of the pontoon in the opposite direction.

2.3.3.2 Evaluation of the connectors

Table (2-8) evaluation of the connectors C C C C C C C C C C 1 2 3 4 5 6 7 8 9 1 0

Constructability + + + + + - + + - - Maintainability + + + + + + + + - + High wave load - - - - - + - - + + Heavy traffic load - - - - - + - - - - High tide variation - - + + + + - + - - High current speed ------Vertical stability (Heave) - - - - + + - - + + Rotational stability (Roll) - - - - - + - + + -

2.3.3.3 Pontoon connector moment

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The moment at the connector (Mc) is created from the difference in the rotation of two adjacent pontoons (ϕi+1- ϕi) multiplied by the connector stiffness (Kt).

Mci = Kt*(ϕi+1- ϕi)

2.3.4 Mooring system

The mooring system must be well designed as should ensure that the floating bridge is kept in position so that the facilities installed on the floating bridge can be reliably operated and to prevent the structure from drifting away under critical sea conditions and storms. A freely drifting floating structure may lead to not only damage to the surrounding facilities but also to the loss of human life if it collides with ships. Note that there are a number of mooring systems such as:

1. The dolphin-guide frame system. 2. Mooring by cable / chain and anchor. 3. Tension leg method. 4. Pier/quay wall method. 5. Mooring by sliding piles.

The design procedure for a mooring system may take the following steps: we first select the mooring method, the shock absorbing material, the quantity, and layout of devices to meet the environmental conditions and the operating conditions and requirements. The layout of the mooring dolphins for example is such that the horizontal displacement of the floating bridge is adequately controlled and the mooring forces are appropriately distributed. The behaviour of the floating bridge under various loading conditions is examined. The layout and quantity of the devices are adjusted so that the displacement of the floating bridge and the mooring forces do not exceed the allowable values. Finally, devices such as dolphins and guide frames are designed by applying the design load based on the calculated mooring forces. The materials for the mooring system shall be selected according to the purpose, environment, durability, and economy.

The Chain/Cable method mooring system consists of two parts: the mooring lines and the anchors. The mooring line is a catenary. The lines themselves could be made up of chains, wires, high technology fibre ropes or a combination. The mooring lines are terminated at the seabed using anchors or piles; such a mooring system is often referred to as a single point mooring (SPM).

The Chain/Cable method mooring systems can generally be divided into the following systems:

Single point mooring (SPM): Vessels are secured by a single line or structure. The floating object is allowed to weather vane; that is, swing around in order to align itself with prevailing wind, wave, and current conditions. This alignment tends to reduce the load on the mooring system. However, the mooring forces enter the structure at one point, which will have to endure a very large force. An SPM requires a lot of space and as such, is mostly preferred at an offshore location.

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Multi-buoy moorings (MBM) or Spread moorings: An MBM holds a vessel in a relatively fixed position and the vessel cannot turn head into the prevailing waves. As a result, an MBM can experience relatively high loads if wind, currents, or waves act at an angle to the mooring. The floating body cannot move and rotate freely, but the mooring forces are distributed better over the structure. Smaller forces are easier to introduce into a structure.

Dynamic Positioning System (DPS): Next to a mooring system a Dynamic Positioning System could be employed, mainly to relieve the structure of some of the loads by turning it head into the waves. This system would only be effective when the structure can rotate freely, such as when located offshore. A fixed location near the shore would not permit such movements; therefore, a DPS will be useless. Mooring system components include anchors, sinkers, anchor chains, buoys, and mooring lines. The type of mooring to be used depends on the location, the water depth, the type of structure, current, wave loads, and other influencing factors.

2.3.4.1 Mooring system alternatives

The floating bridge has to be kept in position so that the facilities installed on the floating structure can be reliably operated and to prevent the structure from drifting away under critical sea conditions and storms. The cable/anchor mooring system consists of two main parts: the mooring line and the anchor. Different alternatives are described below in table (2-9):

Table (2-9) Mooring system alternatives D1 D2

D3 D4

D5 D6

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D7 D8

Sliding piles D9 D10

D11 D12

D13 D14

D1

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The Dolphin-frame guide method represents a truss construction fixed on a foundation in the seabed. The rectangular shape of the cross section provides a sufficient stiffness against the lateral loads. This method is used when the floating structure requires minimum transverse movements at both sides [see ref.24].

D2 The Pier /Quay wall method, this method is used to restrict the transverse movement of the bridge against the high current speed. The water current applies a lateral force from one side.

D3 The Chain /Cable method is the most used method to restrict the floating structures and it can be connected in different ways as shown in the alternatives (D7) and (D14).

D4 The Tension Leg method is used when the floating structure is to be allowed to move transversally at large scale so that applying of the alternatives (D3), (D7), or (D14) cause undesirable forces on the floating structure.

D5 The Overhead Anchor Cable Systems shares features with conventional suspended trail bridges. A cable anchored on both shorelines is run over towers. The towers provide elevation. The elevated anchor cable runs parallel to the floating bridge and is upstream of it. Additional cables (called bridle lines) run from the anchor cable to attachment points on the floating bridge. The overhead cable system helps to keep the bridge in position but does not provide lift. D6 The transverse supporting of the pontoon can be hiding and fixed at the centre line of the bridge. This method provides the required lateral supporting but it is unsuitable for high tide variation sea and it requires an exceptional construction method.

D7 The Submerged Anchor Cable Systems represents the connection of the pontoon with the seabed in a crossing manner. This method converts the horizontal force of the mooring line from tension to compression.

D8 Piles work as many different types of anchors. They can be substitutes for submerged anchors. Drive piles close to the floating bridge, and then hook the bridge to the pile for anchorage. Pile holders can be used to attach the bridge to the piles. External pile holders typically are a hoop or square that surrounds the pile with a solid bracket attached to the edge of the frame. Square holders usually have bearings to reduce wear. A simple chain also will work, but the chain may increase wear on the pile. Internal pile holders are also available for piles that are placed inside the perimeter of the bridge. A pile system will reduce twisting forces on the shore connections and on the connections between sections of the floating structure. Piles are an excellent means of support for structures in areas where water levels fluctuate because they allow vertical movement while still providing anchorage. Their shortcoming is that they restrict horizontal movement. This may result in sections close to shore becoming grounded during periods of low water. The structure may be isolated during high water, making it inaccessible. These issues can be addressed by designing the shore access to accommodate changing water levels.

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D9 Soft soil anchors: so-called types (A) anchors are designed for placement in deep water and very soft soil. They are constructed of reinforced concrete fitted with pipes for water jetting. The anchors weigh from 60 to 80 tons each. They are lowered to the bottom of the lake and the water jets are turned on allowing the anchor to sink into the soft lake bottom to embed the anchors fully. Anchor capacity is developed through passive soil pressure.

D10 Pile anchors: so-called type (B) anchors are pile anchors designed for use in hard bottom and in water depth less than 27m. The type (B) anchor consists of two steel H-piles driven in tandem to a specified depth. The piles are tied together to increase the capacity.

D11 Caisson gravity anchor: so-called type (C) anchors are gravity type anchors, constructed of reinforced concrete in the shape of a box with an open top. They are designed for displacement in deep water where the soil is too hard for jetting. The boxes are lowered into position and then filled with gravel to the specified weight.

D12 Multi-slab gravity anchor: so-called type (D) anchors are also gravity type anchors like the type (C) anchors. They consist of solid reinforced concrete slabs, each weighing about 270 tons. They are design for displacement in shallow and deep water where the soil is too hard for the water jetting. The first slab is lowered into position and then followed by subsequent slabs. The number of slabs is determined by the anchor capacity required. Type (D) anchors are the choice over type (B) and type (C) anchors, because of the simplicity in design, ease in casting, and speed in placement.

D13 The suction pile anchor is made from a steel casing closed from one side lowered into the water driven in the seabed by using the water suction force; therefore, this anchor is only suitable for the soft soil seabed. The required anchoring force determines the pile length. The construction method is also suitable for deep water. D14 The alternative (D14) is the more effective and reliable mooring system. The applying of double cables at each side increases the resisting to the wave load.

2.3.4.2 Evaluation of the mooring system alternatives

Table (2-10) Mooring lines Anchors D D D D The mooring system D D D D D D D D D 1 1 1 1 1 2 3 4 5 6 7 8 9 0 1 2 3

Deep water - - + + + - + - + - + + + High wave load - - + + - - + + High tide variation - - + + - - + - High current speed + + + + + - + + Vertical stability (Heave) + + + + Rotational stability (Roll) + - + +

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Hard seabed soil + + + + - + - - + + - Soft seabed soil - - + + + - + + - - + Min. transverse movement + + - - - + + + Reasonable transverse movement - - + + + - + - Min. vertical displacement - - - - + + + +

 Connection methods of cable/chain mooring system

The cable/chain and anchor mooring method is used to connect floating structures to the seabed by using steel chains or steel ropes with a synthetic jacket to protect them from the sea environment. They can be made in different connecting manners such as the parallel line connecting (D3), the crossing line connecting (D7), and the combined connecting method (D14). The disadvantage of the first method is applying a tension force on the pontoon base while the second method applies a compression force. With regard to the stability of the structure during the wave excitation, the first method provides moment reduction against the wave forces while the second method amplifies the wave effects by increasing the rotational moment round the longitudinal axis.

 The shock absorber

In some of the existing floating bridges, a new system is applied in the mooring lines at the anchor connection. This system is called “Sealink elastomer” which has a damping function to reduce the effect of the wave force during the storm.

Sealink elastomer

Figure (2-8) Sealink elastomer [ref.30]

2.3.5 Navigational opening alternatives

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Although floating bridges cross an obstacle, it also creates an obstacle for marine traffic. Navigational openings must be provided for the passage of boats, smaller watercrafts, and large vessels. These openings may be provided at the end of the bridge. Movable spans may need to be provided for the passage of large vessels. The width of the opening that must be provided depends on the size and the type of vessels navigating through the opening.

2.3.5.1 The navigational opening alternatives

Table (2-11) the navigational opening alternatives F1 F2

F3 F4

F5

F1 The alternative (F1) represents a navigation opening for a floating bridge applied for shallow water. The piles to keep the bascule bridge at the same place and stable support both ends of the fixed parts of the floating bridge at the opening. Furthermore, the piles prevent them from fluctuated motion caused by the sea waves. A Bascule Bridge consisting of two leaves normally should be pointed toward each other and linked together at their ends where they join over the navigation opening. A Bascule Bridge is operated by a hydraulic machinery system.

F2 Part of the floating bridge can be converted to a curve tunnel submerge, as shown in table (2- 11) alternative (F2), to a suitable depth so that can comply with the marine vessel size. This type is suitable for deep water.

F3

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The alternative (F3) is normally used in the deep water. It looks like the alternative (F1) with a compensation of the pile system by a drop pontoon to ensure the continuity of the floating bridge. The lowering distance and the opening width are determined by the size of the marine vessels. A hydraulic machinery system is required. The movable part can be supported by a light structure with its base on the drop pontoon.

F4 [ref.3] The alternative (F4) is called “Draw pontoon movable span”. In the draw type movable span, the draw pontoon retracts into a “lagoon” formed by flanking pontoons. It is suitable for deep water. A hydraulic system is required.

F5 [ref.3] In the lift /draw, type of movable span, part of the roadway will be raised for the draw pontoons to retract underneath it. As far as traffic safety and flow are concerned, the lift /draw type movable span is superior over the draw type. Traffic moves efficiently on a straight alignment with no curves to contend with. Movable spans may be operated mechanically or hydraulically.

2.3.5.2 Evaluation of the navigational opening alternatives

Table (2-12) navigational opening alternatives The requirements F F F F F 2 3 4 5 1

Constructability + - + + - Maintainability + + + + + Marine traffic discharge - + - + + Efficiency + + + + - Heavy traffic load - + + - - High tide variation - + + + + High current speed + + + - - Vertical stability (Heave) + - + - + Rotational stability (Roll) + - + + + The cost - - + + - Deep water - + + + + Shallow water + - + + + Operation energy + * + + - Operating duration + + + - -

2.3.5.3 Location and dimensions of the navigational opening

A floating bridge creates an obstruction to marine traffic. Movable spans may need to be provided for the passage of large vessels. The width of the opening that must be provided depends on the size, the type, and the discharge of vessels navigating through the opening. The location of the navigational opening is related to the seabed profile under the bridge.

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There is a minimum water depth for every vessel size. Furthermore, there are minimum dimensions for each type of the navigational openings. It can be determining the location of the navigational opening with respect to the seabed profile.

2.3.6 Additional members

It is important to focus on other additional structural elements. Beside the mentioned elements of the floating bridge, there are some important additional elements such as the abutment, stability pontoon and wave breaker. 2.3.6.1 Abutment

The two ends of the floating bridge, as for all bridges, should be supported by the abutments. The location of the abutment is determined according to the site configuration. When the sea beach is shallow for a distance, the abutment should be constructed inside the sea.

2.3.6.2 Stability pontoon

The floating bridge is a slender structure excited by the sea wave. Both ends of the bridge are considered to be free. This amplifies the bridge response to the sea wave. The stability pontoons are fixed at both ends of the bridge to reduce the response due to its weight and damping effect, figure (2-9). Figure (2-9) Access bridge details.

2.3.6.3 The wave breaker

A general rule of thumb is to have a breakwater if the significant wave height larger than 4m [Ref.24]. The wave breaker is necessary to mitigate the wave loads on the bridge, figure (2-10). Figure (2-10) Wave breaker 2.4 Creation of different bridge alternatives

The creation of different bridge alternatives requires studying the situations at the actual site. These alternatives are made to be complying with environmental conditions, the site situations, and the functional properties of the required bridge. Most of these alternatives are combined from different alternatives of the structural elements of the floating bridge. The combinations are not arbitrary; they are based on the technical requirements. Some of the elements are applied in more than one situation. Table (2-13) describes the applied structural elements for each bridge alternative.

The bridge The pontoon The connector The mooring system alternative Bridge

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alternative alternative alternative Mooring element Anchor layout The alternative no. 1 B16 C4 D7 D11 A1 The alternative no. 2 B20+B3 C11/C12 D3 D13 A1 The alternative no. 3 B19+B2 C9/C10 D8 - A1 The alternative no. 4 B9+B6 C3 D14 D10 A1 The alternative no. 5 B16 C6 D1 - A8 The alternative no. 6 B17 C4 D14 D9 A13 Table (2-13)

2.4.1 The alternative no. 1

Continuous pontoon floating bridge, in figure (2-11), consist of concrete caissons compartmented in two direction type (B16) and connected end-to-end by the connector (C4) which represents a connecting of two concrete pontoons by a prestressing cables and isolated by a rubber fender. The mooring system is a combination of cruising mooring line (D7) and anchor type (D11).

Figure (2-11) the alternative no.1 of CPFB

The floating bridge alternative no.1 is combined to be reliable for the following situation:

 Deepwater sea: the water depth determines the type of the mooring system; whether it mooring line and anchor or sliding piles. When it is not possible to construct the sliding piles due to the large water depth or the seabed soil weakness or high water wave forces that act on the bridge, it become necessary to use the line /anchor mooring system not only for its constructability but also for its flexibility to absorb the sea wave energy.  Moderate wave height: the wave height determines not only the freeboard of the pontoon but also the type of the connector. The connector (C4) is a very rigid connector and has a limited flexibility. For the heavy waves, it is recommended to use

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more flexible connector to maintain the wave energy absorption and internal forces reduction.  Hard seabed soil: the gravity anchor is always used for the hard soil when pile driving is costly or not possible due to the water depth or soil rigidity.  High hydrostatic pressure: the compartmented concrete caisson in two direction increases the local and global bridge stiffness.

2.4.2 The alternative no. 2

Figure (2-12) the alternative no.2 of CPFB

The Mobile Offshore Base (MOB) which are typical VLFS projects that have been investigated in detail and that are aimed to be realized in the near future, are introduced to be one of the floating bridge alternatives. This type is characterized by resistance to the sea waves. It can be very sensitive to the traffic load or any other vertical load because of reduction in the projected area that is represented by the cross section area of all columns that is less than the projected area of the pontoon. For the reason of large expected response, it should be combined with flexible pontoon connector and compliant mooring system.

This alternative, figure (2-12) is suitable for deep water with a high expected sea wave height. The applying of the suction pile anchor (D13) is practical for deep soft soil seabed.

2.4.3 The alternative no. 3

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Pontoon cross section Pontoon side view

Figure (2-13) the alternative no.3 of CPFB

The alternative nr.3 is a continuous pontoon floating bridge supported laterally by the sliding piles and consists of concrete pontoons that have transversal openings at the water surface level to reduce the wave load on the piles. The pontoons are connected by a hinge with a special technique spring to reduce the rotation. This connection method is constructible and reliable. The system is ideal for shallow waters and moderate wind/wave loads.

2.4.4 The alternative no. 4

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Figure (2-14) the alternative no.4 of CPFB

The alternative no.4 of CPFB, figure (2-14), is a continuous pontoon bridge. The bridge consists of concrete pontoons connected by rigid bars with adjustable confined rubber to control the pontoons rotation. The pontoons have lowered wings to increase the added water mass in both directions, to reduce the up-life force and to increase the water spring modulus. The bridge is suitable for deep water, stable against high wind wave loads and heavy traffic loads. The anchors are typical to the sand soil seabed.

2.4.5 The alternative no. 5

Figure (2-15) the alternative no.5 of SPFB

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The bridge alternative nr.5 is a separated pontoon bridge consisting of concrete girders and pontoons connected by a free hinge. The girders are connected end-to-end by a highly flexible connector with adjustable rotational stiffness. The pontoons are moored by Dolphin-Frame guide Method that provides a limited lateral displacement and free vertical displacement. The bridge can be constructed in shallow water and operated safely in a high wind-wave load region.

2.4.6 The alternative no. 6

Figure (2-16) the alternative no.6 of SPFB

The alternative no.6 in figure (2-16) is ideal to cross deep water because of using the cable mooring system with anchor type (A) which is suitable for the soft soil. The bridge is a SPFB, which cannot be affected by the water current and /or the wind –wave load. Its arch form modifies the global stability of the bridge because the arch-form can enlarge the supporting base of the bridge. In this structural combination, there is no need to use a highly flexible connector between the girders. A protected steel pipe pontoon can be used for two reasons: relatively light weight and the possibility to construct spacing between them to allow more water current to flow easily.

Table (2-14) shows the evaluation of all alternatives with respect to the site situations.

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Table (2-14) Separated Continuous pontoon bridge pontoon bridge 1 2 3 4 5 6

...... o o o o o o n n n n n n

The site situation e e e e e e v v v v v v i i i i i i t t t t t t a a a a a a n n n n n n r r r r r r e e e e e e t t t t t t l l l l l l a a a a a a Deep water + + - + - + High wave load - + + + + + Heavy traffic load + - + + + + High tide variation + + + + - + High current speed - + + - + + Min. transverse movement + - + + + + Reasonable transverse movement + + - + - - Min. vertical displacement + - + + - + Reasonable vertical displacement - + + + + - Hard seabed soil + - + - - - Soft seabed soil - + + + + +

2.5 Mechanical modelling of the floating bridge

The modeling of Floating bridge motion: [Ref. 9]

 A beam on elastic foundation (Static response)

Continuous floating bridges essentially act as beams on elastic foundations in both the vertical and transverse directions. In the vertical direction, buoyancy provides the linear modulus of the vertical support, while the discrete mooring cables provide the nonlinear horizontal support for the bridge under transverse loading. [The design of a floating bridge for traffic is straightforward and typical beam-on-elastic-foundation methods can be used]. However, the stochastic structural loading generated by wind and wave action and the corresponding dynamic response of the floating bridge to this loading presents a very complicated system to be understood. The design of a floating bridge for the environmental loading becomes much more difficult than for traffic loading. Despite the complications, understanding must be achieved if an efficient and safe design for a floating bridge is to be obtained. The eq. (2-4) represents the equation of motion:

d 4w EI  k  w  q (2-4) dx4 d 1

This equation can be used to determine the bridge response under the traffic load and the static response of the bridge under the longitudinal sea wave.

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 A beam on the Viscous -Elastic Kelvin Foundation (Dynamic response)

The buoyancy forces that support the continuous floating bridge behave exactly as a saturated soil within the linearity. We can summarize the following differences:

 The water is infinitely linear while this is limited the soil.  The water has a damping effect while the soil is only when it fully saturated.

The adding of the inertia term of the beam and the damping effect of the foundation to the equation of motion will modify the result response to approach the reality as it written in eq. (2-5):

2w 2  2w w A  EI  k wc   q (2-5) 2 2  2  d d 1 t x  x  t

Where: ρ = the beam mass per unit area. A = beam cross sectional area. EI = beam flexure stiffness. kd = foundation stiffness modulus. cd = foundation damping coefficient. q1 = applied load

 Beam under dynamic torsion (m):

The torsion moment can be applied on the bridge as a result of the lateral incident waves. The wave pressure concentrated at the water level that is usually not the gravity centre level of the bridge element. This eccentric load will lead to the Loading combination. The bridge rotation can be described in eq. (2-6):

 2     J  GJ t   m (2-6) t 2 x  x 

Where: ρ = mass density of beam material. J = polar moment of inertia = Ixx+ Iyy. Jt = torque constant. G = Shear modulus. a = the major dimension. b = the minor dimension.

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For a flat rectangular shape:

3 Jt = k1*a*b k1 = coefficient depends on (a/b) ratio which can determined from the table (2-15) by interpolation method.

Table (2-15) torsion constant [ref.33] a/b 1 1.4 1.8 2 3 4 6 10 ∞ k1 0.141 0.187 0.217 0.229 0.263 0.281 0.299 0.313 0.333

2.6 Construction method

Concrete pontoons are generally used for building major floating bridges. The fabrication and construction of the concrete pontoons must follow the best practices in structural and marine engineering in concrete design, fabrication, and construction with added emphasis on high- quality concrete and water tightness. Quality control should be the responsibility of the fabricators/contractors. Final quality assurance and acceptance should be the responsibility of the owners.

In addition to these traditional divisions of responsibilities, the construction of a floating bridge necessitates a strong partnership arrangement to work together, contracting agencies and contractors to provide full cooperation and joint training, share knowledge and expertise share responsibility and to help each other succeed in building a quality floating bridge. The contractors should have experience in marine construction and engage the services of naval architects or marine engineers to develop plans for monitoring construction activities and identifying flood risks, and prepare contingency plans for mitigating the risks.

Knowledge is power and safety. The construction personnel including inspectors from the contractors should be trained on the background of the contract requirements and the actions necessary to implement the requirements fully. Their understanding and commitment are necessary for complete and full compliance with contract requirements and that bear on personal and bridge safety.

Construction of a floating bridge is well established. Many concrete floating bridges have been built successfully using cast-in-situ, precast or combinations of cast-in-situ and precast methods. Construction techniques are well developed and reported in the literature. Owners of floating bridges have construction specifications and other documents and guidelines for the design and construction of such structures.

Floating bridges may be constructed in the dry in graving docks or on slipways built specifically for the purpose. However, construction on a slipway requires extensive preparation, design, and caution. The geometry and strength of the slipway must be consistent with the demand of the construction and launching requirements. Construction in a graving dock utilizes techniques commonly used in land base structures. Major floating bridges around the world have been constructed in graving docks. Because of the size of a floating

TU Delft 68 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge bridge, the bridge is generally built in segments or pontoons compatible with the graving dock dimensions and draft restrictions. The segments or pontoons are floated and towed to an outfitting dock where they are joined and completed in larger sections before towing to the bridge site where the final assembly is made as shown in figure (2-17).

The fabrication site flooded To bridge site the pontoons towing In onshore site: pontoons fabrication

• Anchored to the seabed • Abutment construction

Pontoons mating (prestressing cables)

Figure (2-17) Construction procedure [ref.31]

It is important to explore the availability of construction facilities and decide on a feasible facility for the project. These actions should carried out prior to or concurrent with the design of a floating bridge to optimize the design and economy. Some key data that may be collected at the time are:

 Length, width and draft restrictions of the graving dock.  Draft and width restrictions of the waterways leading to the bridge site.  Wind, wave, and current conditions during tow to and installation the top site.

2.6.1 The continuous pontoon floating bridge

The construction procedure of the continuous pontoon floating bridge contains the following three steps that start simultaneously:

 The execution of the abutment at both sides  The fixation of the anchors along both sides of the bridge.  The fabrication of the concrete pontoon in the onshore site

The execution of the abutment

The position of the abutment is selected according to the site configuration, the approaches elevation with respect to the water level and the water depth nearby the coach. The shallow part of the sea should be neglected to avoid any contact of the bridge with the seabed in all

TU Delft 69 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge cases. These cases involve the dynamic response of the bridge due to wind- wave loads as well as the tidal range during the day and the submerged depth of the pontoon.

All those distances should be taken into account in the selection of the abutment position. The position of the first pontoon of the continuous floating bridge is selected at a distance from the abutment position. This distance represents the length of the access bridge, which is determined by the tidal variation range during the day. This implies that the access bridge length is directly proportional to the tidal range to maintain a reasonable slope.

The fixation of the anchors along both sides of the bridge

The mooring system for the floating bridge is necessary not only to keep the bridge in the same place but also to introduce the wind-wave forces and to prevent the drifting up of the structure. The mooring system force depends on several factors as follows:

1. The type of the mooring line (cable or chain). 2. The material density of the mooring line. 3. The diameter of the mooring line that determines its weight. 4. The water depth affects the line length, for variable depth, we get variable mooring forces. 5. The anchor position: the large distance between the bridge and the anchor leads to large applied horizontal force.

The required forces that will introduce the wind-wave forces determine the number of anchors and the distances between the anchors. Those distances are not necessarily uniform as the seabed is flat, but it is recommended that they are symmetrical along the bridge to ensure the horizontal equilibrium and the symmetrical response of the entire structure.

The anchor types:

The seabed soil condition varies in different types and this variation determines the anchor types as well as the water depth. In some places where the sea depth is very high, it is difficult to execute conventional anchors like driven piles.

In section 2.3.4.1, several types of anchors are shown. Type A is suitable for the soft soil and type B is used for moderate soil and acceptable water depth. For the rock soil or other hard soil or very deep water, the types C and D are suitable.

The fabrication of the concrete pontoon in the onshore site

The concrete pontoons are constructed as caissons. The caissons are fabricated in closed ports nearby the bridge site. The prefabricating operation of the caissons starts with the concrete preparation. The operation sequence is as follows: A mixer prepares the concrete batch that is then poured into a hopper that feeds a concrete pump. The concrete is then pumped to a delivery pipe that is installed above the working deck. The concrete pouring involves the mixing, transporting, pumping, and vibrating the required concrete. The pouring procedure divides into three phases of the caisson structural elements:

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1. Bottom slab pouring 2. The external and internal walls pouring. 3. Top slab pouring.

Each caisson is built in an ascending sequence starting with the slab. The slab reinforcement cage is assembled in an auxiliary platform, then the cage is moved to the work dock and the slab is poured as a monolithic element. Due to the stiffness requirements of the pontoon, whether the longitudinal or the transversal stiffness, these three elements have to be built integrally with each other, for that reason the precast elements is not recommended.

After the slab is ready, the construction of the upper part of the caissons begins, ascending in increments of one meter using the sliding form. Each of these increments includes placing the reinforcement, sliding the forms, and pouring and vibrating the concrete. This sequence is repeated until the total height of the caisson is reached.

The top slab can be constructed in two manners: using thin precast concrete plates as a form. They are laid on the walls and supported from blow. The reinforcement cage is assembled on it and then the slab is poured as a monolithic element. The second method is by using the conventional form.

The prestressing and injection process starts when the concrete reaches the suitable maturity. The ports floor level has to be lower than the sea water level to makes the floating process of the caisson in the last phase possible. The bottom slab should be fabricated on a flat isolated floor to ensure floating operation by streaming the seawater. The port has to be open to tow the pontoon to the assembling site. The protection requirements, maintenance, operation, and connection facilities should be made during the fabrication procedure.

The bridge assembling procedure:

The first pontoon, which is named as a stability pontoon, has always special damping requirements such as the large width, additional mooring cables or additional weight because it is considered as free end of very long floating structure exited by wind-wave dynamic loads. Furthermore, it carries a part of the access bridge weight.

The first pontoon tows to the position, then connects firstly to the access bridge, and then connects to the seabed by the mooring cables. After that the second pontoon tows to the position firstly has to be connected to the first pontoon and then to the seabed by the mooring lines. This repetitive process goes on in the same manner and has to be starts from both ends of the bridge.

2.7 Durability and concrete technology

2.7.1 The situation analysis

During the operational stage of the floating bridge, the pontoons will be floating at all times. The dimensions of the pontoons are large and all parts of the pontoon are casted in situ.

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The important environmental conditions can be summarized as follow:

 The pontoon is always floating in salt water of limited depth, environmental class IV of NEN 6720 Dutch code.  The water line and spray zone vary, thus the concrete surface in that area will be changing between wet and dry.  The spray zone reaches up to an average of 2 m above the water (This value varies according to the location of the bridge).  The bridge is always subjected to wind-wave loads and response motions. All these loads are dynamic loads that cause always fatigue.

The main mechanical or structural requirements are:

 The individual pontoons have a design lifetime of 100 years.  During the lifetime minimum maintenance is required, maintenance activities will have to be carried out while the bridge is floating and in operation.  All parts of the pontoon are cast at a construction site nearby the location of the bridge.

2.7.2 Durability of marine concrete structures

Marine structures mainly are exposed to salt, water, and air. This combination can cause multiple forms of degradation. Most deterioration mechanisms were found not to determine the lifespan of the structure. The most potential deterioration mechanism in concrete marine structures is chloride ingress, as was concluded from test results from several Dutch marine structures.

Expectable deterioration mechanisms are carbonation, leaching, alkali-silica reactions, freeze- thaw action, erosion, or salt crystallisation. These seemed virtually absent from the structures that have been researched. The most severe deterioration of concrete is expected around the water line and above it, in the splash zone, because the structure will be changing between wet and dries at periods. Carbonation is strongly reduced when concrete is wet for long periods of time; from the water line downwards. Differences in exposure will cause a large amount of scatter in the chloride profiles of different areas on one structure.

Most deterioration mechanisms and in this case especially carbonation and chloride ingress and the following corrosion initiation can be reduced through the choice of materials. The following aspects should be kept in mind when considering the choice of material:

 An Alkali Silica Reaction (ASR) can be suppressed for the main part by using little or no reactive aggregates.  A low water/cement ratio prevents freeze-thaw damage.  High Strength Concrete develops into a dense mature concrete with high strength. Dense concrete is less permeable and chloride ingress and carbonation may be reduced.  The carbonation depth should be reduced to less than the concrete cover on the reinforcement. Therefore, a large concrete cover in marine structures is beneficial to the lifespan.

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 The concrete cover should not crack round the reinforcement in case of heat (fire) or collision.  As blast furnace cement produces a dense concrete with small sensitivity to chlorides, the strongest possible type of concrete composition with blast furnace cement offers the best solution, which is C53/65.  C53/65 with CEM III/B, rough sand, broken stone and small fillers (fly ash or silica fume) is chosen as the best concrete composition for the pontoons.  Additives such as a plasticizer can be used to ensure mortar workability on site.

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2 Design principles

The strategy of the total design procedure involves the arrangement of the design activities into different levels. The level of the fundamental design procedure concerns the selection and creation of the floating bridge geometry and the selection of the suitable structural elements of the floating bridge, which fit in the design requirements, and the environmental circumstances of the bridge site. For instance, the choice of the mooring system should be a mooring cable/ anchor system when the water depth is larger than the distance that can be supported by a sliding pile or when the cost of a sliding pile mooring system is higher than of a mooring cable /anchor system. This step is a global view on design aspects, without intervention into the specified details that will be dealt with later at the design specification level. The design requirements of the floating bridge are very wide and depend on the site situations. Therefore, the availability of several structural element alternatives extends the design options and facilitates reaching the design target. The design requirements can be developed from the following parameters:

7. The seabed condition (soft - sand - rock). 8. The type of mooring system (slide pile - mooring cables) is according to the water depth. 9. The environmental loads determine the bridge type (continuous - separate pontoon bridge), the pontoon shape, and the connection type. 10. The traffic discharge determines the bridge width. 11. The marine traffic determines the size of the navigational opening (if required). 12. The tidal range determines the access bridge length and shape.

Different alternatives for different situations will be created and discussed for each of the mentioned parameters. That will be the base for the fundamental design level. In this chapter, we will deal with different floating bridge alternatives and structural elements alternatives and study the technical characteristics and field of application of each alternative. The combination of different structural elements, which can be complied with different situations, is made to specify the final choice.

This chapter illustrates in tables the alternatives for all structural elements of a floating bridge. Some of them are already applied in constructed floating bridges while the author collects others from literature and adds new ones. Each one has a symbol that consists of a letter to denote the structural element and a number to denote the sequence. Abbreviated description of the geometry and functionality of each alternative is mentioned with symbol reference.

The last two parts deal with a literature study on the mechanical modelling of the continuous pontoon floating bridge and the construction procedure of a floating bridge as an aspect that can determine the design procedure.

2.2 Argumentation of the choice

A floating bridge is constructed, in most cases, in impractical sites in deep water where it is impossible as too costly to construct a conventional foundation or sliding piles. The mooring cable/anchor system is a compliant system that can provide reliable supporting for an offshore structure, such as the floating bridge, which is exposed by the wind/wave loads.

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As mentioned before, floating bridges can be classified into two types: continuous- (CPFB) and separated pontoon floating bridges (SPFB). The latter type represents a continuous beam supported by series of individual floating foundations where the differential displacement between the individual pontoons as a result of the water motion, is a main loading type on the bridge. The first type (CPFB) has other structural characteristics. It represents a continuous beam supported uniformly by the water and the mooring system. The combination of more than one uniform supporting element in the structure can provide an ideal model for the slender floating structure which has exceptional stability and rigidity properties.

The (CPFB) is selected as an ideal option in most constructed floating bridges in the world which are mentioned in chapter one because of the large stability created by the continuity of flexural stiffness, the large contact area with the water which leads to a large supporting area and the uniform distribution of the mooring points.

2.3 Evaluation of floating bridge layouts

The symbols (A1-A7 & A14) represent the already used and suggested layouts of the (CPFB) while the symbols (A8-A13) show the proposed layouts of the (SPFB).

Table (2-1) floating bridge layout alternatives; left CPFB; right SPFB. A1 A8

Side view

A2 A9

Top view and side view Top view and side view A3 A10

Side view Side view A4 A11

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Side view Side view A5 A12

Side view

Side view A6 A13 Top view

A7 A14

Figuur 2 A15

Top view of two crossed floating bridge

2.3.1 The continuous pontoon floating bridge models

The (CPFB) consists of several hollow concrete boxes connected to each other at width- draft face in such a way to create the main part of the bridge body that behaves like the backbone. The width of these boxes is determined according to the traffic demand requirements and the

TU Delft 77 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge draft and length are determined according to the structural design and construction requirements. A1 The alternative (A1) is the simplest style of the continuous pontoon arrangement. This type is already used in the Hood Canal Floating Bridge as shown in the figure (1-7). This alternative is simple and easy in erection and construction. Therefore, it can be considered as the economic option. For instance, the same formwork can be used for all pontoons and the construction can be executed rapidly.

A2 The alternative (A2) represents a normal pontoon dimension with a variable width to increase the stiffness of the water spring (K). The width variability is created by connecting additional concrete wings from both sides. These wings increase the projected area of the pontoon, which increases the water pressure under the bridge during vertical motion. Therefore, it has to be braced to resist the water pressure and the effect of the dynamic amplification due to the bridge response by the sea wave excitation. The wings can be connected at different levels of draft, which will not only affect the water resistance but will increase the mass of the bridge by increasing the movable water mass, which concerns the motion (the added mass term).

A3/A4 The alternatives (A3 and A4) represent a pontoon bridge with a variable draft. This system provides a variable flexural stiffness that affects the characteristic length of the pontoon. It is used when a long pontoon is required. The connection should be located at the smallest draft. The variability of the draft can be linear as shown in (A3) or curved as shown in (A4). The water pressure under this bridge alternative is not uniform due to the variety of the draft and the maximum pressure is concentrated under the deepest part.

A5 Alternative (A5) is a large-scale arch bridge. Every strip represents a pontoon with a prismatic shape. The pontoons depth difference plays a main role in the structural behaviour of the bridge. When this difference is large enough, it may lead to a partial submergence that means that some of the pontoons are fixed above the water level. This type can therefore, provide a navigational opening.

A6 Alternative (A6) is based on the post and beam concept to connect the bridge deck with the pontoon. The method can be modified to be a double deck floating bridge if the pontoons remain partially submerged.

A7 The arch concept, alternative (A7), is another double deck floating bridge using the arch to transform the load from the deck to the pontoon. This system has a higher shear capacity, between the decks, than the post and beam concept.

A14 The tidal effects can be solved by using this alternative. The system works as follows: In the flood case, the ballast water will be taken into tanks inside the pontoon. In this way, the bridge will remain at the same level as where it is connected to land. In the ebb case, the water will be pumped out of the ballast tank to raise the bridge. This system consumes much energy but requires no access bridge (see [ref.32]).

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2.2.2 The separated pontoon floating bridge models The separated pontoon floating bridge consists of two main parts: individual pontoons and girders. The pontoons provide an elastic block foundation of the bridge, which is connected later by the girders to form the body of the bridge. The serious matter in this type of bridge is the differential vertical displacement between the pontoons, which leads to high internal forces in the girders. Flexible connections can solve the problem. The location of the connection at the midspan of the girder increases the rolling of the pontoon while the location of the connection above the pontoon keeps it stable with only the heave motion.

A8/A9 The normal simply separated pontoon bridge has pontoons and simply supported beams that connect the pontoons. It is convenient for normal light traffic. The elliptic shape of the pontoon of (A9) facilitates the water flow and reduces the lateral pressure of the water current.

A10/A11 For a heavy environmental load or for a large span, the application of an arch beam or a prismatic beam seems to be a suitable solution.

A12 For a very long bridge, a large span is required. Alternative (A12) is an exceptional solution. It consists of the very large pontoon, which can lift the total weight of a bridge unit, which consist of the pontoon and two prismatic cantilever beams built integrally with the pontoons to form one unit of the bridge. Pylons and tension cables can provide additional supports for additional length of the prismatic cantilever.

A13 The rotational stability (roll) of the separated pontoon floating bridge is very low due to the high position of the gravity centre and the relatively low position of the meta centre. The arc form of the floating bridge provides a sufficient support for the total structure. The base of the total structure can be considered as being the maximum distance between the arc and the chord. This distance determines the degree of curvature. Furthermore, the arc should be pointed to the opposite direction of the water stream.

A15 The top view of two crossed bridges: the crossing of two continuous pontoon bridges in the middle distance provides a lateral support. The efficiency of the entire geometrical shape depends on the inclination angle of the crossing leg with respect to the centre line of the crossing. The large inclination angles the large lateral support.

2.2.3 Comparison between separated- and continuous pontoon floating bridges

A floating bridge can be constructed in two types: a Continuous Pontoon Floating Bridge (CPFB) and a Separated Pontoon Floating Bridge (SPFB). The decision has to be taken according to the site situation and the functional and structural requirements. In order to reach a clear idea of these requirements, we will highlight the major differences between both types (More comparison aspects can be found in table (2-2)):

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 The CPFB requires a navigational opening while the SPFB creates no obstacle for the marine traffic when the girders have a sufficient clearance with the water surface.

 The rolling stability in the CPFB is higher than the SPFB (except the arc form) for two reasons, the first is that the foundation area of the CPFB is relatively larger than SPFB and the second is that the meta centre –gravity centre distance is larger.

 The heave stability of the CPFB is higher than of SPFB due to the large contact area with the water and the uniform mooring force distribution along the bridge. These are limited in the SPFB.

 The influence of the sea wave on the CPFB is larger than on the SPFB due to the large contact area with the water as well as the structural continuity hinders the water flow generally. In a storm case, the navigational opening is opened to release the lateral wave pressure on the bridge. In the SPFB, usually more (50-70) percentage of the water surface is open to a sea wave.

 The constructability of the CPFB is better than the SPFB. The CPFB is constructed by connecting several units with the same size. Those units are floated and towed in the sea to the bridge site and connected directly while the SPFB generally consists of two different units: the pontoons and the girders. The pontoons are towed to the site and connected by the girders, which are assembled above the pontoons. This process requires a floating crane. Therefore, the construction costs of the SPFB are higher. In some cases, it is necessary to divide the bridge in several uniform units, tow them to the site, and connect them there. Those units should be a series of structural elements (pontoon - girder - pontoon) in different numbers depending on the site possibilities. The unit has to start and end with a pontoon to avoid the using of the floating crane inside the water.

 The wind action on the CPFB is limited and directly proportional to the freeboard height. A compressive force on the side that faces the wind and a suction force on the opposite side as well as a frictional force on the bridge deck represent the wind forces on the CPFB. The influence of wind on the SPFB is very high due to the large contact area of the bridge with the wind because the girder is completely above the water and the wind acts on all sides. In addition to that, the wind speed increases with the elevation, which increases finally the wind force.

 The mooring system that is required for the pontoon of the SPFB should be relatively more intensive than for the CPFB because of the high wind force on the girders. These forces have to be taken by the pontoon mooring system. The forces of the mooring system are distributed in a limited area of the pontoon while the mooring system in the CPFB is distributed along the total bridge length.

Table (2-2) Comparison between SPFB and CPFB No. The parameter Separated Pontoon Continuous Pontoon Floating Bridge (SPFB) Floating Bridge (CPFB) 1 Navigational opening - + 2 Rolling stability - + 3 Heaving Stability + +/-

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4 Sea wave influence + - 5 Water current influence + - 6 Wind influence - + 7 Constructability - + 8 Mooring intensity + - 9 Horizontal arc form efficiency + -

2.4 The main structural elements of the floating bridge with alternatives

Figure (2-1) plan view of the floating bridge

2.4.1 The pontoon

A floating bridge consists of a series of pontoons in different sizes and shapes that are arranged in a different manner (continuous – discrete – longitudinal – transversal) to form different types of floating bridges. The pontoon can be concrete caisson, steel pipes or made of a composite material and it represents the foundation of the floating bridge. The pontoon is a flat-bottomed float used to support a structure on the water and it acts as an elastic foundation. It may be simply constructed from closed cylinders such as pipes or barrels or fabricated as boxes from metal or concrete. The tables (2-3) and (2-4) illustrate different alternatives for the pontoon shape with a functional description of each alternative. Different transversal and longitudinal sections affect the technical properties of the pontoons.

2.4.1.1 Pontoon transverse cross section alternatives

Table (2-3) the pontoons transverse cross section alternatives B1 B2

B3 B4

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B5 B6

B7 B8

B9 B10

B1 The first alternative (B1), of the concrete pontoon represents a cross section of a concrete box with a uniform wall and slab thickness. This type is used for small pontoon dimensions and light loading.

B2 Alternative (B2) shows two built integrally pontoons and provides a large pontoon width and it is used for light loading.

B3/B4 The additional wall thickness in (B3) and (B4) provides an additional longitudinal flexural stiffness as well as space for eventual post-tensioning prestressing. The behaviour of this pontoon in the longitudinal direction is a beam element when length/width (L/W) ratio is large.

B5/B6 The alternatives (B5) and (B6) represent a cross section of the pontoon, which can be considered in one or two direction of the pontoon. Those walls increase the flexural stiffness in both directions too. The behaviour of the pontoon under the loading is a two way ribbed element, which deflects in two directions. The L/W ratio plays an important role in that matter.

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|B7 The advantage of the alternative (B7) that it has an increment in the projected area which provides an increase of the water resistance (hydrostatic stiffness modulus (k)) and an increase of the added mass that increase the stability of the bridge.

B8 The keel under the section in the alternative (B8) increases the added mass and the stability of the bridge against rotational movement and lateral loading (wave forces).

B9 The FDN Company developed alternative (B9). It has two wings to increase the projected area leads to an increase of the hydrostatic stiffness (k). The lower position of the wings increases (in case of dynamic behaviour) the weight of the structure by an increment equal to the water mass above the wings, as well as an increment in the added mass in all directions. The second advantage of the low wings is an increase the draft of the pontoon, which leads to an increase of the reflected wave with respect to the transmitted wave.

B10 Alternative (B10), as it is shown, has a movable column in the transversal direction, which it is connected with a concrete or steel plate at both ends and connected with the bridge by a spring to turn it back to the first position after the movement. The column moves into a hollow concrete beam that connects the two external walls and provides a lateral bracing to them. The position of the column must be at the water level and the plate height must be equal to the significant wave height (Hs). The advantage of this alternative is to transfer the wave force from one side of the bridge to the other side to reduce the wave load on the bridge.

2.4.1.2 The pontoons layout alternatives

The concrete pontoon is generally made as a concrete box with different dimensions and wall thicknesses. The external walls must be thicker than the internal walls because they carry the water pressure. The internal walls are used to increase the flexural stiffness of the pontoon in one or two directions and to reduce the bending moments and the shear forces in the top and the bottom slabs. They also confine the leakage water.

Table (2-4) Pontoon layout and side view B11 B12

Horizontal cross section Horizontal cross section B13 B14a

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Horizontal cross section Horizontal cross section B15a B14b

Isometric Isometric B16a B15b

Horizontal cross section Horizontal cross section B16b B17a

Longitudinal side view Side view B17b B18

Longitudinal side view Longitudinal side view

B11/B12/B13/B14a

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The pontoon alternatives (B11), (B12), (B13), and (B14a) show the horizontal cross sections of different types of caissons that can be used for the pontoons of the CPFB and the SPFB.

B15/B16 The alternatives (B15a-b) and (B16a-b) are only in use for the SPFB. They are made from steel cylinders connected together at the top side by a concrete slab. Alternative (B16) allows the water to pass freely among the cylinders to reduce the current pressure and wave forces.

B17 The longitudinal side view of the pontoon has openings in the rectangular pipes that extend in the transversal direction. The openings are located at the water level. The opening dimensions depend on the design significant wave height. The system functions as a wave energy absorber. It reduces the sea wave pressure on the external wall of the pontoon and as a result, it mitigates the lateral wave load on the total bridge.

B18 The alternative (B18) is taken from the design of the Mobile Offshore Base (MOB). It consists of two parallel concrete slabs connected by steel pipes. The steel pipes spread between the two slabs at different distances depending on the vertical loading and the wave properties.

2.3.1.3 Evaluation

Table (2-5) B B B B B B B B B B B B B B B B B B 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8

Constructability + + + + + + - + - - + + + + + + - - Maintainability + + + + + + + + + + + + + + + + - - High wave load ------+ - + + - + - - - + + + Heavy traffic load - - - - - + + - - - - + + + - - - - High tide variation - - + + + + + + - - + + + + + + + + High current speed ------+ - + Vertical stability (Heave) - - - - + + + - + + + + + + + - + + Rotational stability (Roll) - - - - - + + + + - - + + + - - + -

2.3.2 The access bridge

An access bridge is the link between the pier and the shore or riverbank. For efficient dock operation, the means of access must provide effective circulation and the shortest possible distance from the pier to the floating bridge. This can be achieved in several ways, depending on local conditions. The variation of the bridge elevation due to the tide or the waves could be maintained by using the access bridge. The access bridge rescues the floating bridge from undesirable internal cross sectional forces. The length is the main property of the access bridge, which is determined according to the tidal range during the variation cycle. At high tidal range, a long access bridge is required to keep it within the maximum allowable slope for the traffic.

 Design requirement

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The access bridge must be designed as an inclined simply supported beam with two hinges, loaded by its self-weight and the traffic load. It must be capable to move/rotate in the vertical and horizontal direction as well as in the longitudinal direction. When the floating bridge lowers due to the tide, the access bridge must be elongated to keep the two ends of the floating bridge in the same vertical lines. This implies that an additional length is required. This problem can be solved by using a slide joint, which it will be illustrated later.

2.3.2.2 The access bridge alternatives

Table (2-6) the access bridge alternatives E1 E2

E3

E1 The access bridge (E1) has been used in the Hood Canal Bridge. The approach is extended to a distance where the seabed is shallow.

E2 The alternative (E2) has been used in some floating bridges where the elevation difference between the abutment and the water level is very high so that the suitable traffic slope required a very long access bridge. In this case, an elevated bridge deck for a distance can eliminate the length.

E3 The alternative (E3) is used when the rotation at the bridge end should be restricted.

2.3.2.2 Access bridge length

The connections of the access bridge should be complied with the vertical movement of the floating bridge due to the tide. The construction of sliding - or expansion joint at the abutment

TU Delft 86 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge is necessary to compensate for the variation of distance between the two connection points. Both joints are hinges in order to be able to rotate in the ZX- plane.

Figure (2-2) access bridge details The connections of the access bridge are not stiff enough to restrict the horizontal displacement of the floating bridge in the Y– direction (swaying). Therefore, dolphin – frame guide or sliding piles should be constructed at both bridge ends and sides to restrict the swaying motion.

Figure (2-3) the sliding joint (B) Figure (2-4) the hinge joint (A)

The access bridge length is designed according to the maximum elevation difference between the abutment and the bridge such that the slope does not exceed %15. The access bridge length can be calculated as follows:

LAccessbridge= (XAbutmentspacing + the maximum expected response at the end)/the maximum slope

As mentioned before, the access bridge should be hinged at the abutment while an expansion joint has to be used at the floating bridge to introduce the length difference (∆x) between the access bridge and the distance between the two connection points during the tide. That difference (∆x) can be determined as eq. (2-1), see figure (2-5):

2 2 x  LAccessbridge  habutment( flow)  X Abutmentspacing (2-1)

Where: LAccessbridge = the access bridge length.

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XAbutmentspacing = the spacing between the abutment and the floating bridge. habutment (flow) = the elevation difference between the abutment and the bridge at flow case.

Figure (2-5) the access bridge motion

An additional argument to place the expansion joint on the floating bridge is to enable the pontoon to rotate freely in the XY-plane. Moreover, it is not necessary to make the access bridge a stiff structure in the XY-plane to prevent these rotations to occur. 2.3.3 Pontoon connector

The pontoons on the water can be connected in several different ways according to the bridge design and functionality method. The connection can be rigid or flexible at one or two contact points.

2.3.3.2 The pontoon connector alternatives

Table (2-7) different alternatives of pontoon connectors illustrated in longitudinal section of the pontoon C1 C2

C3 C4

C5 C6

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C7 C8

C9 C10

C1 The alternative (C1) is a connection developed by the Canady Company (IFM) [ref.31]. It allows the horizontal movement in both directions by means of the pieces of rubber, which are present at three positions. The first one is confined between the elements and the other two are at the two ends of the steel bar and screw. This system provides the effect of a spring between the concrete elements and maintains free space between them.

C2 When the rolling motion of the pontoons is partially allowable, the alternative (C2) provides this possibility. The pontoons are connected at the upper edge using pivots and rubber rings in-betweens. This system provides a simple and economic connection method because of the lack of need for intervention by divers in the erection process. C3 When the rotational spacing between the pontoons is required to be moderate, the alternative (C3) provides the solution. It represents a series of three springs that maximize the total displacement. It is important to mention that the spring stiffness at the two ends is equal to summation of the two different parts, eq. (2-2), namely the stiffness of confined and unconfined rubber: 1 N 1   (2-2) k e i  1 k i

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1 1 1   kequivalent kconfinedrubber kunconfinedrubber

C4 This connection is the modified of the already used in the Hood Cannel Floating Bridge figure (1-7). The prestressing cable is used to connect the pontoons. A satisfactory rigid base has to be provided for the prestressing cables, which are distributed along the upper and the lower edges of the pontoons. A steel frame are fixed on both faces of the pontoons with a rubber layer in between and connected by a hard steel ball joint to allow the pontoon to rotate in both directions. The maximum allowable motion is confined by the steel edge as shown.

C5 An alternative (C5) is used to connect two pontoons with small depth and small relative rotation. It is similar to alternative (C7) but the connection is at two points of the depth. The stiffness of this alternative is small and larger than (C7).

C6 The alternative (C6) is made to connect two pontoons with a relatively high depth. The pontoon walls have to extend along the pontoon length with a half circle shape from one side and a wall thickening from the other side. The circle diameter equals to the clear height between the top and bottom slabs. Each pontoon will extend a half circle into the next one and exactly beside each other to form a whole circle contact area, figure (2-6). The first connection point is the steel pin at the center of the circle. The edge of the circular shape should be coated with a steel plate or elastic interface material to protect the concrete to be crushed during the rotation. The wall thickening at the connection zone has to be designed to provide spacing for the prestressing cables which are responsible for the stiffness of the connection. Those cables must be symmetrical in numbers and positions about the rotation center. The connector stiffness (Kconnector) is equal to (see chapter 4 for more details):

Kconnector = ΔM / θ (2-3) ΔM = ∑ [(Fi +ΔFi)* di - (Fi-ΔFi)*di]

Figure (2-6)

C7 The connection (7) is developed by FDN Company to connect wave breakers at one point of the depth, figure (2-7). This method does not provide moment transformation between the pontoons. It is made from steel ring coated by a high stiff rubber. These elements are placed between the pontoons and connected by steel cables. The concrete is not protected against crushing. It has the same technique of alternative (C2).

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Figure (2-7) FDN Company pontoon connector [ref.34]

C8 The alternative (C8) has the same principle of the alternative (C5) except that the rubber part is confined in two steel cylinders to protect it from the environmental effects and to optimize the compressive strength of the rubber by enforcing it to deform in only one direction. Another advantage of this system is that the maximum allowable displacement of the spring can be restricted by the length difference between the rubber and the steel case.

C9 The connector (C9) looks like the alternative (C10). The main difference is the position of the hinge (pivot). It can be applied when the pontoon connector should transform a large moment so that the large distance between the two points reduces the applied force on the pivot and the cables.

C10 The connector (C10) is used when the pontoons of the bridge have to be separated and closed from all sides. The pivot that is fixed at the water level makes the first connection. The prestressing cables make the second point connection. These cables take the shape of a non- closed circle. Each end of the cable is anchored at one pontoon so that when the pontoons try to rotate and the walls try to approach each other, the prestressing cable will prevent that. The two circles in figure of (C10) represent two pulleys, which assist cable elongation. Another straight-line cable is anchored at the same place to prevent the rotation of the pontoon in the opposite direction.

2.3.3.3 Evaluation of the connectors

Table (2-8) evaluation of the connectors C C C C C C C C C C 1 2 3 4 5 6 7 8 9 1 0

Constructability + + + + + - + + - - Maintainability + + + + + + + + - + High wave load - - - - - + - - + + Heavy traffic load - - - - - + - - - - High tide variation - - + + + + - + - - High current speed ------Vertical stability (Heave) - - - - + + - - + + Rotational stability (Roll) - - - - - + - + + -

2.3.3.3 Pontoon connector moment

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The moment at the connector (Mc) is created from the difference in the rotation of two adjacent pontoons (ϕi+1- ϕi) multiplied by the connector stiffness (Kt).

Mci = Kt*(ϕi+1- ϕi)

2.3.4 Mooring system

The mooring system must be well designed as should ensure that the floating bridge is kept in position so that the facilities installed on the floating bridge can be reliably operated and to prevent the structure from drifting away under critical sea conditions and storms. A freely drifting floating structure may lead to not only damage to the surrounding facilities but also to the loss of human life if it collides with ships. Note that there are a number of mooring systems such as:

6. The dolphin-guide frame system. 7. Mooring by cable / chain and anchor. 8. Tension leg method. 9. Pier/quay wall method. 10. Mooring by sliding piles.

The design procedure for a mooring system may take the following steps: we first select the mooring method, the shock absorbing material, the quantity, and layout of devices to meet the environmental conditions and the operating conditions and requirements. The layout of the mooring dolphins for example is such that the horizontal displacement of the floating bridge is adequately controlled and the mooring forces are appropriately distributed. The behaviour of the floating bridge under various loading conditions is examined. The layout and quantity of the devices are adjusted so that the displacement of the floating bridge and the mooring forces do not exceed the allowable values. Finally, devices such as dolphins and guide frames are designed by applying the design load based on the calculated mooring forces. The materials for the mooring system shall be selected according to the purpose, environment, durability, and economy.

The Chain/Cable method mooring system consists of two parts: the mooring lines and the anchors. The mooring line is a catenary. The lines themselves could be made up of chains, wires, high technology fibre ropes or a combination. The mooring lines are terminated at the seabed using anchors or piles; such a mooring system is often referred to as a single point mooring (SPM).

The Chain/Cable method mooring systems can generally be divided into the following systems:

Single point mooring (SPM): Vessels are secured by a single line or structure. The floating object is allowed to weather vane; that is, swing around in order to align itself with prevailing wind, wave, and current conditions. This alignment tends to reduce the load on the mooring system. However, the mooring forces enter the structure at one point, which will have to endure a very large force. An SPM requires a lot of space and as such, is mostly preferred at an offshore location.

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Multi-buoy moorings (MBM) or Spread moorings: An MBM holds a vessel in a relatively fixed position and the vessel cannot turn head into the prevailing waves. As a result, an MBM can experience relatively high loads if wind, currents, or waves act at an angle to the mooring. The floating body cannot move and rotate freely, but the mooring forces are distributed better over the structure. Smaller forces are easier to introduce into a structure.

Dynamic Positioning System (DPS): Next to a mooring system a Dynamic Positioning System could be employed, mainly to relieve the structure of some of the loads by turning it head into the waves. This system would only be effective when the structure can rotate freely, such as when located offshore. A fixed location near the shore would not permit such movements; therefore, a DPS will be useless. Mooring system components include anchors, sinkers, anchor chains, buoys, and mooring lines. The type of mooring to be used depends on the location, the water depth, the type of structure, current, wave loads, and other influencing factors.

2.3.4.1 Mooring system alternatives

The floating bridge has to be kept in position so that the facilities installed on the floating structure can be reliably operated and to prevent the structure from drifting away under critical sea conditions and storms. The cable/anchor mooring system consists of two main parts: the mooring line and the anchor. Different alternatives are described below in table (2-9):

Table (2-9) Mooring system alternatives D1 D2

D3 D4

D5 D6

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D7 D8

Sliding piles D9 D10

D11 D12

D13 D14

D1

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The Dolphin-frame guide method represents a truss construction fixed on a foundation in the seabed. The rectangular shape of the cross section provides a sufficient stiffness against the lateral loads. This method is used when the floating structure requires minimum transverse movements at both sides [see ref.24].

D2 The Pier /Quay wall method, this method is used to restrict the transverse movement of the bridge against the high current speed. The water current applies a lateral force from one side.

D3 The Chain /Cable method is the most used method to restrict the floating structures and it can be connected in different ways as shown in the alternatives (D7) and (D14).

D4 The Tension Leg method is used when the floating structure is to be allowed to move transversally at large scale so that applying of the alternatives (D3), (D7), or (D14) cause undesirable forces on the floating structure.

D5 The Overhead Anchor Cable Systems shares features with conventional suspended trail bridges. A cable anchored on both shorelines is run over towers. The towers provide elevation. The elevated anchor cable runs parallel to the floating bridge and is upstream of it. Additional cables (called bridle lines) run from the anchor cable to attachment points on the floating bridge. The overhead cable system helps to keep the bridge in position but does not provide lift. D6 The transverse supporting of the pontoon can be hiding and fixed at the centre line of the bridge. This method provides the required lateral supporting but it is unsuitable for high tide variation sea and it requires an exceptional construction method.

D7 The Submerged Anchor Cable Systems represents the connection of the pontoon with the seabed in a crossing manner. This method converts the horizontal force of the mooring line from tension to compression.

D8 Piles work as many different types of anchors. They can be substitutes for submerged anchors. Drive piles close to the floating bridge, and then hook the bridge to the pile for anchorage. Pile holders can be used to attach the bridge to the piles. External pile holders typically are a hoop or square that surrounds the pile with a solid bracket attached to the edge of the frame. Square holders usually have bearings to reduce wear. A simple chain also will work, but the chain may increase wear on the pile. Internal pile holders are also available for piles that are placed inside the perimeter of the bridge. A pile system will reduce twisting forces on the shore connections and on the connections between sections of the floating structure. Piles are an excellent means of support for structures in areas where water levels fluctuate because they allow vertical movement while still providing anchorage. Their shortcoming is that they restrict horizontal movement. This may result in sections close to shore becoming grounded during periods of low water. The structure may be isolated during high water, making it inaccessible. These issues can be addressed by designing the shore access to accommodate changing water levels.

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D9 Soft soil anchors: so-called types (A) anchors are designed for placement in deep water and very soft soil. They are constructed of reinforced concrete fitted with pipes for water jetting. The anchors weigh from 60 to 80 tons each. They are lowered to the bottom of the lake and the water jets are turned on allowing the anchor to sink into the soft lake bottom to embed the anchors fully. Anchor capacity is developed through passive soil pressure.

D10 Pile anchors: so-called type (B) anchors are pile anchors designed for use in hard bottom and in water depth less than 27m. The type (B) anchor consists of two steel H-piles driven in tandem to a specified depth. The piles are tied together to increase the capacity.

D11 Caisson gravity anchor: so-called type (C) anchors are gravity type anchors, constructed of reinforced concrete in the shape of a box with an open top. They are designed for displacement in deep water where the soil is too hard for jetting. The boxes are lowered into position and then filled with gravel to the specified weight.

D12 Multi-slab gravity anchor: so-called type (D) anchors are also gravity type anchors like the type (C) anchors. They consist of solid reinforced concrete slabs, each weighing about 270 tons. They are design for displacement in shallow and deep water where the soil is too hard for the water jetting. The first slab is lowered into position and then followed by subsequent slabs. The number of slabs is determined by the anchor capacity required. Type (D) anchors are the choice over type (B) and type (C) anchors, because of the simplicity in design, ease in casting, and speed in placement.

D13 The suction pile anchor is made from a steel casing closed from one side lowered into the water driven in the seabed by using the water suction force; therefore, this anchor is only suitable for the soft soil seabed. The required anchoring force determines the pile length. The construction method is also suitable for deep water. D14 The alternative (D14) is the more effective and reliable mooring system. The applying of double cables at each side increases the resisting to the wave load.

2.3.4.2 Evaluation of the mooring system alternatives

Table (2-10) Mooring lines Anchors D D D D The mooring system D D D D D D D D D 1 1 1 1 1 2 3 4 5 6 7 8 9 0 1 2 3

Deep water - - + + + - + - + - + + + High wave load - - + + - - + + High tide variation - - + + - - + - High current speed + + + + + - + + Vertical stability (Heave) + + + + Rotational stability (Roll) + - + +

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Hard seabed soil + + + + - + - - + + - Soft seabed soil - - + + + - + + - - + Min. transverse movement + + - - - + + + Reasonable transverse movement - - + + + - + - Min. vertical displacement - - - - + + + +

 Connection methods of cable/chain mooring system

The cable/chain and anchor mooring method is used to connect floating structures to the seabed by using steel chains or steel ropes with a synthetic jacket to protect them from the sea environment. They can be made in different connecting manners such as the parallel line connecting (D3), the crossing line connecting (D7), and the combined connecting method (D14). The disadvantage of the first method is applying a tension force on the pontoon base while the second method applies a compression force. With regard to the stability of the structure during the wave excitation, the first method provides moment reduction against the wave forces while the second method amplifies the wave effects by increasing the rotational moment round the longitudinal axis.

 The shock absorber

In some of the existing floating bridges, a new system is applied in the mooring lines at the anchor connection. This system is called “Sealink elastomer” which has a damping function to reduce the effect of the wave force during the storm.

Sealink elastomer

Figure (2-8) Sealink elastomer [ref.30]

2.3.5 Navigational opening alternatives

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Although floating bridges cross an obstacle, it also creates an obstacle for marine traffic. Navigational openings must be provided for the passage of boats, smaller watercrafts, and large vessels. These openings may be provided at the end of the bridge. Movable spans may need to be provided for the passage of large vessels. The width of the opening that must be provided depends on the size and the type of vessels navigating through the opening.

2.3.5.2 The navigational opening alternatives

Table (2-11) the navigational opening alternatives F1 F2

F3 F4

F5

F1 The alternative (F1) represents a bascule bridge navigation opening for a floating bridge applied for shallow water. The piles to keep the bascule bridge at the same place and stable support both ends of the fixed parts of the floating bridge at the opening. Furthermore, the piles prevent them from fluctuated motion caused by the sea waves. A Bascule Bridge consisting of two leaves normally should be pointed toward each other and linked together at their ends where they join over the navigation opening. A Bascule Bridge is operated by a hydraulic machinery system.

F2 Part of the floating bridge can be converted to a curve tunnel submerge, as shown in table (2- 11) alternative (F2), to a suitable depth so that can comply with the marine vessel size. This type is suitable for deep water.

F3

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The alternative (F3) is normally used in the deep water. It looks like the alternative (F1) with a compensation of the pile system by a drop pontoon to ensure the continuity of the floating bridge. The lowering distance and the opening width are determined by the size of the marine vessels. A hydraulic machinery system is required. The movable part can be supported by a light structure with its base on the drop pontoon.

F4 [ref.3] The alternative (F4) is called “Draw pontoon movable span”. In the draw type movable span, the draw pontoon retracts into a “lagoon” formed by flanking pontoons. It is suitable for deep water. A hydraulic system is required.

F5 [ref.3] In the lift /draw, type of movable span, part of the roadway will be raised for the draw pontoons to retract underneath it. As far as traffic safety and flow are concerned, the lift /draw type movable span is superior over the draw type. Traffic moves efficiently on a straight alignment with no curves to contend with. Movable spans may be operated mechanically or hydraulically.

2.3.5.2 Evaluation of the navigational opening alternatives

Table (2-12) navigational opening alternatives The requirements F F F F F 2 3 4 5 1

Constructability + - + + - Maintainability + + + + + Marine traffic discharge - + - + + Efficiency + + + + - Heavy traffic load - + + - - High tide variation - + + + + High current speed + + + - - Vertical stability (Heave) + - + - + Rotational stability (Roll) + - + + + The cost - - + + - Deep water - + + + + Shallow water + - + + + Operation energy + * + + - Operating duration + + + - -

2.3.5.3 Location and dimensions of the navigational opening

A floating bridge creates an obstruction to marine traffic. Movable spans may need to be provided for the passage of large vessels. The width of the opening that must be provided depends on the size, the type, and the discharge of vessels navigating through the opening. The location of the navigational opening is related to the seabed profile under the bridge.

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There is a minimum water depth for every vessel size. Furthermore, there are minimum dimensions for each type of the navigational openings. It can be determining the location of the navigational opening with respect to the seabed profile.

2.3.6 Additional members

It is important to focus on other additional structural elements. Beside the mentioned elements of the floating bridge, there are some important additional elements such as the abutment, stability pontoon and wave breaker. 2.3.6.2 Abutment

The two ends of the floating bridge, as for all bridges, should be supported by the abutments. The location of the abutment is determined according to the site configuration. When the sea beach is shallow for a distance, the abutment should be constructed inside the sea.

2.3.6.2 Stability pontoon

The floating bridge is a slender structure excited by the sea wave. Both ends of the bridge are considered to be free. This amplifies the bridge response to the sea wave. The stability pontoons are fixed at both ends of the bridge to reduce the response due to its weight and damping effect, figure (2-9). Figure (2-9) Access bridge details.

2.3.6.3 The wave breaker

A general rule of thumb is to have a breakwater if the significant wave height larger than 4m [Ref.24]. The wave breaker is necessary to mitigate the wave loads on the bridge, figure (2-10). Figure (2-10) Wave breaker 2.4 Creation of different bridge alternatives

The creation of different bridge alternatives requires studying the situations at the actual site. These alternatives are made to be complying with environmental conditions, the site situations, and the functional properties of the required bridge. Most of these alternatives are combined from different alternatives of the structural elements of the floating bridge. The combinations are not arbitrary; they are based on the technical requirements. Some of the elements are applied in more than one situation. Table (2-13) describes the applied structural elements for each bridge alternative.

The bridge The pontoon The connector The mooring system alternative Bridge

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alternative alternative alternative Mooring element Anchor layout The alternative no. 1 B16 C4 D7 D11 A1 The alternative no. 2 B20+B3 C11/C12 D3 D13 A1 The alternative no. 3 B19+B2 C9/C10 D8 - A1 The alternative no. 4 B9+B6 C3 D14 D10 A1 The alternative no. 5 B16 C6 D1 - A8 The alternative no. 6 B17 C4 D14 D9 A13 Table (2-13)

2.4.1 The alternative no. 1

Continuous pontoon floating bridge, in figure (2-11), consist of concrete caissons compartmented in two direction type (B16) and connected end-to-end by the connector (C4) which represents a connecting of two concrete pontoons by a prestressing cables and isolated by a rubber fender. The mooring system is a combination of cruising mooring line (D7) and anchor type (D11).

Figure (2-11) the alternative no.1 of CPFB

The floating bridge alternative no.1 is combined to be reliable for the following situation:

 Deepwater sea: the water depth determines the type of the mooring system; whether it mooring line and anchor or sliding piles. When it is not possible to construct the sliding piles due to the large water depth or the seabed soil weakness or high water wave forces that act on the bridge, it become necessary to use the line /anchor mooring system not only for its constructability but also for its flexibility to absorb the sea wave energy.  Moderate wave height: the wave height determines not only the freeboard of the pontoon but also the type of the connector. The connector (C4) is a very rigid connector and has a limited flexibility. For the heavy waves, it is recommended to use

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more flexible connector to maintain the wave energy absorption and internal forces reduction.  Hard seabed soil: the gravity anchor is always used for the hard soil when pile driving is costly or not possible due to the water depth or soil rigidity.  High hydrostatic pressure: the compartmented concrete caisson in two direction increases the local and global bridge stiffness.

2.4.2 The alternative no. 2

Figure (2-12) the alternative no.2 of CPFB

The Mobile Offshore Base (MOB) which are typical VLFS projects that have been investigated in detail and that are aimed to be realized in the near future, are introduced to be one of the floating bridge alternatives. This type is characterized by resistance to the sea waves. It can be very sensitive to the traffic load or any other vertical load because of reduction in the projected area that is represented by the cross section area of all columns that is less than the projected area of the pontoon. For the reason of large expected response, it should be combined with flexible pontoon connector and compliant mooring system.

This alternative, figure (2-12) is suitable for deep water with a high expected sea wave height. The applying of the suction pile anchor (D13) is practical for deep soft soil seabed.

2.4.4 The alternative no. 3

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Pontoon cross section Pontoon side view

Figure (2-13) the alternative no.3 of CPFB

The alternative nr.3 is a continuous pontoon floating bridge supported laterally by the sliding piles and consists of concrete pontoons that have transversal openings at the water surface level to reduce the wave load on the piles. The pontoons are connected by a hinge with a special technique spring to reduce the rotation. This connection method is constructible and reliable. The system is ideal for shallow waters and moderate wind/wave loads.

2.4.4 The alternative no. 4

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Figure (2-14) the alternative no.4 of CPFB

The alternative no.4 of CPFB, figure (2-14), is a continuous pontoon bridge. The bridge consists of concrete pontoons connected by rigid bars with adjustable confined rubber to control the pontoons rotation. The pontoons have lowered wings to increase the added water mass in both directions, to reduce the up-life force and to increase the water spring modulus. The bridge is suitable for deep water, stable against high wind wave loads and heavy traffic loads. The anchors are typical to the sand soil seabed.

2.4.5 The alternative no. 5

Figure (2-15) the alternative no.5 of SPFB

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The bridge alternative nr.5 is a separated pontoon bridge consisting of concrete girders and pontoons connected by a free hinge. The girders are connected end-to-end by a highly flexible connector with adjustable rotational stiffness. The pontoons are moored by Dolphin-Frame guide Method that provides a limited lateral displacement and free vertical displacement. The bridge can be constructed in shallow water and operated safely in a high wind-wave load region.

2.4.6 The alternative no. 6

Figure (2-16) the alternative no.6 of SPFB

The alternative no.6 in figure (2-16) is ideal to cross deep water because of using the cable mooring system with anchor type (A) which is suitable for the soft soil. The bridge is a SPFB, which cannot be affected by the water current and /or the wind –wave load. Its arch form modifies the global stability of the bridge because the arch-form can enlarge the supporting base of the bridge. In this structural combination, there is no need to use a highly flexible connector between the girders. A protected steel pipe pontoon can be used for two reasons: relatively light weight and the possibility to construct spacing between them to allow more water current to flow easily.

Table (2-14) shows the evaluation of all alternatives with respect to the site situations.

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Table (2-14) Separated Continuous pontoon bridge pontoon bridge 1 2 3 4 5 6

...... o o o o o o n n n n n n

The site situation e e e e e e v v v v v v i i i i i i t t t t t t a a a a a a n n n n n n r r r r r r e e e e e e t t t t t t l l l l l l a a a a a a Deep water + + - + - + High wave load - + + + + + Heavy traffic load + - + + + + High tide variation + + + + - + High current speed - + + - + + Min. transverse movement + - + + + + Reasonable transverse movement + + - + - - Min. vertical displacement + - + + - + Reasonable vertical displacement - + + + + - Hard seabed soil + - + - - - Soft seabed soil - + + + + +

2.5 Mechanical modelling of the floating bridge

The modeling of Floating bridge motion: [Ref. 9]

 A beam on elastic foundation (Static response)

Continuous floating bridges essentially act as beams on elastic foundations in both the vertical and transverse directions. In the vertical direction, buoyancy provides the linear modulus of the vertical support, while the discrete mooring cables provide the nonlinear horizontal support for the bridge under transverse loading. [The design of a floating bridge for traffic is straightforward and typical beam-on-elastic-foundation methods can be used]. However, the stochastic structural loading generated by wind and wave action and the corresponding dynamic response of the floating bridge to this loading presents a very complicated system to be understood. The design of a floating bridge for the environmental loading becomes much more difficult than for traffic loading. Despite the complications, understanding must be achieved if an efficient and safe design for a floating bridge is to be obtained. The eq. (2-4) represents the equation of motion:

d 4w EI  k  w  q (2-4) dx4 d 1

This equation can be used to determine the bridge response under the traffic load and the static response of the bridge under the longitudinal sea wave.

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 A beam on the Viscous -Elastic Kelvin Foundation (Dynamic response)

The buoyancy forces that support the continuous floating bridge behave exactly as a saturated soil within the linearity. We can summarize the following differences:

 The water is infinitely linear while this is limited the soil.  The water has a damping effect while the soil is only when it fully saturated.

The adding of the inertia term of the beam and the damping effect of the foundation to the equation of motion will modify the result response to approach the reality as it written in eq. (2-5):

2w 2  2w w A  EI  k wc   q (2-5) 2 2  2  d d 1 t x  x  t

Where: ρ = the beam mass per unit area. A = beam cross sectional area. EI = beam flexure stiffness. kd = foundation stiffness modulus. cd = foundation damping coefficient. q1 = applied load

 Beam under dynamic torsion (m):

The torsion moment can be applied on the bridge as a result of the lateral incident waves. The wave pressure concentrated at the water level that is usually not the gravity centre level of the bridge element. This eccentric load will lead to the Loading combination. The bridge rotation can be described in eq. (2-6):

 2     J  GJ t   m (2-6) t 2 x  x 

Where: ρ = mass density of beam material. J = polar moment of inertia = Ixx+ Iyy. Jt = torque constant. G = Shear modulus. a = the major dimension. b = the minor dimension.

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For a flat rectangular shape:

3 Jt = k1*a*b k1 = coefficient depends on (a/b) ratio which can determined from the table (2-15) by interpolation method.

Table (2-15) torsion constant [ref.33] a/b 1 1.4 1.8 2 3 4 6 10 ∞ k1 0.141 0.187 0.217 0.229 0.263 0.281 0.299 0.313 0.333

2.6 Construction method

Concrete pontoons are generally used for building major floating bridges. The fabrication and construction of the concrete pontoons must follow the best practices in structural and marine engineering in concrete design, fabrication, and construction with added emphasis on high- quality concrete and water tightness. Quality control should be the responsibility of the fabricators/contractors. Final quality assurance and acceptance should be the responsibility of the owners.

In addition to these traditional divisions of responsibilities, the construction of a floating bridge necessitates a strong partnership arrangement to work together, contracting agencies and contractors to provide full cooperation and joint training, share knowledge and expertise share responsibility and to help each other succeed in building a quality floating bridge. The contractors should have experience in marine construction and engage the services of naval architects or marine engineers to develop plans for monitoring construction activities and identifying flood risks, and prepare contingency plans for mitigating the risks.

Knowledge is power and safety. The construction personnel including inspectors from the contractors should be trained on the background of the contract requirements and the actions necessary to implement the requirements fully. Their understanding and commitment are necessary for complete and full compliance with contract requirements and that bear on personal and bridge safety.

Construction of a floating bridge is well established. Many concrete floating bridges have been built successfully using cast-in-situ, precast or combinations of cast-in-situ and precast methods. Construction techniques are well developed and reported in the literature. Owners of floating bridges have construction specifications and other documents and guidelines for the design and construction of such structures.

Floating bridges may be constructed in the dry in graving docks or on slipways built specifically for the purpose. However, construction on a slipway requires extensive preparation, design, and caution. The geometry and strength of the slipway must be consistent with the demand of the construction and launching requirements. Construction in a graving dock utilizes techniques commonly used in land base structures. Major floating bridges around the world have been constructed in graving docks. Because of the size of a floating

TU Delft 108 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge bridge, the bridge is generally built in segments or pontoons compatible with the graving dock dimensions and draft restrictions. The segments or pontoons are floated and towed to an outfitting dock where they are joined and completed in larger sections before towing to the bridge site where the final assembly is made as shown in figure (2-17).

The fabrication site flooded To bridge site the pontoons towing In onshore site: pontoons fabrication

• Anchored to the seabed • Abutment construction

Pontoons mating (prestressing cables)

Figure (2-17) Construction procedure [ref.31]

It is important to explore the availability of construction facilities and decide on a feasible facility for the project. These actions should carried out prior to or concurrent with the design of a floating bridge to optimize the design and economy. Some key data that may be collected at the time are:

 Length, width and draft restrictions of the graving dock.  Draft and width restrictions of the waterways leading to the bridge site.  Wind, wave, and current conditions during tow to and installation the top site.

2.6.1 The continuous pontoon floating bridge

The construction procedure of the continuous pontoon floating bridge contains the following three steps that start simultaneously:

 The execution of the abutment at both sides  The fixation of the anchors along both sides of the bridge.  The fabrication of the concrete pontoon in the onshore site

The execution of the abutment

The position of the abutment is selected according to the site configuration, the approaches elevation with respect to the water level and the water depth nearby the coach. The shallow part of the sea should be neglected to avoid any contact of the bridge with the seabed in all

TU Delft 109 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge cases. These cases involve the dynamic response of the bridge due to wind- wave loads as well as the tidal range during the day and the submerged depth of the pontoon.

All those distances should be taken into account in the selection of the abutment position. The position of the first pontoon of the continuous floating bridge is selected at a distance from the abutment position. This distance represents the length of the access bridge, which is determined by the tidal variation range during the day. This implies that the access bridge length is directly proportional to the tidal range to maintain a reasonable slope.

The fixation of the anchors along both sides of the bridge

The mooring system for the floating bridge is necessary not only to keep the bridge in the same place but also to introduce the wind-wave forces and to prevent the drifting up of the structure. The mooring system force depends on several factors as follows:

6. The type of the mooring line (cable or chain). 7. The material density of the mooring line. 8. The diameter of the mooring line that determines its weight. 9. The water depth affects the line length, for variable depth, we get variable mooring forces. 10. The anchor position: the large distance between the bridge and the anchor leads to large applied horizontal force.

The required forces that will introduce the wind-wave forces determine the number of anchors and the distances between the anchors. Those distances are not necessarily uniform as the seabed is flat, but it is recommended that they are symmetrical along the bridge to ensure the horizontal equilibrium and the symmetrical response of the entire structure.

The anchor types:

The seabed soil condition varies in different types and this variation determines the anchor types as well as the water depth. In some places where the sea depth is very high, it is difficult to execute conventional anchors like driven piles.

In section 2.3.4.1, several types of anchors are shown. Type A is suitable for the soft soil and type B is used for moderate soil and acceptable water depth. For the rock soil or other hard soil or very deep water, the types C and D are suitable.

The fabrication of the concrete pontoon in the onshore site

The concrete pontoons are constructed as caissons. The caissons are fabricated in closed ports nearby the bridge site. The prefabricating operation of the caissons starts with the concrete preparation. The operation sequence is as follows: A mixer prepares the concrete batch that is then poured into a hopper that feeds a concrete pump. The concrete is then pumped to a delivery pipe that is installed above the working deck. The concrete pouring involves the mixing, transporting, pumping, and vibrating the required concrete. The pouring procedure divides into three phases of the caisson structural elements:

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4. Bottom slab pouring 5. The external and internal walls pouring. 6. Top slab pouring.

Each caisson is built in an ascending sequence starting with the slab. The slab reinforcement cage is assembled in an auxiliary platform, then the cage is moved to the work dock and the slab is poured as a monolithic element. Due to the stiffness requirements of the pontoon, whether the longitudinal or the transversal stiffness, these three elements have to be built integrally with each other, for that reason the precast elements is not recommended.

After the slab is ready, the construction of the upper part of the caissons begins, ascending in increments of one meter using the sliding form. Each of these increments includes placing the reinforcement, sliding the forms, and pouring and vibrating the concrete. This sequence is repeated until the total height of the caisson is reached.

The top slab can be constructed in two manners: using thin precast concrete plates as a form. They are laid on the walls and supported from blow. The reinforcement cage is assembled on it and then the slab is poured as a monolithic element. The second method is by using the conventional form.

The prestressing and injection process starts when the concrete reaches the suitable maturity. The ports floor level has to be lower than the sea water level to makes the floating process of the caisson in the last phase possible. The bottom slab should be fabricated on a flat isolated floor to ensure floating operation by streaming the seawater. The port has to be open to tow the pontoon to the assembling site. The protection requirements, maintenance, operation, and connection facilities should be made during the fabrication procedure.

The bridge assembling procedure:

The first pontoon, which is named as a stability pontoon, has always special damping requirements such as the large width, additional mooring cables or additional weight because it is considered as free end of very long floating structure exited by wind-wave dynamic loads. Furthermore, it carries a part of the access bridge weight.

The first pontoon tows to the position, then connects firstly to the access bridge, and then connects to the seabed by the mooring cables. After that the second pontoon tows to the position firstly has to be connected to the first pontoon and then to the seabed by the mooring lines. This repetitive process goes on in the same manner and has to be starts from both ends of the bridge.

2.7 Durability and concrete technology

2.7.2 The situation analysis

During the operational stage of the floating bridge, the pontoons will be floating at all times. The dimensions of the pontoons are large and all parts of the pontoon are casted in situ.

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The important environmental conditions can be summarized as follow:

 The pontoon is always floating in salt water of limited depth, environmental class IV of NEN 6720 Dutch code.  The water line and spray zone vary, thus the concrete surface in that area will be changing between wet and dry.  The spray zone reaches up to an average of 2 m above the water (This value varies according to the location of the bridge).  The bridge is always subjected to wind-wave loads and response motions. All these loads are dynamic loads that cause always fatigue.

The main mechanical or structural requirements are:

 The individual pontoons have a design lifetime of 100 years.  During the lifetime minimum maintenance is required, maintenance activities will have to be carried out while the bridge is floating and in operation.  All parts of the pontoon are cast at a construction site nearby the location of the bridge.

2.7.2 Durability of marine concrete structures

Marine structures mainly are exposed to salt, water, and air. This combination can cause multiple forms of degradation. Most deterioration mechanisms were found not to determine the lifespan of the structure. The most potential deterioration mechanism in concrete marine structures is chloride ingress, as was concluded from test results from several Dutch marine structures.

Expectable deterioration mechanisms are carbonation, leaching, alkali-silica reactions, freeze- thaw action, erosion, or salt crystallisation. These seemed virtually absent from the structures that have been researched. The most severe deterioration of concrete is expected around the water line and above it, in the splash zone, because the structure will be changing between wet and dries at periods. Carbonation is strongly reduced when concrete is wet for long periods of time; from the water line downwards. Differences in exposure will cause a large amount of scatter in the chloride profiles of different areas on one structure.

Most deterioration mechanisms and in this case especially carbonation and chloride ingress and the following corrosion initiation can be reduced through the choice of materials. The following aspects should be kept in mind when considering the choice of material:

 An Alkali Silica Reaction (ASR) can be suppressed for the main part by using little or no reactive aggregates.  A low water/cement ratio prevents freeze-thaw damage.  High Strength Concrete develops into a dense mature concrete with high strength. Dense concrete is less permeable and chloride ingress and carbonation may be reduced.  The carbonation depth should be reduced to less than the concrete cover on the reinforcement. Therefore, a large concrete cover in marine structures is beneficial to the lifespan.

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 The concrete cover should not crack round the reinforcement in case of heat (fire) or collision.  As blast furnace cement produces a dense concrete with small sensitivity to chlorides, the strongest possible type of concrete composition with blast furnace cement offers the best solution, which is C53/65.  C53/65 with CEM III/B, rough sand, broken stone and small fillers (fly ash or silica fume) is chosen as the best concrete composition for the pontoons.  Additives such as a plasticizer can be used to ensure mortar workability on site.

Chapter IV: Structural analysis .

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4 Structural analysis

Introduction

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Much of the previous research on floating bridges was conducted in the interest of understanding the response of a floating bridge to wind and wave loading. These studies have resulted in improvements in the ability to model a floating bridge and to determine the extreme structural responses of the bridge under environmental loading. In this chapter, static and dynamic analysis will be discussed as pertains to the specific methodologies used to model and analyze floating bridges. Other studies have been conducted on various issues that are relevant to the overall understanding of floating bridges, but these studies were not necessarily conducted with floating bridges in mind.

The construction of the bridge is a very wide topic. The main loading is the wave load. The prediction of the accurate values of the wave parameters such as the wavelength, height, and period is impossible. As known, the ocean waves are irregular wave or they consist of superposition of several regular waves with different heights and periods.

Significant efforts have been made to understand floating bridge behaviour, both experimentally and analytically, by researchers associated with the WSDOT (2) in the years since the failure of the Hood Canal Floating Bridge as well as by several European researchers and designers. The following discussion presents a brief account of the development of the understanding of floating bridge behaviour and corresponding analytical techniques which have been developed, some specifically as a result of research conducted through WSDOT funding and initiative. Modern analysis techniques for floating structures subjected to wind and wave loading fall into one of two main categories: time-domain analysis or frequency domain spectral analysis.

Because of the shortage in the experimental or the theoretical information about the dynamic behaviour of the floating bridge under wind and wave loading, the first floating bridges were designed using a simplified technique presented by Stoker (1957). The floating bridge was assumed to be either a rigidly fixed floating beam or a freely floating beam, and the waves were considered as simple harmonic loading acting on the floating bridge. Stoker’s theory was based on some assumptions to be corresponding to some limited field observation of existing floating bridges.

The resonance effects that can occur between the waves and the response of the floating bridge have been taken into account by using an amplification factor. The original methods to determine the structural response of the floating bridge exited by a wave loading were relatively straightforward. The methods did not consider the spectral distribution of the wave frequencies and the stochastic nature of neither the loading, nor the extreme structural responses expected for a given magnitude storm event.

4.1 Local design

A conceptual design is used to consider the technical and economical feasibility of the project. It is a first structural design of shape and dimensions. The method for the conceptual design of this project should be a rather simple and fast method to calculate the internal forces of a structure by hand and to design the reinforcement or prestressing needed. The calculations are

(2) WSDOT = Washington State Department of Transportation made according to a conservative approach of the structure. The safety margins in this design will allow for both structural and economical optimisation in the next detailed design. From the conceptual design, the following can be deduced:

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· Dimensions and shape of the structure · Type of materials and material qualities · Quantities of materials etc

4.1.1 The total bridge length

The length of the floating structure has a large influence on its response against the exited sea wave. The classifications of structural behaviour of float are shown in figure (4-1). Firstly, the length of floating structure is proportioned with the wavelength. When the wavelength is equal to or larger than the length of the floating structure, the float will respond as ship-like motion. When the wavelength is smaller than the float length; the float will be stable and remain horizontal. The stability increases directly with the ratio of the float length to the wavelength.

Secondly, the length of the floating structure is related to its characteristic length (λc). When the length of the float is equal to or smaller than its characteristic length; the float will respond as a rigid body. When the length of the float is larger than its characteristic length, the float will respond as an elastic body. From equation (4-1) we can see that the characteristic length (λc) proportions directly with the longitudinal flexural stiffness (EIz) and inversely with the buoyancy stiffness modulus (k) which proportions directly with the width of the pontoon. Suzuki and Yoshida (1996) have proposed this formula.

Figure (4-1) Structural behaviour classification

/1 4  EIz  λc = 2π *   ------(4-1)  k  k = Buoyancy stiffness modulus = ρw*g*A(x) ------(4-2) ρw = water density. g = gravity acceleration. A(x) = the projected area of the beam per unit length. EIz = the bending stiffness of the beam in the longitudinal direction.

This equation is derived from the characteristic length equation of a beam and it represents the minimum length of the beam to behave as an infinite beam:

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3 l  2 * 2 4/1 4/1 k  EIz  l  EIz  λ = 4  l  3 2 *    .2 12 *  4* EIz  k  2  k 

The bridge length should preferably be not only larger than the characteristic length and the wavelength but it should also be multiples of the characteristic length to ensure high stability.

The bridge deflection in (mm) for different cases mentioned in figure (4-1) Lbridge /Lcharacteristic= 1704/426 = 4 ; Lbridge/Lwave= 1704/213 = 8

Lbridge /Lcharacteristic= 1704/426 = 4 ; Lbridge/Lwave= 1704/3408 = 0.5

Lbridge /Lcharacteristic= 213/426 = 0.5 ; Lbridge/Lwave= 213/26.625 = 8

Lbridge /Lcharacteristic= 213/426 = 0.5 ; Lbridge/Lwave= 213/426 = 0.5

4.1.2 Pontoon dimensions (length-width- depth)

 Pontoon length

The pontoon length relates to the construction feasibility and erection requirements. For the design requirements, firstly, the stiffness of the connectors between the pontoons plays an important role in the determination of the pontoon length. When the flexural stiffness of the pontoon is equal to the connector stiffness, the bridge will be considered as a continuous beam so that there is no influence of the pontoon length. Secondly, the maximum allowable

TU Delft 117 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge vertical relative displacement between the pontoons determines the pontoon length defined in figure (4-26).

 Pontoon width (bridge width)

In most cases, the pontoon width is usually made equal or larger than the road width. According to the design requirements, the pontoon width should be determined. The buoyancy stiffness modulus (k) depends on the pontoon width. The value of (k) is calculated from the equation (4-2) which proportions directly with the pontoon width see figure (4-2).

Figure (4-2) the buoyancy stiffness modulus as a function of the pontoon width

The road dimensions:

The road transverse profile on the bridge deck is defined using Dutch criteria (ROA & RONA) [ref.35]. These criteria provide the minimum required road width, which depends on two factors: the lane number and the maximum allowable traffic velocity (vo). The table (4-1) shows all dimensions of the selected road profile which is constructed on the structural members:

Table (4-1) the road transverse profile dimensions (m). [ref.35] vo (120 km/h) vo (90 km/h) Lane width (a) 3.50 3.25 Divide strip (b)* 0.15 0.15 Side strip (c) 0.20 0.20 Hard strip (d) 1.10 0.30 Breakdown lane (e) 3.50 3.25 Side strip (l) 0.50 0.50 Object margin distance (m) 1.50 1.00 (*) Divide strip is used between the lanes for more than one lane without any influence on the total width.

Figure (4-3a) the road transverse profile dimensions [ref.35]

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In case of one lane in each direction, the minimum pontoon width is restricted by the road dimensions, which are in case of one lane in each direction equal to (22600mm) including the middle strip, the parapet and the safety barrier, see figure (4-3).

The total width (w) = 2*[safety barrier (1.41m) + m + c + a + c + e + l ] + middle strip (0.8m) = 22.6m for maximum traffic velocity = 120 km/h = 20.6m for maximum traffic velocity = 90 km/h

Figure (4-3b) the road transverse profile dimensions in meters

The parapet and the safety barrier:

The floating bridge must be provided with a parapet and the safety barrier. The standard dimensions of the parapet and the safety barrier as illustrated in figure (4-4) are obtained from the Dutch code (ROA). The total width of the parapet and the safety barrier is 1.41m.

Figure (4-4) the parapet and safety barrier in meters [ref.35] The middle strip:

The middle strip is recommended between the two road directions. It consists of a safety barrier (0.8m); a side strip (l) and a breakdown lane (e) for both sides.

The total width of the middle strip = safety barrier (0.8) +2*[0.5+3.5/3.25] = 8.8m /8.3m

 Pontoon/Girder depth (pontoon draft)

The freeboard and the draft of the floating structure should be calculated based on the weight of concrete, weight of reinforcing steel, weight of appurtenances, weight of marine growth as appropriate, and the vertical component of the mooring line force. The weight of the pontoon is higher than the computed weight because of form bulging and other construction tolerances. Based on experience, the weight increase varies from (3-5) % percentage of the

TU Delft 119 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge theoretical weight [ref.3]. This increment should be included in the draft calculations. The definitions of the draft and the freeboard are displayed in figure (4-5). The draft (d) of the pontoon should not be too large to provide a minimum clearance. This means that a sufficient buoyant force should be present. The under-water volume of the pontoon (Vw) determines this buoyant force (Fw). The draft has to be investigated for two cases, namely (1) when it is loaded with a full traffic load and (2) without traffic load.

Figure (4-5) Pontoon depth

The pontoon depth = freeboard + draft The draft (d) = the total load per unit length (Fw) / the pontoon width (w) F d  w (4-3) w w The total load per unit length = Traffic load + bridge weight + vertical mooring load

The freeboard of a single floating pontoon is assumed to be in the range of (1.5-2.5) m according to the significant wave height and it is calculated from the road level to the water surface for an unloaded bridge. The maximum settlement of the bridge due to the traffic load, the wave amplitude and the maximum expected vertical response due to the wind/wave load should not exceed the freeboard in all load combinations. The freeboard should be the largest of the following extreme cases:

 Freeboard (1) = normal wave amplitude + maximum bridge settlement (full traffic load)  Freeboard (2) = extreme wave amplitude ( unloaded bridge)

4.1.3 Pontoon compartmentalization

As strength requirements, the maximum allowable deflection of the slabs and the traffic arrangements on the upper deck of a bridge may determine the distance between the vertical partitioning walls in the pontoon as well as the slab thickness and the later has to have a satisfactory shear and bending strength. All these requirements should be taken into account to determine the size of the pontoon compartment. The variation of compartments numbers related to the applied loads on the pontoon, because of the water pressure that increases by the pontoon depth, the wall thickness, the concrete grade and the required global flexure of the pontoon. The figure (4-6) shows the relationship between the pontoon stiffness and its depth for a different numbers of compartments for the same size of the pontoon, concrete grade and wall thickness.

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Stiffness/depth relationship for different compartments 1,60E+15

1,40E+15 )

4 1,20E+15 ^ m

m 1,00E+15 (

t n

e 8,00E+14 m o m 6,00E+14 2 a i t

r 3 e

n 4,00E+14 I 4 5 2,00E+14 6 0,00E+00 4 5 6 7 8 9 10 The pontoon depth (m)

Figure (4-6) stiffness / depth relationship of concrete pontoon for different compartmentalisations.

The shape of the compartment (length /width ratio) has an influence on the local flexural stiffness of the pontoon according to the effective width of the flanges that is defined in the Dutch norm (see figure (4-7)).

panel (5X5) m 7

) 6 bxe m ( support h

t 5 d i w

bye

e 4

v support i t c

e 3 f

f bxe e

e span

g 2 n a l f bye 1 span 0 1 1,5 2 lx/ly ratio Figure (4-7) the panel shape effect (length/width ratio) on the effective width of the flange (Dutch norm)

4.1.4 Pontoon slabs and walls design

As a first estimate, the pontoon is considered as a beam supported by the waves. The Still Water Bending Moment, mostly used for ships, approximates the maximum bending moment in the hull. Further, the governing cross sections are chosen. The governing cross sections are considered as a framework and thus, the internal forces are estimated. However, the transversal walls in the pontoon cannot be taken into account in a cross sectional analysis. For a more accurate concrete design, the structure will be divided into pieces: Structural members such as a floor, a deck and walls, and connections. The parts will be designed to form the whole structure. This design method is presented with drawings.  Longitudinal section: The waves support the pontoon by an upward load. This is modelled as springs underneath the walls of the pontoon with a stiffness derived from the buoyancy force, combined with a distributed upward load.

 Transverse cross section:

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Most loads do not vary much in the longitudinal direction. Therefore, one centre cross section is considered with a full deck load or ballast load, in storm conditions. The waves can provide a hogging or sagging condition in the transversal direction. The buoyancy force is modelled as springs underneath the walls of the pontoon with stiffness equal to the buoyancy force, combined with a distributed load upward.

 Top slab: The entire top slab should be considered as one statically indeterminate slab with many spans. Most fields are evenly loaded. However, for the conceptual design, the top slab of the pontoon is considered as the top slab of a single compartment. The walls of the compartment uniformly, rigidly support the plate. It is not recommended to use precast concrete elements because a high torsional stiffness of the pontoon is required; therefore, it should be cast in situ.

 Bottom slab: The bottom slab of the pontoon is cast in situ, and is supported by the buoyancy force. The hydrostatic pressure of the buoyancy force is evenly distributed in a calm situation (no wave), but it may take a sinusoidal distributed load when excited by sea wave. The sinusoidal load has the same length and amplitude as the transmitted wave. The bottom slab is considered as a bottom slab of one compartment, which is uniformly and rigidly supported by the walls.

 Outer wall slabs: The inner walls support the outer wall slabs. The hydrostatic load, the current load, and the wave load are unevenly distributed.

 Inner wall slabs: The inner walls can be considered with the dimensions of the compartments. They are loaded in compression by the normal force due to the deck load and by the hydrostatic load from ballast water. The ultimate limit state load is a hydrostatic load from a flooded compartment (after collision/accident). The plate design can be simplified by using the plate loaded by a hydrostatic pressure from one side.

The pontoon design considerations:  The entire shell of the pontoon may be loaded in torsion, caused by an obliquely incoming wave. The cross sections of the pontoon present a closed section, which can bear a torsional load.  The connector and pontoon design are integrated by introducing the connection forces into the pontoon hull structure and the longitudinal inner walls. However, the connection forces are analysed locally in the pontoon and are thus treated separately from the general distribution of internal forces in the pontoon.  The thickness of the inner walls is equal to the thickness of the outer walls, because one compartment can be flooded. In that case, the inner walls have to bear the full hydrostatic pressure, but they experience no wave load.

The two requirements that the moments of the cross section to be met are:

(1) Mu ≥ Md

(2) Mu ≥ Mr

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 The concrete cover limitation: The concrete cover is determined in the table (4-2) [ref.3]. The table contains the required concrete cover for each member and a specific water quality. These values are relatively larger than the concrete cover specified in the Dutch norm for structures subjected to seawater (see table 44 in NEN6720 [ref.15]).

Table (4-2) Concrete cover [ref.3] Fresh Water Salt water Top of the road way slab 65 mm 65 mm Exterior surfaces of pontoons and barrier 40 mm 50 mm All other surfaces 25 mm 40 mm

4.1.5 Pontoon rigidity (flexural – and torsional stiffness)

 Flexural rigidity

The flexural rigidity of the pontoon plays an important role in the behaviour of the floating 1/4 bridge. Firstly, the global flexural rigidity of the pontoon (EIz) proportions directly with the characteristic length (see eq. (4-1)). Secondly, it determines the value of the local vertical displacement due to the traffic load.

The global flexural rigidity is applied for the global structural analysis of the bridge under the wave load and is calculated by considering the entire cross section of the pontoon, while the local flexural rigidity is applied for local structural analysis of the pontoon under the traffic load. It is calculated by considering the walls of the pontoon (internal and external) and the effective flanges that are defined in the Dutch code NEN 6723 VBB (1995) (see appendix).

 Torsional rigidity

The multi-cellular cross section is regarded as thin-walled cross section and the principle of membrane analogy [ref.37] has to be applied to determine the torsional rigidity of the pontoon (see figure (4-8)). The closed cross section has a much higher torsional stiffness than the open one. Therefore, we can neglect the portion of the wings and other possible loose parts in the cross section. The torsional stress in the thin wall is higher than in the thick one.

M w  2 21 a  b  22 a  b

M w  GIw

1 1 1 2 2 1 2 2 2 1  ; 2  ; 3  ; 4  ; 5  ; 6  ; 7   0 t1 t2 t3 t1 t3 t2 t2 w w w w  w pab  aS 1  bS 1  aS 1  bS 2 1 t1 t2 t3 t2 1 w w  w w w  ; p  2 ;S  pab  aS 2  bS 2 1  aS 2  0 G t1 t2 t3

M The tensional rigidity I  w w G

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Where; τ = the shear stress t = the wall thickness

Figure (4-8) the flow of the shear stress in the pontoon section

4.1.6 Design and analysis of the mooring line

4.1.6.1 Static equilibrium equations

Figure (4-9) details of an element of a mooring line [Ref.1+2]

Figure (4-9) shows an element of a mooring line. In still water, the static equilibrium equations for the element in its own plane can be written by resolving forces tangentially and normally to the element. After several mathematical substitutions the resulting equation is: 2 d 2 y w  dy   1   (4-5) dx 2 H  dx  w = the submerged weight per unit length H = the horizontal force ɸ = the angle of the mooring line to the horizontal T = the tension force in the line S = distance along the line h = the water depth

Solving the ordinary differential equation and imposing the boundary condition provides the result:

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H   wx   y  cosh  1 (4-6) w   H  

A few important physical observations regarding the equations may be made:

1. The bending stiffness of the mooring line material is neglected. That is important in analysing the static and dynamic behaviour of the flexible line. 2. The above equation neglects the effects of the elasticity. This can result in a significant overestimation of tensile forces and therefore elasticity effects are routinely included in mooring analysis. 3. Any direct environmental loading and response of the mooring line is neglected.

Two nonlinear springs Kh and Kv (vertical and horizontal) are used to replace the wire rope for structural analysis.

The designed mooring line force is affected by several factors such as the elasticity of the line material, the friction with the seabed, buoys, dynamic response and damping.

 Influence of elasticity

The elastic material properties of the mooring line materials can make a significant difference to the tension levels.

Figure (4-10) Mooring line element with and without axial stretch [Ref.1+2]

Axial stretch will result in the element extending to ds (1+T/AE), where AE is the axial stiffness:  T  dx  ds1 cos (4-7)  AE   T  dy  ds1 sin (4-8)  AE 

The equations can be solved analytically to provide the complete solution for a catenary that includes the effects of elasticity. These show the following results comparable to those without elasticity: 2  T  2wh H  AE  1   AE (4-9)  AE  AE

 Effect of seabed

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The friction in the grounded length is frequently ignored in a static calculation but its inclusion simply reduces the horizontal load as one progress from the touchdown point to the anchor. The tension variation from the touchdown point to the anchor is generally given by the equation: Tg = H – f . xg . w (4-10) Where: Tg = the effective horizontal force on the anchor. xg = the grounded distance from the touch down point to the anchor. f = the coefficient of friction (1 for chain/0.6 for wire rope).

 Effect of buoys

Buoys are often attached to mooring lines along their length to lift the mooring line away from any seabed obstructions. Buoys reduce the effective weight of the mooring line and therefore increase the stiffness of the line. This increased stiffness increases the slowly varying and wave frequency forces in the mooring system. However, it beneficially reduces the displacement of the structure under the effects of mean and slowly varying loads and reduces the vertical load carried by the platform, so increasing the payload.

 Effect of the dynamic response

Figure (4-11) dynamic response of the mooring line [Ref.1+2]

The figure illustrates the differences in mooring line behaviour predicted using quasi-static and dynamic analyses. Both analysis techniques deal with the steady loads in an identical manner. The slowly varying responses can also be accounted for quasi-statically in view of their long periods that are of the order of minutes rather than seconds.

Floating Bridge motion at wave frequency normally imposes both horizontal and vertical motions at the fairlead. In quasi-static analysis, only the horizontal component of the motion in the plane of the mooring line is taken into account and the bridge’s horizontal motion is simply imposed as a displacement and a static equilibrium calculation is used to compute the mooring line tension.

The figure shows the catenary positions under the various force and motion components. In dynamic analysis, the line’s inertia and drag are included together with both horizontal and vertical motions. As a result, the mooring line is generally unable instantaneously to follow

TU Delft 126 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge the bridge motion, which is then accommodated through a combination of catenary and axial deflection.

We can summarise in table (4-3) the applicable equations to design the mooring line. They are derived from the already mentioned basic equations and the following boundary conditions:  The seabed should be considered horizontal, flat and stable.  The mooring line applies no uplift force on the anchors at all cases (V = w*L).  The yield stress is the maximum stress in the mooring line.  The effect of the dynamic response of the mooring line is neglected.

Table (4-3) the applied equations to determine the mooring line parameters. [Ref.1+2] No. of The parameter Static, inextensible Static, extensible equation

The minimum length 2T 1 2 2 (4-11) L  h 1 L  T  H required (L) wh w  2  The horizontal force  T  2wh (4-12) H= T – w h H  AE  1  1 at the pontoon (H)  AE AE     

H 1  wL  The horizontal scope X  sinh   H 1  wL  HL (4-13) w  H  X  sinh    distance (X) w  H  AE The vertical force at (4-14) V = w*L V = w*L the pontoon (V)

4.1.6.2 Mooring line technical specifications

Historically, floating exploration and production platforms have been moored by catenary systems utilizing steel cable and chain solutions. In ultra deep water, a fundamental feature of a catenary mooring – weight – becomes its greatest disadvantage. The solution is presented by use of synthetic fiber tethers in either taut leg or catenary mooring systems. The taut leg system relies on the elasticity of the mooring tether to provide the restoring force rather than the weight of the catenary. A synthetic fiber insert within a catenary system may reduce the suspended weight to manageable levels.

The primary criteria to be addressed by the designer of a taut mooring are offset, peak load, fatigue and tether extension. Offset and peak load are determined by environmental forces interacting with floating structure and mooring geometry is influenced by the length and mechanical properties of the tether. Peak load will depend upon the maximum displacement and hence the extension experienced by the rope and prevailing rope stiffness.

All synthetic fibre ropes will display a mixture of permanent and elastic extension.  The first element of permanent extension occurs during the first hours of loading when the rope is subject to tensile loads significantly higher than generated during manufacturing. The resultant reduction in cross section area as the structure beds down leads to a permanent extension in length.  The second element of permanent extension, following application of a constant load is caused by molecular realignment within the yarn structure and is known as yarn

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creep. Yarn creep increases with mean load, temperature and time but is insignificant when considering polyester in most tether applications.  The third element of permanent extension is rope creep. Rope creep is due to physical damage of the rope structure through internal abrasion which allows further yarn and strand realignment within the structure, in effect creating increased compaction. Damage will increase with greater cyclic loadings. The primary element of visco-elastic extension is purely elastic. When the load is removed, the rope will recover the elastic element immediately. The secondary element is time dependent and non-linear. The table below is investigated by the equations in table (4-3). Table (4-4) the technical specification of the applied mooring cables [Ref. 23] Cross Minimum Weight Weight in Axial No. Diameter section Maximum breaking load in air seawater stiffness cable (mm) area length (m) (tons) (kg/m) (kg/m) EA (MN) (mm2) C1 500 132 13.3 3.4 13690 180 2160 C2 600 143 15.3 3.9 16067 210 1875 C3 700 153 17.3 4.4 18393 250 1660 C4 800 162 19.3 5.0 20620 290 1480 C5 900 173 21.9 5.6 23515 320 1300 C6 1000 181 23.9 6.1 25740 360 1200 C7 1250 206 30.6 7.8 33342 450 940 C8 1500 224 36.0 9.2 39424 550 800 C9 2000 256 46.7 12.0 51492 780 615

4.1.6.3 The converting of the mooring line to the non-linear spring

The mooring system provides a lateral supporting for the floating bridge. This lateral supporting represents by a two orthogonal forces. The vertical force represents by the submerge weight of the mooring line and the horizontal force represents by the horizontal force that is applied on the anchor in additional to the submerge weight component of the mooring line and the eventual friction force with the seabed. The values of these forces depend on several factors such as the water depth (h), the anchor position which represents the horizontal distance (X) and the submerge weight of the mooring line (w).

Figure (4-13) the deviation of the mooring line

For the global design requirements, we need to replace the mooring line by two orthogonal non-linear springs. Therefore, we have to consider each displacement separately. When the

TU Delft 128 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge pontoon moves horizontally with a displacement equal to (∆x), the horizontal distance to the anchor will change to (X+∆x) (see figure (4-13)) and that will alerts the value of the horizontal force H(X) to H(X+∆x). The procedure starts with the available information’s as follow:  The water depth (h)  The submerge weight of the mooring line (w) chosen from table (4-4).  The introduced wave force per each mooring line (H)  The designed maximum allowable horizontal displacement (∆Xd,max) which it is determined according to the global design requirements of the bridge.

H  K xx K xy x       V  K yx K yy y

H V K  K  h x v y

By applying this information in the equations of table (4-3), we can calculate the tension force in the mooring line (T), the required length of the mooring line (L) and the vertical force (V) of the mooring line on the bridge.

w (4-15) K  xx      w  h  2 Cosh 1 1       H   2  H    1      w  h  

The wave forces according to the linear theory

700

600 ]

m 500 / N k [ Rigid wall along the whole depth e 400 c r pontoon with opening o f

a e 300 pontoon without opening v a w

e 200 h T

100

0 39km/h 74km/h 180km/h wind speed (km/h)

Figure (4-14) the wave force / wind speed relationship for three different cases

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Figure (4-15) the tension force / length relation for mooring line C4 for a different water depth The choice of the mooring line from table (4-3) depends on the wave force of the extreme storm of 100-year (192kN/m), the maximum length, see table (4-5), and the mooring line density:

Tmax lm  (4-16) Fwave lm = the distance between two mooring lines along the bridge.

Table (4-5) mooring line density

Wave The cable Mooring line Required force No. density l (m) Length L (m) (kN) m

C2 31 1852 C3 27.5 1642 86.3 C4 25 1469 C5 21,5 1287 C6 20 1190 C2 16 1855 C3 14 1633 167.6 C4 13 1476 C5 11 1284 C6 10 1173 C2 7 1840 C3 6 1604 377.31 C4 5,5 1440 C5 5 1298 C6 4.5 1179

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The difference between the maximum breaking load and the design load determines the safety factor and the maximum allowable deviation. If the pontoon moved, the horizontal load will increase sharply. Therefore, the choice of the mooring line diameter depends on the maximum allowable horizontal displacement of the bridge.

By using the cable C4 for the wave force (167.6kN) @ 10m for both side we obtain the following:

The required length = 1294.6 =1295 m If we move the pontoon (1mm) to the right side, for example, the horizontal force of the left line will increase 3.7kN and the force in the line on the right side will decrease 1.5kN. The total force difference is (5.2kN). The initial stiffness is Kh = (5.2/0.001) = 5200 kN/m.

To determine the maximum allowable displacement, we repeat the same procedure until we reach the maximum breaking load see table (4-4). With the preceding calculations, the derivation of the non-linear spring equation of the mooring line becomes very simple: H H X  x H X  H X  x H X  K    (4-17) h x x X  w H X   (4-18) 1  w.L  sinh    H X  X  x.w X  x.w H X  x  H X  x  1  w  L  1  w  L  sinh   sinh    H X  x  H X  x

Table (4-6) the non-linear spring modulus of the mooring line H(X+∆x) ∆H left ∆H right ∆x(m) (kN) (kN) (kN) Kh[kN/m] 0 1676 0 0 0 0,001 1680 3.736 1.5 5236 0,01 1704 27.9 24.4 5228 0,1 2021 345 211.5 5565 0,2 2730 1054 359.5 7067 0,3 6508 4832 470.3 17674 0,31 8924 7248 460.5 24865 Exceeds the max. break load 0,32 25780 24000 1226 78830 (800Tons = 8000kN) see table (4-4) mooring line C4

From eq. (4-14), we notice that the value of the horizontal force (H) is already exited in the hyperbolic term, which causes the non-linear relationship between the horizontal force (H) and the horizontal distance (∆x), and this relation will create a non-linear horizontal spring. To solve this equation we have to use the trial and error method to obtain the real value by substitution of several values of the horizontal deviations as shown in figure (4-16). The balance case is that the substituted H(X+∆x) is equal to the quotient.

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Figure (4-16) the horizontal multi- deviation of the mooring line Final report Mega Floating Concrete Bridge

The initial value of the horizontal spring is determined by move the pontoon just (1mm) horizontally. One mooring line horizontal force will increase, the other one will decrease, and the resultant represents the summation of the deviations of both forces. By dividing the resultant by (1mm) we will obtain the initial spring modulus of the couple mooring lines.

By substitution of this value in the eq. (4-9), we will get the maximum horizontal deflection. The second step is to replace the spring modulus by the real value according to the table (4-3).

We should notice the following:  This method neglects the elastic and plastic extension of the mooring line.  This method neglects any erection mistakes, which has a large influence on the spring modulus value.  The maximum allowable displacement of the mooring line proportions inversely with its length.  The maximum allowable displacement (∆Xmax) is defined as a maximum displacement to break the mooring line.  The factor of safety can be calculated by dividing the breaking load of the cable on the maximum applied load H(X+∆Xd,max).

The factor of safety = The minimum breaking load / H(X+∆Xd,max) X Alternatively: The factor of safety = max X d ,max

The non-linear stiffness modulus of the mooring line

90000

) 80000 m / m / 70000 N k (

s 60000 u l u

d 50000

o The non-linear stiffness m 40000 modulus of the mooring s

s line e

n 30000 f f i t

s 20000 s

e

h 10000 T 0 0.001 0.01 0.1 0.2 0.3 0.31 0.32 The pontoon sway (m) Figure (4-17) the non-linear spring of the mooring line

Table (4-6b) the wave forces for different cases due to a different wind speed The wind speed km/h 180 74 39 Rigid wall [kN/m] e 590 156 49.5 c r

Pontoon without opening o [kN/m] f 192 83 39.5

e

Pontoon with opening v [kN/m]

a 159.4 70 31

Rule of thumb W [kN/m] 205.7 89. 5 43

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Example:

In order to design the mooring line for the floating bridge to introduce the wave forces that define in the table (4-6b), we have to start with the extreme wave force. The mooring line density and the cable diameter from table (4-3) are chosen according to the design requirements. For the wave force of (192 kN) we shall calculate the following:

Given:

Water depth (h) = 25m Cable type = C4 Cable submergible weight (w) = 50N/m Mooring line density (lm) = 1@10m

Solution: Using the equations in the table (4-3) to determine the following:

The horizontal force (H) = the extreme wave force × the mooring line density = 191.9 × 10 = 1919kN The tension force (T) = H + w*h = 1919000 + 50*25 = 1920 kN 2T The cable length L  h 1 = 25*√ (2*1920000/50*25-1) wh = 1385.4m H  wL  The horizontal distance to the anchor position X  sinh 1   w  H  X = (1919000/50)* sinh-1(50*1385.4/1919) = 1385.09m

The vertical reaction of the cable on the pontoon (V) = w * L = 69.27kN

The spring modulus of the mooring line is calculated by using try and error concept. The reaction of the pontoon on the mooring line at (y = 0) is assumed theoretically to be zero.

When the pontoon moves in y-direction create the reaction from both sides as follows:

The left line: y1 = 1385.09–1385.15 = – 0, 06 m ∆H1 = 1919000 – 2144730 = –225730 N

The right line: y1 =1385.09 –1385.03 = 0, 06 m ∆H2 = 1919000 – 1751865 = 167135N

∆H = -∆H1 +∆H2 = - (- 225730) +167135 = 392865 N ≈ 39500*(10m) see table (4-6) (The 1-year windstorm wave force on one cable calculated for a 10m cable spacing)

H K  = (167135-(-225730))/0.06 = 6547.8 kN/m for one mooring line. h x

The equivalent spring modulus along the bridge = 6547.8/10 = 654.8 kN/m/m

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Because of the above shown analysis, we can conclude that the horizontal displacement y1 at the point of the mooring line connection generates a resistant equal to the summation of the horizontal force variation of all mooring lines.

4.1.6.4 The connection point of the mooring line /pontoon

Figure (4-12) the steel structure to connect the mooring cable with the concrete structure [Ref.26]

The mooring lines are designed to be able to carry very large forces in order to introduce the huge sea wave forces that act laterally on the floating bridge. These sea wave forces vary from (50 to 500) kN or more, per meter length of the bridge depending on the pontoon draft and the significant wave height. The mooring line force depends not only on the sea wave force but also on the distribution manner of the mooring line on the bridge (mooring line distribution density). It is easy to imagine the impact of bulkiness of the concentrated force of the mooring line on the pontoon walls. It has to be introduced the concrete safely without cracking or fracture failure regardless of the dynamic amplification of this force.

To eliminate the negative effects of the mooring line force on the floating bridge generally, we propose the following recommendations:

1 The mooring lines of both pontoon sides have to be connected at the same action line (against each other) to eliminate the load eccentricity. 2 The mooring lines should be distributed uniformly along the bridge in order to avoid the asymmetric response. 3 Steel crossheads should be used to connect two opposite mooring lines and should be built integrally in the transversal partition in order to distribute the force on a large area. See figure (4-12). This method is used either in the pontoon or in the concrete anchor. 4 Bearing springs and /or dashpots can be used in the connection point to moderate the amplification effects of the dynamic response. 5 Elastomer is recommended at the anchor connection point.

The design requirements of the steel cross head

The steel beams should be fixed inside the transversal internal walls and should be built integrally with it as mentioned before. This can be achieved by using headed studs that are already welded on the top side of the steel beam. These studs provide the required shear resistance that should be larger than the breaking load of the mooring line. In this manner, we

TU Delft 134 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge ensure the prevention of any fracture failure in the pontoon. The shear resistance of the stud is determined from the following equation according to the NEN-1994 (6.6.3) [Ref.29]:

2 8.0 fud 4/ Steel failure: PRd  (4-19)  v 2 .0 29d f ck Ecm Or: concrete failure PRd  (4-20)  v Taken the smallest value of the eq. (4-15) and eq. (4-16), with:

 hsc    2.0  1 for 3 < hsc /d < 4 and α =1 for hsc /d > 4  d  Where: γv = partial factor (1.25) d = the diameter of the shank of the stud, 16mm < d < 25mm 2 fu = the specified ultimate tensile strength of the steel of the stud < 500N/mm fck = characteristic strength of the concrete. Ecm = concrete modulus of elasticity.

4.1.7 Loads determination and load combinations

4.1.7.1 Loads determination The structure should be proportioned in accordance with the loads (traffic loads) and load combinations for service load design and load factor design outlined in the Euro code. Additional combinations must be considered which cause the higher eccentric torsion moment round the connections, except the floating portion of the structure which shall recognize other environmental loads and forces and modify the loads and load combinations accordingly.

Winds and waves are the major environmental loads, while water currents, hydrostatic pressures (including buoyancy), and temperature changing’s, abnormal loads (such as impact loads due to collision of ships with the floating structure), also have effects on the final design. Depending on the site conditions other loadings, such as tidal variations, marine growth (corrosion and friction), ice pressure, drift, earth pressure on mooring system such as dolphins, wind load, effects of waves (including swell), effects of earthquakes (including dynamic water pressure), effects of seabed movement, effects of movements of bearings, snow load, effects of tsunamis, effects of storm surges, ship waves, seaquake, brake load, erection load may need to be considered. In this report, the following loads will be considered:

 The traffic load

According to the Eurocode (EN 1991-2:2003 E), the traffic loads are represented by a uniform distributed load (qi) and tandem that has (350X600) mm contact area with the road for each wheel. The load model that is defined in this code should be applied for the design of bridges with loaded lengths less than 200m. Our case has no span limitation because it is a beam on an elastic foundation. The divisions of the carriageway into notional lanes should be made as the table (4-7). These divisions are made only for traffic loading determination and do not relate to the real road divisions in paragraph 4.1.2:

Table (4-7) number of lanes in the carriageway [ref.7]

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Carriageway width Number of notional Width of a notional Width of the (w) lanes lane (w1) remaining area w < 5,4 m N1 = 1 3 m w – 3m 5,4 m < w < 6 m N1 = 2 w/2 0 6 m < w N1 = int(w/3) 3 m w-3 x N1

The carriageway width (w) is the distance between the kerbs or the safety barriers as shown in the figure (4-3). The bridge is designed for two-way traffic. The carriageway on a bridge deck should be physically divided into two parts separated by a central reservation and then each part should be separately divided into notional lanes if the parts are separated by a permanent road restraint system. According to Euro-code, each part has to be loaded as shown in table (4-8).

[ref.7] Table (4-8) traffic load distribution on the lanes 1.2 m Location UDL (qi) Tandem (Qi) 2 2.0 Lane 1 9.0 kN/m 2 X 300 kN lane 3 m 2 2.5 Lane 2 2.5 kN/m 2 X 200 kN 2 1.0 2 kN/m m Lane 3 2.5 kN/m 2 X 100 kN lane 2 2.0 Other lanes 2.5 kN/m2 0 m 2 1.0 Remaining area 2.5 kN/m 0 lane 1 9.0 m kN/m2 2.0 m

Figure (4-18) axel load modelling [ref.7]

The number of the lanes in each direction = int [((bridge width – 2*(safety barrier) – middle strip)/2)/width of the notional lane] = int [((22.6 – 2*1.41-0.8)/2)/3m]= 3 lanes

The traffic load in Lane (1) has to be applied on all lanes in three different cases to determine the hull moment.

 The hydrostatic load

The buoyancy is computed by the integration of hydrostatic pressure. The specific weight of seawater may be taken to be 10.09 kN/m3 or 1.03 t/m3. In the design of very large pontoon floating structures, the change in water level due to tide, tsunami and storm surge may dominate the design loads when the structure is designed with a fixed vertical position relative to the seafloor. Since the point of action of buoyancy depends on the tide and water level, the most unfavourable case will be considered.

The following procedure determines the hydrostatic pressures and the forces acting on the floating structure see the figure (4-19) for details:

P = ρw*g*h

2 P = water pressure in (N/m ). 3 Ρw = water density (kg/m ) 2 g = gravity acceleration (m/s ) h = water head (m).

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Fh = ρw*g*d*(d/2) per unit length of the bridge. Fv = ρw*g*d*b per unit length of the bridge. Figure (4-19) hydrostatic pressure on a pontoon d = bridge draft b = bridge width.

 The current load The current load is the load that acts on the structure due to the water flow and it is similar to the wind flow force in the calculations and assumptions so that the structure must be static. The static load on a relatively large floating object can be determined by means of the momentum that is transferred. For the static load, we find: 1 F   C  A 2 …………………………… (4-21) c 2 w s

Where: ρw = the water density. Cs = shape coefficient (1 for rectangular construction). A = the submerged area of structure, perpendicular to the stream direction. v = water current velocity.

 The collision load

It is important to take into account the possibility that the surface structure can be a sailing ship. We discuss a method to determine the acceptable load. We can determine the maximum acceptable load by taking a quantity to kinetic energy.

Fcollision = k.Δx = √ (2*k*Ekin.max )

Where: k = Structural stiffness = 3 MN / m Δx = the deflection due to Fcollision 2 Ekin.max = the kinetic energy = ½ * ms * vs * Ch*Ce*Cs*Cc vs = acceptance speed = 3 m / s ms = mass indicative ship assumed 200 tonnes Ch = Hydrodynamic coefficient Ce = Eccentricity coefficient Cs = Softness factor Cc = coefficient of configuration

The hydrodynamic coefficient Ch: Calculate the effects of the moving mass of water with respect to the mass of the ship. For Ch applies as on approximation: Ch = 1+ Draft/ Base The underwater volume is 200 m3. On this basis, we estimate: L = 20m; B = 5m; D = 2m the Ch becomes: (1.4).

Eccentricity coefficient Ce: The eccentricity coefficient takes into account the energy dissipation caused by the ship during collision. In the case of collision, in the decisive event, where is no break. We can make (Ce =1 upper approximation).

Softness factor Cs:

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The coefficient of elasticity, the hull will be charged. When there is a relatively weak consumption structure, the influence of the hull negligible: (Cs = 1). For rigid structures will be approximately (Cs = 0.9) amounts. We appreciate Cs = 1 (upper approach).

The configuration coefficient Cc: The configuration, the coefficient of friction in hydrodynamic account, there arises, as it were a water-absorbing cushion between construction and ship just before the moment of collision. Cc will take values between 0.8 and 1.0. We assume Cc = 1 (upper approximate).

 The wind load: (see Chapter 3 section 3.1.3)  The sea wave loads: (see Chapter 3 section 3.5)  The mooring system loads: (see Chapter 4 section 4.1.6) 4.1.7.2 Load combinations

Six loading conditions have to be considered:

1. Dead weight of structure. 2. Dead weight and local traffic load. 3. Dead weight, unsymmetrical local traffic load and wind/wave load of 1- year windstorm. 4. Transverse loading including current load, sea wave load and wind load of 20-year windstorm. 5. End damaged condition. 6. Transverse damaged condition.

Load combinations on the pontoon elements:

For the local design of the pontoon elements, we consider the following combinations: 1. Internal wall: the hydrostatic pressure of one compartment flooding. 2. External wall:  The hydrostatic pressure of the whole pontoon depth.  The hydrostatic pressure of the draft + current load + sea wave pressure of the extreme wind storm 100-year.  The hydrostatic pressure of the draft + current load + wind pressure of the extreme wind storm 100-year. 3. Bottom slab: the hydrostatic pressure of the whole pontoon depth. 4. Top slab: the euro code defined traffic load combinations.

Load distributions cases:

The behavior of the bridge is influenced not only by the load value but it is also affected by the load distributions. The following cases are applied on the floating bridge:

. Concentrated load is applied on the middle of continuous beam. . Concentrated load is applied on the middle of the freely connected sires of discrete rigid beams. . Concentrated load is applied on the all connectors of the freely connected sires of discrete rigid beams. . Concentrated load is applied on the different connectors of the freely connected sires of discrete rigid beams to investigate the load influence zone.

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. Applying the uniform distributed load (UDL) on the whole bridge. . Different length of UDL applied on the middle of continuous beam. . Different length of UDL applied on the middle of the freely connected sires of discrete rigid beams.

Potential damage:

A floating bridge must have adequate capacity to sustain safely potential damage resulting from small vessel collision, debris or log impact, flooding and loss of a mooring cable or component. Considering only one damage condition and location at any one time, the pontoon structure must be designed for at least the following:

1. Collision: Apply a 45kN horizontal collision load as a service load to the pontoon exterior walls. Apply a 130kN horizontal collision load as a factored load to the pontoon exterior walls. The load may be assumed to be applied to an area no greater than 0.3x0.3 m.

2. Flooding:  Flooding of any two adjacent exterior cells along the length of the structure.  Flooding of all cells across the width of pontoon.  Flooding of all the end cells of an isolated pontoon during towing.  Flooding of the outboard end cells of a partially assembled structure.

3. Loss of a mooring cable or component. 4. Complete separation of the floating bridge by transverse or diagonal fracture. This condition should be applied to the factored load combinations only.

Every floating structure has unique and specific requirements. Maritime damage criteria and practices such as those for ships and passenger vessels should be reviewed and applied where applicable in developing damage criteria for a floating structure.

However, a floating bridge behaves quite differently than a vessel, in that structural restraint is much more dominant than hydrostatic restraint. The trim, list and sinkage of the flooded structure are relatively small. With major damage, structural capacity is reached before large deformations occurred or were observed. This is an important fact to note when comparing with stability criteria for ships.

4.2 Global design

 Introduction

The design procedure of the floating bridges, such as mentioned before, involves the local design procedure and the global design procedure which consist also of two processes, the static structural analysis and the dynamic structural analysis. In this section we will deal with the static structural analysis only. The dynamic analysis will be defined. Some of the basic information’s are required to be defined before in the beginning:

 Deflection and Motion

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Floating bridges should be designed to be comfortable for the traffic to ride on during normal storm (1-year storm) conditions and to avoid undesirable structural effects during extreme storm (20-year storm) conditions. Deflection and motion criteria have been used to meet these objectives. The maximum deflections and motions limits that are shown in table (4-9) for normal storm (1-year storm) conditions may be used as guidelines.

Table (4-9) the maximum allowable deflections [ref.3] Loading Condition Type of deflection Maximum Maximum or Motion Deflection Motion Vehicular load Vertical L/800 Lateral (drift) 0.3m Winds - static Rotation (heel) 0 .5 ̊ Vertical (heave) ±0.3m 0.5 m/s^2 Waves - Dynamic Lateral (sway) ±0.3m 0.5 m/s^2 Rotation (roll) ±0 .5 ̊ 0.05 rad/s^2

The objective of the motion limits are to assure that the people will not experience discomfort walking or driving across the bridge during a normal storm. The motion limit for rotation (roll) under the dynamic action of the waves should be used with care when the roadway is elevated a significant distance above the water surface. The available literature contains many suggested motion criteria for comfort based on human perceptions. A more-detailed study on motion criteria may be warranted for unusual circumstances. The following diagram shows the deflection value classification to comply with the design wind classifications. The floating bridge rigidity should be satisfying for the design requirements of the three motions.

Figure (4-20) the design limitation of the bridge motion

 Loads – motions combinations

Several loadings are described in section 4.1.7. These loads are acting on the bridge in different directions and different planes. The classification of these loads into their acting planes (in the same way of the motion classification) will simplify the study of the bridge response. That can be done by combining the loads with the motions according to the planes as it shown in table (4-10).

Table (4-10) loads- motions combinations Parallel* Perpendicular* Traffic Wind Current Reflected Degree of freedom Transmitted transmitted load load load Wave load wave load wave load Heave and Pitching + - - -/+ + -

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Swaying and Yawing - + + - - + Rolling + + + + - + * Parallel/perpendicular to the longitudinal axis (x –axis).

4.2.1 Structural modeling of a floating bridge

The continuous pontoon floating bridge can be modeled as discrete rigid beam segments connected end-to-end by a connector with a certain rotational stiffness. The beam on elastic foundation method typically can be used to form the deflection equation. Realistic load combinations for the traffic load and environmental load should be distributed in a way that can ensure the maximum deflection and /or the maximum internal forces as it described in section 4.1.7.2. The modeling of the floating bridge will be made according to the motion classification planes as follow:

4.2.1.1 Heaving and pitching motion (XZ-plane)

Heave and pitching motions represent the motion of the bridge in XZ-plane (see section 1.7.1), therefore; these motions are created by some of the vertical forces which act on the bridge such as the traffic load and the transmitted wave load especially when the wave excites the bridge in its longitudinal direction as it defined in table (4-10).

 Equation of motion in XZ- plane (Heave and Pitching):

Figure (4-21) modelling of the floating bridge motion in XZ - plane

A floating bridge motion in XZ – plane will be resisted statically by the pontoon flexure stiffness (EI) and the buoyancy force and dynamically by water damping and the deceleration of the bridge element mass and the added water mass. The vertical vibration of the bridge is governed by the dynamic equilibrium of the vertical forces, which act on infinitesimal element of the bridge. The w (x, t) is the vertical displacement of the bridge. In accordance with the Euler- Bernoulli theory of beams, this equilibrium reads:

 2 wx,t  4 wx,t wx,t m  a   EI  C   K  wx,t  F x,t (4-22) z t 2 z x 4 dz t buoyancy wave

The terms in Eq. (4-22) have the following physical meaning:  2 w(x,t) 1. (m  a )   the force of inertia. z t 2  4 w(x,t) 2. EI z   the force due to the bending stiffness. x4 wx,t 3. C   the water damping force. dz t

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4. K buoyancy  w(x,t)  the force imposed by the elastic foundation.

Where: m = mass of the bridge per unit length 2   b  az = added mass for the heave motion (see appendix A.1.1) =   2  2  EIz = flexure stiffness of the bridge in the longitudinal direction (full cross section).

Cdz = damping coefficient for the heave motion  2 (m  az ) Kbuoyancy 

Kbuoyancy = buoyancy stiffness modulus per unit length = ρw *b b = bridge width. ζ = shape factor

 The boundary conditions The boundary conditions are assumed to be as follows: - At (x = 0) we consider the bridge at this point as a free end and connected by a hinge with the access bridge that results in a free vertical motion and rotation so that the moment M = 0 and the shear force V = the reaction of the access bridge on the floating bridge:

2 2 EI z  w1 x,t/ x  0 3 3  w1 x,t/ x  Raccessbridge

- At (x = i. L) the connection points between the pontoons, the deflection (w), shear force (V) and the moment (M) should be the same at both pontoons except the rotation angles (θ) which depend on the connectors rotation stiffness (Kconnector):

L = pontoon length, i = 1, 2, 3, 4… n. (n) =pontoon number

wi (x,t)  wi1 x,t

wi x,t x  wi1 x,t x

2 2 2 2  wi wi1  EI z  wi x,t/ x  EI z  wi1 x,t/ x  K connector     x x  3 3 3 3  wi x,t/ x   wi1 x,t/ x

- At (x = n. L) the situation of the other end will be considered free end so that: 2 2 EI  wn x,t/ x  0 3 3  wn x,t/ x  Raccessbridge

From the beam example analysis, we noticed that the response of the free end is not only large in comparison with the other positions of the beam but it increases the response of the whole beam. The solution for this phenomenon is represented by applying dynamic forces on both ends of the bridge to restrict the response of the bridge at these points, which lead to response reduction for the whole bridge. The characteristics of the dynamic forces like a mass or a dashpot can resist the response in either a negative or a positive direction.

So-called stability pontoon, which has relatively a larger width and mass per unit length as well as the reaction force of the access bridge, can play a reasonable role in the response

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4.2.1.2 Swaying and Yawing (XY-plane)

The lateral displacement of the bridge can be occur due to several loading like the current load, wind load and the reflected wave load which it can excites the bridge in different length according to the angle of the incident wave with the bridge.

Normally, the waves are generated by the wind and incident the floating bridge in the same direction. When the direction of these forces coincides with the direction of the water current force direction, the critical case will occur especially when the resultant of these forces concentrates on the connectors which they represent the weak points on the structure. Those lateral forces will be introduced by the mooring system and the connector’s spring rigidity round the z-axis (Yawing).  Equation of motion in XY- plane (Swaying and Yawing):

The motion of the bridge in the XY-plane is excited mainly by the sea waves as well as the wind force and the water current. The bridge resistance in this direction is represented by the inertia force, flexure rigidity, water damping and the non-linear mooring springs. The horizontal vibration of the bridge v(x, t) are governed by the dynamic equilibrium of the horizontal forces, which act on infinitesimal element of the bridge The equation of motion can be written as follow:

Figure (4-22) modelling of the floating bridge motion in XY- plane

 2vx,t  4vx,t vx,t m  a   EI  C   K  vx,t  F x,t (4-23) y t 2 y x 4 dy t mooring wave

Kmooring = spring modulus Kh of couple mooring line /distance between the lines (lm) m = mass of the bridge per unit length. Cdy = damping coefficient for swaying motion. EIy = flexure stiffness of the pontoon round Z-axis. 2   d  ay = the added mass for the swaying motion (see appendix A.1.1) =    2  2  d = the draft [m].

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 The boundary conditions

The start point of the bridge represents by the connection point of the bridge with the access bridge. This connection cannot be stiff enough to restrict the horizontal motion of the bridge. Therefore, both ends of the bridge have to be supported by pair of piles or dolphin frame guide which allows only the vertical motion.

-At (x = 0):

v1 x,t  0 2 EI y  v1 x,t  0 3  v1 x,t  Rdolphin

-At (x = i. L)

vi (x,t)  vi1 x,t 2 2 EI  vi x,t  EI  vi1 x,t  K connector  vi  vi1  3 3  vi x,t   vi1 x,t

- At (x = n. L) the situation of the other end will be considered free end so that:

vn x,t  0 2 EI y  vn x,t  0 3  vn x,t  Rdolphin

4.2.1.3 Rolling (ZY-plane)

Rolling occurs due to an eccentric load such as the eccentric traffic load, current load, wind load, reflected wave load and the parallel-transmitted wave force. The ψ (x, t) is the bridge rotation, which can be written as follow (see eq. (2-6)):

 2x,t  2x,t x,t m J  a   G  J   C   k x,t  m x,t (4-24)  2t t 2 x d t  

Where: m = mass of the bridge per unit length J = polar moment of inertia aϕ = added mass for the roll motion (see appendix A.1.2) Jt = Torque constant (section 4.1.5) G = Shear modulus Cdϕ = damping coefficient for the heave motion (see appendix A.1.2) kϕ = hydraulic spring modulus (see appendix A.1.2)

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Figure (4-23) the loading of the rolling motion

The torque mϕ = R traffic *at + R wave * a wave +R current *ac +R wind * a wind +R wave2*a wave2

Table (4-11) boundary conditions X = 0 X= i*L X = n*L

W(x) W(0,t) ≠ 0 Wi(x) = wi+1(x) Wn(x) ≠ 0 g

n e i θ(x) θ(0,t) ≠ 0 θi(x) ≠ θi+1(x) θn(x) ≠ 0 ) v h a c Z d t

e M(x) M(0) = 0 Mi(x) = Mi+1(x) Mn(x) = 0 i n X H a P ( V(x) V(0) = R access bridge Vi(x) = Vi+1(x) Vn(x)= Raccess bridge

W(x) W(0,t) = 0 Wi(x) = wi+1(x) Wn(x) = 0 g g n i n )

i θ(x) θ(0,t) ≠ 0 θi(x) ≠ θi+1(x) θn(x) ≠ 0 y

Y a w d

a M(x) M(0) = 0 Mi(x) = Mi+1(x) Mn(x) = 0 X w n

S a Y ( V(x) V(0) = R dolphin frame Vi(x) = Vi+1(x) Vn(x)= Rdolphin frame 4.2.2 Hydro-static analysis The traffic load consists of two parts the UDL and the axels load. When the UDL is applied on the total bridge, a uniform settlement will occur and that will only increases the hydrostatic pressure on the bottom slab and the external walls. Only the differential settlement in the bridge can creates internal forces in the longitudinal direction of the bridge. That can be happened when we apply a concentrated load or UDL for a certain distance. Applying both type of the traffic load in different distribution ways and considering also both cases of freely and rigidly connected pontoons will assist us to get the critical situation. If we combine these cases with the perpendicular transmitted wave load we will get the real critical position especially when the position of the wave trough coincides with the maximum deflection due to the traffic load.

In the global design we will consider the whole bridge as several beam segments (pontoons) hinged end-to-end. The hinge can be have a variable rotational stiffness (Kconnector) ranged from 0 to (EI = pontoon flexure rigidity). In the Maple sheet we use the factor fa (01) to find out the Kconnector where:

Kconnector = fa * EI

The beam flexure rigidity EI is calculated in the local design section. The global moment of inertia of the pontoon has to be considered in the flexure rigidity. The applied loads are three types:

1. The concentrated traffic load (F): represents the passing the vehicle axels (defined in section 4.1.7.1) on both carriageways at the same transversal line or in another word at the same point on the bridge.

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F = 2*(2*300 + 2*200 + 2*100) = 2400 kN

2. The traffic UDL (qmax ): the applying of all UDL on both carriageways at the same time can be replaced by the following magnitude:

qmax = 2*3*9 + (22.6-2*1.41-2*3) *2.5 = 54 + 34.5 = 88.5 kN per meter length

3. The sinusoidal wave load (qwave): applying the extreme wind storm of 100-year storm (180km/h) as a critical case in the longitudinal direction of the bridge and the resulting sea wave is applied as sinusoidal distributed load which it has a maximum pressure :

Awave = ½ (Hs) * sea water density (ρw)* g* pontoon width (W) = ½*9.81*1030*22.6*Hs qwave (x) = Awave *sin (2π x/Lwave) = 114.18*Hs*sin (2π x/Lwave) kN/m

The structural analysis bases on the static response determination by using equation (4-22). The water damping (third term) and the inertia force (first term) will be neglected here. The bridge will be analyzed statically as a beam on an elastic foundation and modeled as shown in figure (4-24). Solving eq. (4-22) after omitting of the first and the third term (dynamic terms) and substituting the boundary conditions described in section 4.2.1.1, are made by assistance of the Maple mathematic software (see Appendix). In this structural analysis we will consider only the Heave and Pitching motion and by applying the above-mentioned loads in different cases we can reach to the following results:

Figure (4-24) bridge analyses model

1. Applying the force F on the hinge every two pontoons (Kconnector = 0): the settlement of every hinge under this loading case, when there are no rotational resistance, shows an uplifting of the in between hinge. The maximum deflection is at the two ends.

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0;Lcharacteristic=426m no.1 N k

0 0 4

2 = F

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e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

2. Applying the force F on the hinge every two pontoons (Kconnector = EI): when the rotational resistance of the connections equal to the bending rigidity of the pontoon for the same loading case, we will notice a large reduction in the settlement with a uniform value for all hinges except the two ends.

18 2 Case Lpontoon=50m; EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector =EI; no.2 Lcharacteristic=426m N k

0 0 4 2 = F

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

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3. Applying the force F on the hinge every four pontoons (Kconnector = 0): it is necessary to study the maximum deflection under one individual axel load and its influence range when the connector stiffness = 0.

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0;Lcharacteristic=426m no.3 N k

0 0 4 2 = F

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

4. Applying the force F on the hinge every one pontoon with (Kconnector =0): applying the axle load on all hinges shows a uniform deflection except at the two ends.

18 2 Case Lpontoon=50m;EI =4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0;Lcharacteristic=426m no.4 N k

0 0 4 2

= F

e v r u c

n ) o i t m c e m l ( f e d

e h T

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m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

5. Applying the force F on the hinge every pontoon with (Kconnector = EI): the use of stiff connectors reduces the deflection at the ends only with a large internal moment reduction.

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector= EI; no.5 Lcharacteristic=426m N k

0 0 4 2

= F

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

6. Applying the force F and qmax on the hinge every pontoon with (Kconnector = EI):

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector= EI; no.6 Lcharacteristic=426m

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N 5 . k

8 0 8 0 =

4 x 2 a

m = F q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d e c ) r N o ( f

r m a a e r h g s

a i e d h T

7. Applying the force F and qmax on the hinge every pontoon with (Kconnector = 0):

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0; Lcharacteristic=426m no.7 N k

N 5 . k

8 0 8 0 =

4 x 2 a

m = F q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

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e c ) r N o ( f

r m a a e r h g s

a i e d h T

8. Applying the qwave on every pontoon with (Kconnector = EI) and wave length smaller than characteristic length: The sea wave loading is created by the extreme windstorm in the longitudinal direction of the bridge. Using Bretschnieder method to determine the wave characteristics with a fetch equal to the bridge length (2000m):

18 2 Case Lpontoon= 50m; EI=4.818×10 N/mm ;Kbuoyancy= 0.228N/mm/mm ; Kconnector= EI; Lcharacteristic= no.8 426m; Hs = 2.07m, Ts = 4.7 sec; windstorm = 180km/h

x

π 2 ( n i s 5 . 9 4 N 1 k

) = e

v e a v a w w L q / ) m m (

e v r u c

n o i t c e l f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

9. Applying the qwave on every pontoon with (Kconnector = 0) and wave length = pontoon length:

18 2 Case Lpontoon= Lwave =50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0; no.9 Lcharacteristic=426m

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=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

10. Applying the qwave on every pontoon with (Kconnector = 0) and wave length > pontoon length: Wave load wave length > pontoon length, rigid pontoon +free connector

18 2 Case Lpontoon= 50m < Lwave ;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0; no.10 Lcharacteristic=426m N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T

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m t n m e - m N o ( m

m e a r h g T a i d e c ) r N o ( f

r m a a e r h g s

a i e d h T

The short wave (shorter than the characteristic length) causes a larger ends response as it shown below.

Bridge deflection for different wave lengths

4.2.2.1 Pontoon stiffness influence

The global stiffness of the pontoon has a large influence on the global response of the bridge exactly as the other beams on elastic bedding that can be shown in the figures below, which represents the applying of the same traffic loads on the same beam length and width with different flexure stiffness. Increasing the flexural stiffness of the pontoon will result in an increase of the radius of curvature and eliminate the large vertical displacement under the concentrated load.

h t d g a n o l e

l

c i f m f / a N r t k

e 5 h . 8 T 8

e v r I u c E

) n = o m s i s t m c e

e 2 n l f f 2 ( f e i d t

s e h T

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e I v r E u 1 c

. ) 2 n 0 o m m i = t s m c

m s e / 0 l e f 9 n ( N e f d f

i e t h s T

e I v r E u 1 c

) 0 . n m 0 o i t m = c s 0 e s l 2 f e 2 e ( n d f

f e i t h s T

4.2.2.2 Pontoon connector stiffness influence

The connector moment will be equal to the difference in the rotation of to adjusted pontoon multiply by the linear rotation stiffness of the connector.

M connector  Kconnector (i1 i )

 The connection moment effect

In the continuous pontoon bridge, the pontoons are connected by partially rigid connections, which cause moments at both ends of the pontoon.

Continuous pontoon bridges consist of several pontoons with (L) length and bending stiffness (EI), buoyancy stiffness modulus (k) and the rotational stiffness of the connection (Kconnector). A concentrated load (F) or UDL (q) at the middle connection exposes the bridge. The deflection curve is determined by assistance of the Maple software as shown below. The pontoon behaves as rigid body and remains a straight line because of two reasons. The first reason is using a pontoon length less than the characteristic length and the second one is using a very small value of Kconnector /EI.

Firstly, the bridge will behave as a continuous beam when Kconnector /EI equal to one. In this case, the relative deflection will be minimized. When the connectors’ stiffness is reduced, the deflections under the connectors and at the ends are increased sharply.

 Response conceptual analysis

The response of the floating multi-discrete rigid body in either the XZ- plane or XY- plane can be defined by the term of the relative displacement of the connectors which it means the deviation a connector with respect to the straight line that passes through the two adjacent connectors as it is illustrated schematically in figure (4-25).

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Figure (4-25) relative displacement definition

The relative displacement determines the rotation in the connector (θ) which is responsible about the generation of the connector moment. The rotation value is proportion directly with the relative displacement and inversely with the pontoon length. The connector moment (Mc) is equal to the connector rotational stiffness (Kconnector) multiply by the created angle of rotation (θ) between two pontoons.

2  w  w  w    2 1 3 (4-25) L

M connector  K connector  (4-26)

0.12 The relative displacement (w) θ 0.1 100mm 200mm 0.08 300mm 400mm 0.06 500mm 600mm 700mm 0.04 800mm 900mm 0.02 1000mm

0 10 20 30 40 50 60 70 80 90 100

The pontoon length(m) Figure (4-26) the pontoon length, pontoon rotation and connector relative displacement relationship (w = 2*w2-w1-w3)  The maximum allowable deflection to the pontoon connector stiffness relation The maximum allowable deflection of the floating bridge has to be limited for different reasons. The deflection limitation is responsible for the global stability of the bridge, the general safety and the control of the internal forces. The compliance of the pontoon connectors introduces the large loading pressure or the impulse loading. It is responsible about the absorption of its effects and mitigates the internal forces. The determination of the maximum allowable deflections depends on the rigidity of the pontoon connectors because of the considering the pontoon as a rigid body. Therefore, the total deflection is represented by the summation of the connectors’ deflections (cumulative deflection). The deflection curve can be considered as a second degree curve between two zero deflection points. w (x) = a. x2 a = maximum allowable deflection / (L/2)2

 The connector/pontoon stiffness influence on the deflection Applying a concentrated load on a continuous beam will create to a certain deflection. This deflection will increase sharply if there is a hinge under the load. Between those two

TU Delft 155 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge conditions, the deflection will vary according to the rotational stiffness of the hinge. The discrete beam will be behave as a continuous beam when the logarithm of connector / pontoon stiffness ratio is between (0 → -3) and it will behave as a discrete beam when this ratio is between (-8 → -18) as shown in figure (4-27b). These limitations are valid for all load cases.

Figure (4-27a) the pontoon connector stiffness effect 14 2 Log Lpontoon= 50m ;EI=3.75×10 N/mm ;Kbuoyancy=0.228N/mm/mm ; (connector / pontoon The axle load (F)= 2400kN stiffness)

0

-3

-8

-18

The critical zone of the connector stiffness

400

350

300 )

m 250 m (

n

o 200 i t c e

l deflection(mm) f

e 150 d

100

50

0 0 -1 -2 -3 -3.5 -4 -5 -6 -7 -8 -8.5 -9 -10 -11 -12 -14 -16 -18 Log (connector stiffness/pontoon stiffness) Figure (4-27b) the critical zone of the relative connector stiffness with respect to the deflection

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the relation between the angle of rotation to the log of the connector stifness to the pontoon stiffness 0.02

0.018 n e

e 0.016 ) i w t h e

p 0.014

b

a t n l 0.012 e o i d t ( a

t 0.01 phi s o r n

f

o 0.008 o o

t e l n 0.006 g o n p a

0.004 e h

t 0.002 0

0 1 2 3 5 4 5 6 7 8 5 9 0 1 2 4 6 8 - - - . - - - - - . - 1 1 1 1 1 1 -3 -8 ------Log(connector stiffness/pontoon stiffness)

Figure (4-27c) the critical zone of the relative connector stiffness with respect to the rotation

4.2.2.3 Mooring system stiffness influence

 The Anchor position:

The water depth - Horizontal distance(X) relation for different cables and constant horizontal force H=200 Ton

2400

2200 ) m (

n

i 2000 w=34N/m e c

n w=39N/m

a 1800 t s

i w=44N/m d

l

a 1600 w=50N/m t n

o w=56N/m z i

r 1400 o H 1200

1000 20 30 40 50 The water depth (m) Figure (4-28) water depth/horizontal distance relationship for different mooring lines

The mooring lines from both sides support the floating bridge laterally. These mooring lines have a catenary shape, which applies two orthogonal forces at the connection points. The flat catenary applies a large horizontal component than the sharp one and in the same time, it will be stiffer against the motion. In order to optimize the mooring system it is recommended to use the equation in table (4-3) which provides a very high horizontal distance to the anchor position with respect to the water depth.

Additional factors can influence the distance represented by the submerged weight of the mooring line (w). The figure (4-28) shows the relation between the horizontal distance to the anchor position (X) and the water depth for a constant horizontal force (H). The diagram shows also the effect of the submerged weight of the cable by illustrating cables with different diameters.

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The mooring lines distributions for different wave forces and cable diameters

35

30 ) m (

g 25 n i c

a 86,268

p 20 s

e 167,623 n i

l 15

377,310 g n i r 10 o o M 5

0 C2 C3 C4 C5 C6 Mooring line symbol

Figure (4-29) the mooring line distributions for different wave forces and cable diameters

Figure (4-30) the wave pressure along the depth for different wavelength

 The global analysis of the mooring system

The continuous pontoon floating bridge can be analyzed XY-plane motion according to the equation of motion (4-23) which can be simplified to consider flexural stiffness and the non- linear horizontal mooring line spring only. The loading can be considered in different combinations. The wind-wave loading is the most important combination. By applying the three design forces of the sea wave on the entire length of the bridge in combination with the wind forces, we obtain the following result of the maple sheet:

The wind –wave force attach the bridge

The applying of the static sinusoidal wind-wave force is equal to:

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      2  x   q   F sin   F sin wind wave wave L wind   wave     cos  Where ϕ represents the angle between the bridge and the wind-wave direction

The non-linear stiffness modulus of the mooring line

90000

) 80000 m / m

/ 70000 N k (

s 60000 u l u

d 50000 o The non-linear stiffness m 40000 s modulus of the mooring s

e line n

f 30000 f i t s s

20000 e h

T 10000

0 0,001 0,01 0,1 0,2 0,3 0,31 0,32 The pontoon sway (m)

19 2 Case Lpontoon= Lwave =50 m; EI=2.34×10 N/mm ; Kmooring= 654.8 kN/m/m ; Kconnector= EI; no.1 Lcharacteristic= 426 m; Wind storm 1-year (39 km/h); wave force = 39.5 kN/m; wind force = 3.52 kN/s.m; ϕ= 90o e v a w - d n i w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

19 2 Case Lpontoon= Lwave =50 m; EI=2.34×10 N/mm ; Kmooring= 779.4kN/m/m ; Kconnector= EI; no.2 Lcharacteristic= 426 m; Wind storm 20-year (74 km/h); wave force = 82.6kN/m; wind force = 11.43kN/s.m

TU Delft 159 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

19 2 Case Lpontoon= Lwave =50 m; EI=2.34×10 N/mm ; Kmooring= 872.1kN/m/m ; Kconnector= EI; no.3 Lcharacteristic= 426 m; Wind storm 100-year (180km/h); wave force = 192kN/m; wind force = 67.65kN/s.m N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

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e c ) r N o ( f

r m a a e r h g s

a i e d h T

19 2 Case Lpontoon= Lwave =50 m; EI=2.34×10 N/mm ; Kmooring= 872.1kN/m/m ; Kconnector= EI; no.4 Lcharacteristic= 426 m; Wind storm 100-year (180km/h); wave force = 192kN/m; wind force = 67.65kN/s.m; the extreme sea wave only on the middle pontoon N k

=

e v a w q e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

4.2.5 Hydro-dynamic analysis

Floating structures are dynamically charged by wave. This may be cause an excitation of the structure. It is important to give more attention to the dynamic loads due to wave, because in certain circumstances, the movements can take extreme forms, which can result a possible collapse of the structure. This should be avoided.

 Excitation of waves in the bridge by harmonic sea wave:

It is necessary to understand how harmonic waves propagate in the bridge. We excite the bridge by the harmonic sea wave as in eq. (4-27):

w x , t   Aˆ exp i  t   x  (4-27) Where:

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A = the wave amplitude. Ω = the wave frequency = 2π/T. γ = the wave number = 2π/λ = (k in chapter 3). λ = the wave length (m)

Substituting of eq. (4-27) into the equation of motion (4-22), will obtain the following dispersion equation for the flexural waves in the beam on elastic foundation: 2 4    m  a   EI  i  C d  K  0  C (4-28)   2   4  4  i d   2  0 m  a  o

2 4 In which ω o = K/ (m + a) is the cut-off frequency and α = EI/ (m + ɑ). In accordance to the dispersion equation (4-28) the wave number γ depends on the wave frequency Ω as follows:

1 2 Cd 2    4   i  (4-29) 4,3,2,1  m  a o Where: 1 1 4 4 1  2 Cd 2  2 2 1  2 Cd 2  2 2 1   i o  ,if o 2   i o  ,if o   ma    ma 

1 1 4 4 1 1i  2 Cd 2  2 2 1 1i 2 Cd 2  2 2 1    i o  ,ifo  2    i o  ,ifo    2  ma    2  ma  1 1 4 4 i  2 Cd 2  2 2 i  2 Cd 2  2 2  3   i o  ,if  o  4   i o  ,if o   ma    ma  1 1 4 4 1 1i  2 Cd 2  2 2 1  1i  2 Cd 2  2 2  3    i o  ,ifo    4    i o  ,ifo    2  ma    2  ma 

Using maple sheet to draw the quotient of eq. (4-29) which has two real values (γ1& γ2) and two imaginary values (γ3& γ4) as show in the figure (4-31). The transition point of the curves represents the resonance status of the system when the wave frequency (Ω) is equal to the Eigen frequency (ωo) of the system (Note: the eq. (4-29) is drawn by using the values of the case in chapter 5).

The Eigen frequency in the Heave motion: K gb g  2    o 2 b m  az    b  bd    d  2  2  8 -1 = 9.81/ (5+3.1416*22.6/8) = 0.707  ωo = 0.841 s

When the wave frequency is smaller than the Eigen frequency, the real and imagine values of the wave number has two different values while those values approach each other when the wave frequency is larger than the Eigen frequency.

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Figure (4-31) wave number wave frequency relationship [Appendix c] 4.3 Prestressing design

The design of the concrete pontoon of the continuous pontoon floating bridge is not conventional procedure because of the typical properties of the loading on the bridge. The loading can be whether in the positive or negative direction at the same point. The uniform distributed load on the whole bridge creates no any internal force except the effect of hydrostatic pressure variation. The deflection variations or loading variations can create internal forces. For this reason, the moment capacity of the pontoon has to be symmetry and have the same value whether in the positive or in the negative direction at any point along the pontoon. This recommendation is valid whether in the XY-plane or in ZX-plane to ensure the global rigidity of the pontoon. The pontoon should be reinforced by centric prestressing cables in the longitudinal direction and in the four external faces of the pontoon. The serious issue in this design procedure is the existence of the prestressing cable in the compression zone. The initial prestressing stress should have a satisfied capacity to cover the shrinkage and relaxation losses and the stress losses due to concrete compressive strain. The following procedure represents the determination of the prestressing:

1. Stress losses due to concrete compressive strain in the linear phase = ϵ’c *Ep = 1.75*10-3 x 2*105 = 350N/mm2 2. Shrinkage and relaxation losses 15%.

4.3.1 The maximum moment capacity of the pontoon

4.3.1.1 Serviceability limit state

The linear deformation in the concrete and the prestressing steel should be considered to determine the cross sectional forces. The linear strain of the concrete should not exceed (1.75*10-3) while the maximum linear strain of the prestressing steel is (7.605*10-3). From those two conditions we can determine the minimum elastic compression zone depth of the concrete (xe) which can leads to large concrete deflection within the elastic phase. The elastic deflection of the concrete structure can be reduced by increasing the concrete compression zone depth (xe) which leads to increasing in the concrete force and the prestressing steel area. The minimum crack width and minimum deformation are the most important design requirements of the concrete pontoon which floating always on the water. Therefore, we shall choose a large concrete depth (xe).

The horizontal forces equilibrium of the cross section can be determined the relation between the (xe) and the prestressing steel area (Ap). Using the figure (4-33) to determine the relation between the (xe) and the strain of the prestressing (ϵp) according to the following equations:

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 d   x  ∆ϵ = '  p e  (4-30) p c    xe    x d '  '  e  p  ∆ϵ’p =  (4-31) c  x   e   x  t  ' '  e topflange   cof   c   (4-32)  xe 

Figure (4-32)  d  x  '  s e   s   c   (4-33)  xe 

Where: ϵ’c = the concrete elastic strain = 0.00175. ϵ’cuf = concrete strain under the flange. ϵs = conventional steel strain. ttopflange = top flange thickness. ∆ϵp = the strain of the tensile prestressing.

∆ϵ’p = the strain of the compressive prestressing. dp = the arm of the tensile prestressing steel at the positive moment. d’p = the arm of the compressive prestressing steel at the positive moment.

The strain of the prestress ∆ϵpmax is determined from the total elastic strain after the subtraction of the prestressing strain (ϵpw) which is calculated on base of %15 shrinkage and relaxation losses from the initial prestressing force (Fpi).

9.0  f pu .0 85 pi 9.0 1690 .0 851350 3 3 3  pmax  ptotal  pw    5  5  .7 60510  .5 737510  .1 8710 Ep Ep 210 210

Where: 2 fpu = 1690 N/mm . 2 Ep = the linear Young’s modulus of the prestressing steel =200000N/mm . σpi = 1350 N/mm2.

The substitution of these values in the equation (4-30) determines the minimum compression depth of the concrete (xe):

d p 7750 xe min   3  3749mm (4-34)  p max .1 867510 1 3 1  'c .1 7510 The area of the prestressing steel is determined according to the chosen value of (xe) which has to be more than (xemin) and the chosen strand diameter and cable size. To increase the bending capacity of the pontoon, it is necessary to use large prestressing steel quantity.

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Figure (4-33) the material strain values for the serviceability and ultimate limit states. ' f c 39 The concrete elastic modulus of elasticity Ec'elastic    22286 Mpa  c .0 00175 According to the preceding relation, we can calculate the forces of the steel and concrete from the horizontal equilibrium as follow:

Σ Fx = 0 Fpw + Ns + Σ Np - Σ N’p - Σ Nc = 0 (4-35)

Where:

Fpw = the total prestressing area (in tension and compression zones)* σpw

N’c = concrete force = Ec elastic *ϵc elastic *b * xe

Np = prestressing force in tension = Ap * Ep * ∆ϵp

N’p = prestressing force in compression = Ap’ * Ep * ∆ϵp’

Ns = conventional steel force = As * Es * ϵs -3 ϵc elastic = the elastic behavior of the concrete = 1.75x10 Ap = area of the prestressing cable. As = area of the conventional steel. b = the width of the concrete compression zone. xe = the depth of the concrete compression zone.

σpw = the stress in the prestressing after relaxation = 0.85* σpi. ∆ϵp’ = the strain in the prestressing due to the loading.

ϵs = the stress in the conventional steel.

The position of the Fpw is in the centroid of the total pontoon cross section area. The applied moment will creates stress variation in the prestressing in both sides. Therefore, these variations should be taken into account. The prestressing cable distribution and the cross section configuration of the pontoon should also taken into account in the accurate calculation of the moment capacity.

By solving the eq. (4-35), after some substitutions, we can determine (xe) which has to be larger than xemin in the equation (4-34).

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4.3.1.2 Ultimate limit state

The behaviour of concrete and the prestressing steel in the ultimate limit state converts totally or partially into the plastic deformation. The upper half of the concrete compression block deforms plastically and the strain reaches the maximum allowable concrete strain (3.5*10-3). The prestress steel takes another linear response stage. The maximum allowable stress is taken from the Dutch Norm NEN6720 and should not exceed (0.95*fpu). The maximum allowable strain is calculated as follow:

 f pu  9.0  f pu  1690 1521 2 E p2    6206 4. N / mm  pu  p.el.max   .0 035  .0 0076091

9.0  f pu  .0 95 f pu  9.0  f pu  1521 84 5.  p max    5   .0 0212 E p E p2 210 6206 4.

 9.0  f pu  pw   .0 95 f pu  9.0  f pu  373 5. 84 5.  p max    5   .0 0155 E p E p2 210 6206 4.  d  x   x  d '  ∆ϵ = '  p u  ; ∆ϵ’ = '  u p  p cu   p cu    xu   xu   x  t   d  x  ' '  u topflange  '  s u   cof   cu   ;  s   cu    xu   xu 

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Figure (4-34)

ϵp.el.max = the maximum elastic strain in the prestressing. xu = the depth of the concrete compression zone in the ultimate limit state. ds = the arm of conventional reinforcement. dp = the arm of the prestressing steel in tension. dp’ = the arm of the prestressing steel in compression. zb = the distance between the extreme compression fibre to the centriod of the prestressing steel.

ϵcof = the concrete strain in the bottom flange. -3 ϵu = concrete strain in the ultimate limit state = 3.5*10

Applying the forces values in the equation (4-35) determines the value of concrete compression zone depth (Xu). The moment capacity (Mu) is calculated from the moment equilibrium round the centriod of the pontoon cross section, which is in most cases in the middle because of the symmetrical necessity of the pontoon section:  M  0  h  t   h  t   pontoon topflange   pontoon bottomflange  M u  N'c armNc  N p    N' p     N pwalls  armNp   2   2   h   h  N arm N d pontoon  N' d' pontoon    pwalls   N 'p  s  s    s  s    2   2  Where:

∑∆Np-walls = the summations of the tension forces in all prestressing cables in the walls. ∑∆N’p-walls = the summations of the compression forces in all prestressing cables in the walls.

4.3.2 The maximum shear capacity of the pontoon

The shear capacity of the pontoon is determined according to the Dutch norm NEN6720. The shear force is carried by the longitudinal walls. The shear forces that are carried by the top and the bottom slabs are very small and can be neglected. The shear force that can be carried by the concrete is calculated from the following equations:

. . 1 ≤ 0. 4 fc + 0.15 σ´bm (4-36)

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Vd d = (4-37) b d . . . 2 = 0.2 f’c kn k (4-38)

Where: 1 = shear strength of the concrete. fc = the concrete tensile strength. σ´bm = the compression stress. Vd = the applied shear force. b = the width of the concrete cross section. d = the depth of the concrete cross section. 2 = maximum shear strength of the concrete. d = the applied shear stress.

4.4 Evaluation

It is recommended to use a high mooring line density on the pontoon nearby both ends of the bridge to reduce the large curvature and the internal moment.

The following results are obtained:

1. The deflection under the connection is higher the other location. 2. The deflection under the connection proportions inversely with the connector stiffness Kconnector . 3. The deflection under UDL proportions inversely with the length.

The results for these combinations can be briefly summarized as follow:

 The wavelength: deflection proportions inversely with the wavelength.  The wave height: the deflection increases directly with the wave height.  The pontoon flexure rigidity: however the pontoon length is shorter than the characteristic length, behaves the bridge segment (pontoon) as an elastic beam where the deflection is limited locally and relatively small but when we use a higher flexure rigidity, the deflection jumps to a higher level and spreads to a larger zone.  The connector rigidity: rigid connector reduces the deflection to the minimum and the free connector stiffness provides the maximum value.  The maximum deflection occurs at both free ends.  The superposition principles can be used to calculating the total deflection.  The large internal forces create under the axel load or at both ends of UDL.  The reduction in the distribution density of the concentrated load on the connectors increases the relative deflection and decreases the entire value of the deflection.

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5. Case study

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“The Case of a Floating bridge”

Figure (5-1) longitudinal cross section

 The bridge specification and collected data

Table (5-1) No. parameter Units value 1 Total bridge length m 2090 2 The traffic direction - 2 3 Lanes number per direction - 1 4 The pontoon length m 50 5 Water depth m 25 6 The sea bed topography - flat 7 Seabed soil bearing capacity kN/m2 sand 8 Extreme storm wind speed (100 year) km/h 180 9 The normal wind storm every 20 year km/h 74 10 The operational wind storm every 1 year km/h 39 11 The fetch distance km 100 12 The water current speed m/s 0.5 13 Tide variation m 2 14 The sea water quality - salt water 15 The freeboard m 3.0 16 The max. traffic velocity km/h 120 17 Concrete grade - C55/65 18 Pontoon top slab thickness mm 500 19 Pontoon bottom slab thickness mm 500 20 Pontoon external wall thickness mm 400 21 Pontoon internal wall thickness (longitudinal) mm 400 22 Pontoon internal wall thickness (transversal) mm 300

 The results specifications Table (5-2)

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No. parameter Units Symbol value 1 Bridge width m w 22.60 2 Buoyancy Stiffness kN/m /m k 228.36 3 Pontoon depth m d 8.00 4 The draft m d’ 5.00 5 Pontoon local inertia moment m4 I 203.44 6 Pontoon torsional inertia m4 J 1.696 7 Modulus of Elasticity N/mm2 Ec 38500 8 Shear Modulus N/mm2 G 19250 9 Water current force kN /m Fcurrent 0.644 10 Wind force (extreme) kN/m/sec Fwind 67.65 11 The pontoon characteristic length m lc 426 12 The torque constant mm4 Jt 7.589*104 13 Pontoon global inertia moment m4 Ixx 1824.6 14 Pontoon global inertia moment m4 Izz 375.45 15 The maximum deflection (traffic load) mm 16 The maximum deflection (wave load) mm

The methodology:

The methodology of design a mega floating structure is general difficult and need to much experimental information’s and assumptions. In our case and due to the large number of variables, we will try to simplify the design and calculation method to approach to real response of the floating bridge and we can summarize it as follow:

1. Determination of the wind speeds so that the entire design limitation will base on the environmental forces. 2. Global dimensioning of the bridge (section 5.1) depending on the side configurations such as the position of the abutments, design of the access bridges, max. traffic velocity, no. of lanes, freeboard and so on. 3. In section 5.2 is the hydrostatic analysis of the selected bridge dimensions. That includes the determination of the environmental loads, the mooring system and the concrete design of the pontoon. The sea wave force is calculated by considering no- move floating structure that results a force larger than reality due to the neglecting of the energy dissipating. 4. In section 5.3 is the static global structural analysis of the entire bridge without considering the dynamic effects and in two directions motion. Studying widely the effects of the following parameters:(bridge length-characteristic length- pontoon length- wave length- pontoon width- pontoon flexure rigidity- pontoon rotation rigidity-fixation of the free ends- internal forces) by using the maple software. Applying the Froude-Krilov method on individual pontoon to determine the response and compare it with static analysis to approach the real response. 5. In section 5.3.3 is the prestressing design of the pontoon for the ultimate- and the serviceability limit state according to the results of section 5.3. In additional to the connector design according to allowable rotation of the connector, the maximum expected vertical displacement results from section 5.3 and the ideal connector stiffness with respect to the pontoon rigidity.

5.1 Dimensioning

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The case description:

The case study of this thesis represents design of a floating bridge that can connect the island with the coast over a distance about two kilometers, see figure (5-1). The bridge crosses a sea with a sandy flat seabed. The average water depth under the bridge centerline is 25 m. The bridge connects two points with different elevations. The elevation of point A at the coast with respect to the normal sea level is 5m and the elevation of point B at the island with respect to the normal sea level is 9.5m. Access bridges have to be used to overcome the elevation difference between the abutment and the floating bridge. The inclination of the access bridge should be acceptable for the vehicles and not exceed 15%. The climatological data for the region is collected as follow (these values are chosen from Beaufort scale wind classification, table (3-1)):

Table (5-3) the design wind speeds Unit value The extreme recurrent wind storm 100-year km/h 180 The extreme recurrent wind storm 20-year km/h 74 The normal recurrent wind storm 1-year km/h 39 The tide variation m 2

5.1.1 Global dimensioning

The seabed profile

The seabed profile is one of the important requirements of the global dimensioning. It has to be taken exactly under the bridge centerline. The bridge length is determined according to the water depth and the minimum required clearance between the seabed and the bottom face of the pontoon. The maximum bridge length should not be exceeding the zone length in the seabed profile where the minimum required clearance is satisfactory.

Minimum required clearance under pontoon ≤ water depth – draft – maximum expected bridge response Determination of the access bridge length:

The access bridge should be hinged at the floating bridge while an expansion joint has to be used at the abutment to introduce the length difference between the access bridge and the distance between the two connection points during the tide. That difference can be determined as follows (See figure (2-5)):

2 2 x  LAccessbridge  habutment ( flow)  X Abutmentspacing ∆x for abutment A = √ (30.3362-2.52) – 30 = 232 mm ∆x for abutment B = √ (60.6712-7.02) – 60 = 266 mm

The expansion joint has to have a displacement capacity more than the calculated (∆x) because of the thermal expansion of the access bridge itself.

The total length (abutment to abutment) = 2090 m The length of the floating part = 2000 m (40 pontoons x 50 m) The maximum slope of the access bridge = 15%

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Table (5-4) Access bridge elevation Ebb (m) Flow Floating bridge/ Access bridge (m) Abutment spacing length (m) The elevation of the sea -2.00 0 - - The elevation of the abutment A 4.50 2.50 30.00 30.336 The elevation of the abutment B 9.00 7.00 60.00 60.671

The slope of the access bridge A at ebb = 4.5/30 = 15% The slope of the access bridge B at ebb = 9/60 = 15%

5.1.2 Local dimensioning and load combinations

5.1.2.1 The bridge width

 The road dimensions:

Refer to the road transverse profile on the bridge deck is described in the Dutch criteria (ROA & RONA) [Richtlijnen ontwerpen voor / (niet) auto-snelweg]. These criteria provide for us the minimum road width that is required in this case. The width dimension is depending on two factors: the lane number and the maximum allowable velocity (Vo). In page 103 of the ROA, the details of the main road profile which is constructed on the structural members. The table (3-3) shows all dimensions of the profiles:

In case of one lane in each direction, the minimum pontoon width is restricted by the road dimensions which are in case of one lane in each direction equal to (22600mm) including the middle strip, the parapet and the safety barrier, for more details see figure (3-7a).

The total width (w) = 2*[safety barrier (1.41m) + m + c +a +c +e +l] + middle strip (0.8m) = 22.6m for max. Traffic velocity = 120 km/h = 20.6m for max. Traffic velocity = 90 km/h

 Calculating the buoyancy stiffness:

The buoyancy stiffness is depends on the pontoon width and is calculated per unit length of the bridge:

K = ρw. g. A = 1030 * 9.81 * 22.6* 1 = 228.36 kN/m per meter length K = 0.228 N/mm/mm

5.1.2.2 The bridge depth

 Freeboard (1) = Hs/2 + maximum bridge settlement (fully traffic load (2.1)) = 3.070/2 + 0.602 = 2.137 m (loaded bridge + normal wave)  Freeboard (2) = 6.200/2 = 3.100 m (unloaded bridge +extreme wave)  The draft determination:

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The draft has to be investigated for two cases when loaded with fully traffic load and without traffic load.

The total load per unit length = Traffic load + Bridge weight + Vertical mooring load

The traffic load = 2*3*q1+ q2 (w- (2*1.5+2*3)) + [2*2*Q1+2*2*Q2+ (n- 4)*2*Q3] / (22.6*50) = 2*3*9 + 2.5*(22.6 – (3 + 6)) + [2*2*300 + 2*2*200 + (6 - 4)*2*100]/ (22.6*50) = 54 + 34 + [1200 + 800 + 400]/ (50) = 54 + 34 + 48 = 136 KN /m The traffic load contribution pressure = the traffic load/w = 136/22.6 = 6.02 kN/m2

Therefore the weight of the concrete should be increased by the absorption percent which is almost 4%. The pontoon weight (50×22.6×8.0) m:

Table (5-5) Member Volume[m3] Weight[kN] slabs (500+500)*22600*50000 1130 28250 walls 5*400*7000*50000 700 17500 partition 4*10*7000*5150*300 432.6 10815 2262.6 56565

The bridge weight contribution pressure = 1.04*weight /w*L + pavement and superstructure = 1.04*56565 / (22.6*50) + 1.5 kN/m2 = 53.56kN/m2

The vertical component of the mooring line V = submerged cable weight * cable length = ω*L = 50*1294.93 = 64.747 kN

2 The mooring lines contribution pressure = 2*V/ (w* lv) = 2*64.747/ (22.6*10) = 0.573 kN/m

Assume the distance between the mooring cables lv = pontoon length/5 = 50/5 =10m Applying the equation (4-3): The maximum draft by fully traffic = (6.02 + 53.56 + 0.573) / γw = 60.153/10 = 6.015 m The minimum draft without traffic = (53.56 + 0.573) / γw = 54.13/10 = 5.413 m

We need to avoid the fully submerging of the pontoon due to the traffic load. Therefore, the draft has to be larger than the required draft for the loaded bridge.

5.1.2.3 Determination of the additionally required coefficients

 The Meta centre height (see section 1.6.2): The gravity centre of the pontoon cross section KG (partitions weight is neglected): V e  KG   i i i Vi  i KG = [500*22600*250 +5*400*7000*4000+500*22600*7750]/ (22600*1000+ 5*400*7000) = 4000 mm BM is distance between the Meta centre and the gravity centre (figure (1-18)):

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b 2 BM  = 22.6 2 / (12*5.413) = 7.86 m 12d b 2 KM   d = BM + d/2 = 7.86 + 5.413/2 = 10.57 m 12d 2 b 2 h   d  KG = KM – KG = 10.57 – 4.00 = 6.57 m m 12d 2

The Meta centre height is satisfactory large and higher than the gravity centre G.

 The Added mass (az) (see section A.1.1)

The draft will be taken (5m) as a worst case. 2   b  The added mass for heave motion (az) =   per unit length of the body. 2  2  2 az = 1030*3.1416/2*(22.6/2) = 206593 kg 2 2 The added mass for sway motion (ay) = ρ π T /2 = 1030*3.1416* 5 /2 = 40448.1kg 2 2 2   b   d   d   The added mass for roll motion a  L      r             4   2   2   2 2 2 aθ = 1*1030*3.1416*[(22.6/2) + (5/2) + (4.00 -5/2) ] = 437454 kg per meter length

 The damping coefficient (c):

The mass of the bridge per meter length (m) = ρw*d*b = 1030*5*22.6 = 116390 kg/m

- Damping coefficient for heave motion: c  2 (m  a)k = 2* 0.1 * √ ((116390 + 206593)* 228357) = 54316 Ns/m/m

- Damping coefficient for Sway motion: c = 2* 0.1 * √ (116390 +40448.1)* 228357 = 37849.7Ns/m/m

- Damping coefficient for roll motion: 2 m  m  i y  iz 

The spring constant: kθ = kθhydrostatic + kθgeometric = 9719642 + 255303 = 9974.95 kN 3 b 3 kθhydrostatic  gL = 1030*9.81*1*(22.6 /12) = 9719642 N per meter length 12  d  kθgeometric  gLbd   KG  = 1030*9.81*1*22.6*(3.618 – 5/2)  2  = 255303 N per meter length

c  2 (m  a ) k  = 2* 0.1 * √ (116390 + 437454)* 9974945 = 470.1 kN

 The Eigen frequency o : Referring to the section A.1.1 in appendix A, the Eigen frequency can be calculated as: -The Eigen frequency in the Heave motion:

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K gb g  2    o 2 b m  az    b  bd    d  2  2  8 -1 = 9.81/ (5+3.1416*22.6/8) = 0.707  ωo = 0.841 s

 The Eigen frequency in the Sway motion:

Kmooring = 152500 N/m/m (see 2.5.1.5 in chapter Mooring System)

K mooring 152500 -1 o   = 0.9861 s m  a y  116390  40448

 The Eigen frequency in the Roll motion:

k 9974945 -1 o    4.244 s m  a  116390  437454

5.1.3 Pontoon rigidity

Figure (5-2) the effective cross section of the pontoon for the global design

The pontoon should be compartmentalized in both directions to increase its local and global flexure rigidity as well as its torsional rigidity. The second purpose is to confine flooding of the bridge due to a collision.

5.1.3.1 The cross section specifications:

At the beginning, we assume the following dimensions as it is shown in the figure (5-2):  The pontoon is divided into foursquare compartments in the transverse direction.  The external and internal walls thickness = 400mm.  The transversal walls and bulkheads thickness = 300mm.  The bottom slab thickness = 500mm.  The top slab thickness = 400mm.

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The compartment width = (pontoon width – external wall thickness)/4 = (22.6 - 0.4)/ 4 = 5.550 m The number of compartments in the longitudinal direction = (pontoon length- bulkhead thickness)/compartment width = (50 - 0.3)/5.55 = 8.95 say (9) The compartment length = (50 - 0.3)/9 = 5.522 m

-The compartment size (LXW) = (5.522 X 5.550) m c/c

The top flange area = 22.600*0.500 = 11.3 m2 The bottom flange area = 22.600*0.500 = 11.30 m2 The walls area = 5*0.400* (8.0-0.500-0.500) = 14.20 m2

-The total cross section area = 36.6m2

5.1.3.2 The bending stiffness:

 The local bending stiffness: The pontoon should be design as a caisson. It has to be as a grillage. The local bending stiffness has to be calculated by using only the effective flange width defines in the NEN 6723 VBB (1995). For the global design requirements, it is recommended to consider the whole cross section of the pontoon.

 The position of the gravity centre (G) calculated from the bottom side of the pontoon: KG = 4000 mm  The pontoon depth = 8.00 m

The concrete modulus of elasticity Ec = 22250 +250*65 = 38500 MN/m2

The concrete modulus of elasticity after the creep and shortening effects:

E E   c = 38500/ (1+0.8*2.5) = 12833.3 N/mm2 c 1    

- Longitudinal direction of the pontoon: l = 5.05 m bw = 0.4m bw2 = b w3 = 5.05-0.4 = 4.65 m l / bw2 = 5.05/ 4.65 =1.09 from figure (3-14) b2/bw2 =0.1  b2 = 0.465

The effective flange width of the middle strip (be) = bw + 2*b2 = 0.4 + 2*0.465 = 1.33 m The effective flange width of the external strip (be) = bw + b2 = 0.4 + 0.465 = 0.865 m

- The transversal direction of the pontoon (square compartment):

The effective flange width of the middle strip (be) = bw + 2*b2 = 0.4 + 2*0.465 = 1.33 m The effective flange width of the external strip (be) = bw + b2 = 0.4 + 0.465 = 0.865 m

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The total flange width top and bottom in both direction= 2*0.865+3*1.33 = 5.72 m

- The inertia moment Ix, Iy = Σ bh3/12 +A*d2 = 5*(0.4*5.53/12) + 8*0.465*0.23 /12+8*0.465*0.2* (5.5-3.618-0.15)2 +8*0.5*0.53 /12 +8*0.5*0.5*(3.618-0.25)2 + 22.6*0.43/12 + 22.6*0.4*(7.9-0.2-3.618)2 = 203.44 m4

- The flexure stiffness of the pontoon in both direction EIz, EIy = 203.44*12833 = 2610791.6 MN-m2

 The global bending stiffness:

The moment of inertia of the pontoon for the global design requirements is determined by considering the whole cross section. That leads to the fact that the global flexure rigidity of the pontoon is larger than the local flexure rigidity.

3 3 2 2 Ixx = 1000*(22600) /12 + 5*7000(400) /12 + 2*11100 (7000*400) + 2*5550 (7000*400) = 1824.6 m4 3 2 3 Izz = 2*(22600*(500 )/12 + 22600*500*(4000 - 250) ) + 5*400*(7000) /12 = 375.45 m4 Ip = Ixx + Izz = 1824.6 + 375.45 = 2200.04 m4

The polar inertia radius then is j = √Ip/Ac = √2200.04/36.6 = 7.753 m 2  j The natural oscillation period is = T  = 2*3.1416*7.753/√ (68.47*9.81) = 5.79sec hm  g

5.1.3.3. Checking the characteristic length of the pontoon:

/1 4 /1 4  EIz   375 .45  12833  10 3  The characteristic length λc = 2 π *   = 2*3.14*    k   228 .36  = 426 m << 2000m elastic behaviour

5.1.3.4 The pontoon Torsional rigidity:

The tensional rigidity of the multi-cellular cross section is regarded as thin-walled cross section and the principle of membrane analogy has to be applied to determine the torsional rigidity of the pontoon. To determine the torsional rigidity of the pontoon we will apply the formulae in section 4.1.5:  ,7 55   ,7 55  G 2  ,5 55  ,7 55   w G 2  ,5 55  ,7 55   w  G  4,0 2   G  4,0 1  w    ...... w    1  ,5 55 2  ,7 55 ,5 55  2  ,5 55 ,7 55 ,5 55           4,0 4,0 5,0   4,0 4,0 5,0 

w1 = 1,336.G.θ + 0,301. w2 ; w2 = 1,911.G. θ + 0,43.w1

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w1 = 2.1953.G.θ ; w2 = 2.855.G. θ

M w  2 21 a  b  22 a  b

M w  GIw Mw = 2( 2*2.1953.G.θ *5,55*7.55 + 2* 2.855.G. θ*5,55*7.55) = 192.88 G.θ

4 14 4 Iw = 192.88 m = 1.9288×10 mm

5.2 The hydrostatic analysis

5.2.1 The sea wave

1. Sea wave generation by wind (Bretschnieder method)

It is necessary at the beginning to determine the characteristics of the sea wave which can excite the bridge. The Bretschnieder method determines the significant wave height (Hs) and the significant wave period (Ts) depends on the wind speed, water depth and the fetch distance. The fetch distance depends on the site configurations. We assume an open sea fetch of (100km) when the wind blows perpendicular to bridge in (Y-direction) and the fetch equal to the bridge length in the parallel direction.

Given:

The wind speed at 10m above the water surface with 1 min. duration (u) The extreme wind storm every 100 year (Ue) = 180 km/h (breaking condition) The normal wind storm every 20 year (Un) = 74 km/h (closing condition) The normal wind storm every 1 year (Uo) = 39 km/h (operational condition) The water depth (d) = 25 m The distance wind travels unobstructed (F) = 100 km (Y-direction) The distance wind travels unobstructed (F) = 2 km (X-direction)

Solution:

The wind velocity (u) = 180 *1000/3600 = 50 m/s g  F g  d Fˆ  = 9.81*105/(50)2 = 392.4 dˆ  = 9.81*25/(50) 2 = 0.0981 U 2 U 2

By applying the equations (3-18) and (3-19) we obtain:

Hˆ = 0.024378 , Tˆ = 1.9484 U 2  Hˆ H  = 0.024378* 502 /9.81 = 6.213 m s g U Tˆ T  = 1.9484 x 50/9.81 = 9.93 sec s g

2. The sea wave characteristic:

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The water depth (h) = 25m 2 The wave length (L) = g. Ts /2π*tanh (2 π d/L) = 9.81*9.932 / (2*3.1416)*tanh (2*3.14*25/129.16)= 129.16 m The wave length classification [L < 25*4 =100m deep water] [25*25 = 625m > L > 100m transient] [L > 625m shallow water] The maximum wave period within the deep water Ts = √ (h*4*2* π/g) = 8.003sec (when the wave length = pontoon width) The min. wave period to rigid body motion dominant Ts = 3.805 sec The wave velocity (C) = L/Ts = 129.16/9.93 = 13 m/s The wave number (k) = 2π /L = (2*3.1416)/129.16 = 0.0486 m-1 -1 The wave angular frequency (ω) = 2π / Ts = (2*3.1416)/ 9.93 = 0.6327 sec The wave amplitude (a) = Hs /2 = 6.213 /2 = 3.1063 m

The equation of motion of the sea wave: η(x, t) = a. sin (k.x – ω.t) η(x, t) = 3.1063 .sin (0.0486.x- 0.6327.t)

Table (5-6) the wave characteristics The parameter unit Extreme wind Normal wind Operational storm storm wind The wind speed km/h 180 74 39 The wind speed m/s 50 20.55 10.83 The wind speed Beaufort 15 8 5 scale Significant wave height Hs m 6.213 3.07 1.58 Significant wave period Ts sec 9.93 6.71 4.84 The wave number (k) m-1 0.0436 0.0521 0.0716 The wave length (L) m 129.16 68.8 36.5 The wave amplitude (a) m 3.106 1.535 0.79 The wave angular frequency (ω) sec-1 0.6327 0.9364 1.2982 The wave velocity (C) m/s 13.01 10.25 7.54 The wave force without opening (F) kN/m 502.86 199.73 90.898 The wave force with opening (F) kN/m 377.31 167.623 86.268

5.2.2 The loading

1. The wave force: For a pontoon which is submerged a depth (d) = 5m in the water, the sea wave acts the following force (F) on the pontoon side that is perpendicular to the wave direction:

The wave force on the float =

This force (F) represents the sea wave force that acts on a rigid vertical wall and extend along the whole water depth (h) with a 100% reflected energy. We can use this theory to approximate the wave force on the floating pontoon with a draft (d). Firstly, we have to determine the water pressure at the critical points (p1, p2,…, p7), then it become easy to calculate the forces that they act on the pontoon. The total force that results from this method

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Figure (5-3) the sea wave pressure on a floating structure with opening

The water pressure above the sea level is determined by the following equation:

P = ρ .g .Hs [1-z/Hs] for 0 < z < Hs (for P1, P2, P3, P4)

The water pressure under the sea level is determined by the following equation:

P = ρ. g .Hs [cosh (k (d+z))/cosh (kd)] for -d < z < 0 (for P5 )

P1 = 0, P7 = 0, P5 = P6

For example:

F3 = (P4+P5)*d*1

Table (5-7) the wave characteristics Units Extreme wind Normal wind Operational storm storm wind The wind speed km/h 180 74 39 Rigid wall kN/m e 589,805 156,08 49,507 c r

Pontoon without opening o kN/m f 191,869 82.62 39.5

e

Pontoon with opening v kN/m

a 159,404 70,205 31,129

Rule of thumb W kN/m 205.7 89.45 43.07 The pressure at point P5 kN/m2 25,856 9,975 3,378 The pressure at point P4 kN/m2 31,389 15,51 7,982 The pressure at point P3 kN/m2 26,337 10,458 2,930 The pressure at point P2 kN/m2 6,128 0 0 The force F1 kN/m 1,858 0 0 The force F2 kN/m 14,431 6,492 2,728 The force F3 kN/m 143,114 63,713 2,84

This force can be converting to uniform distributed load acts on an area equal to the submerged depth and extends to a distance equal to the half of the wave height as follow:

The draft (d) = 5 m The equivalent uniform distributed load of the wave force = F/ ((d+0.5)*1) = 377.31/ (5+0.5)

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= 68.6 kN/m2

The wave forces according to the linear theory

700

600 ]

m 500 / N k [ Rigid wall along the whole depth e 400 c r pontoon with opening o f

e 300 pontoon without opening v a w

e 200 h T

100

0 39km/h 74km/h 180km/h wind speed (km/h)

Figure (5-4) wind speed / wave force relation

By using the technical specification of the mooring lines that shown in the table (4-1) we can calculate the mooring line density along the both side of the bridge and also the required length of the mooring line for all applied wave forces. That could found in the table (4-5).

2. The current load

We assume the current (water flow) velocity (v) equal to 0.5m/sec in one direction, although the current as result to the tide can be in two directions. The current force is calculated by eq. (4-21) in section 4.1.7.1 as follow:

1 2 2 F   C  A Fc = (1/2)*1030*1*(5*1)*0.5 = 0.644 kN/m length. c 2 w s

3. The wind load

The design wind velocity is the extreme storm velocity which is assumed (u) =180km/h. The wind forces depends not only on the geometrical shape of the structure, the wind density affects the force value. The wind density depends on the air temperature and its moisture content. The total wind load on the bridge such as defined in the section 3.1.3 as follow:

Ftotal = Fcompression + Fsuction + Ffriction

2 2 2 Pw = ½. * ρair *g* vwind = ½* 1.225*9.81*50 = 15.02 kN/m .s Ac = As = (8-5)*1 = 3.0 m/m Fcompression = Pw. Cpe. Ac = 15.02 *0.8*(3*1) = 36.05 kN/s.m meter length Fsuction = Pw. Cpe. As = 15.02 *(-0.4)*(3*1) = - 18.02 kN/s.m meter length Ffriction = Pw. Cf. Af = 15.02 *0.04 *(22.6*1) = 13.58 kN/s.m meter length

Ftotal =36.05 + 18.02 + 13.58 = 67.65 kN/s.m meter length

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Table (5-8) the wind forces The parameter unit Extreme wind Normal wind Operational wind storm storm The wind speed [km/h ] 180 74 39 [m/s] 50 20.55 10.83 The wind pressure [kN/m2] 15.02 2.537 0.705 The compression force [kN/s.m] 36.05 6.09 1.692 The suction force [kN/s.m] -18.02 -3.04 -0.85 The friction force [kN/s.m] 13.58 2.3 0.637 The Total wind force [kN/s.m] 67.65 11.43 3.519

4. The traffic load: defined in section 4.1.7.1

5. The hydrostatic pressure:

The expected hydrostatic pressure on the pontoon is concern only three sides. The pressure is depends on the water head. On the bottom slab the uniform hydrostatic pressure cannot exceed the pontoon depth by the seawater density. While on the both external walls can appear the triangle water pressure with the same maximum water pressure.

Figure (5-5) description of loading combinations

5.2.3 Slabs and walls thicknesses verification

The design of the pontoon slabs for the conventional reinforcement is made according to the Dutch norm NEN 6720 and the table (4-2) for the concrete cover. The procedure involves the considering of one strip of the transversal pontoon compartments. The strip width is (5.522m) c/c. Moreover, the strip is divided into the following individual elements:

1. The internal wall (11 walls) 2. The external wall (2 walls)

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3. The bottom slab (4 slabs) 4. The top slab (4 slabs)

To simplify the analysis we will only deal with the critical cross sections and due to the symmetrical geometry and loading we can find the same section in both sides as shown in figure (5-6).

Figure (5-6) the section numbers of the transversal cross section of the pontoon YZ-plane.

Checking for the maximum applied bending moment:

Firstly, we have to define the applied load and determine the govern load combinations to determine the maximum applied bending moment (Md) and shear forces (Vd). In additional to that, we need to need to check the already assumed dimension and determine the moment capacity (Mu) and compare it with the applied moment and the fracture moment Mr (crack control). The two requirements that the moment of the cross section to be met are:

(1) Mu ≥ Md

(2) Mu ≥ Mr ≥ Md

With respect to the Md, the percentage of the reinforcement steel can be determined as follow:

fs Mu = As  fs  d  (1-0,52ω  ) As = ω b  d f´b

Md ω fs fs 2  (1-0,52ω  ) b d f´b f´b fb

Md fs 2  (1-0,52 )  = ω b d f´b fb

The second condition Mu ≥ Mr:

The cracking moment (Mr) should be also larger than the moment capacity of the cross section. The cracking moment is time dependant value (Mbr,o - Mbr, ∞) and can be determined as follow:

2 f´bm,o = 0.85*(f’ck +1.64* σ) = 0.85*(65 +1.64*5) = 62.2N/mm 2 f´bm,∞ = 0.85* f´bm,o = 0.85*62.2 = 52.89 N/mm 2 fbm,o = 1.05 + 0.05*(f’ck +1.64* σ) = 1.05 + 0.05*(65 + 1.64*5) = 4.71 N/mm

TU Delft 184 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge fbm,∞ = 0.7* fbm,o = 0.7* 4.71 = 3.3 N/mm2 2 fbr,o = (1.6 - h)* fbm,o = (1.6 - 0.4) *4.71 = 5.65 N/mm 2 fbr,∞ = (1.6 – h)* fbm,∞ = (1.6 – 0.4)*3.3 = 3.96 N/mm Where: h = the section depth. 1 Mr = f  b  h2 br,o 6 2 Mbr,o = 5.65*(1000*400 )/6 = 150.67kN-m 2 Mbr,∞ = 3.96*(1000*400 )/6 = 105.6 kN-m

The shear force:

The applied shear stress (d) should not exceed the shear strength of the concrete without shear reinforcement as the following values:

. . d ≤ 1 = 0,4 fb + 0,15 σ´bm ( the influence of the compression stress) . . 2 d ≤ 1 = 0,4 fb = 0, 4 2.15 = 0.86 N/mm

Where:

Vd d = b d σ´bm = the compression stress in the section = F/Ap F = the compression force. Ap = the section area.

The normal forces on the pontoon elements are variable due to the variation of the loads and the position of the pontoon in the water. Therefore, we will take only the almost permanent normal forces on the pontoon elements. The loading case, that shown in the figure (5-7) is the most permanent case and the normal forces, which created from this case, will be taken in the shear capacity modification of the pontoon elements.

Figure (5-7) the most permanent loading case

There are no any normal forces on the top slab: Fbottom slab = (5.55*2.775/2)*(50+27.75)/2 = 299.36 kN (hydro static pressure) Ftransversal internal wall = [(5*5.55)*(50/2) - Fbottom slab] /2 = 197.95kN (hydro static pressure)

Flongitudinal internal wall = [0.4*24*2*(1/2*5.522*5.55/2)] = 147.1kN (top slab weight) Fexternal wall = [0.4*24*(1/2*5.522*5.55/2)] = 73.55kN (top slab weight)

5.2.3.1 The design of the internal wall:

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Given: The panel size (lx x ly) (5.55x7.55) m and (5.522*7.55) m or (5.25x7.10) and (5.222*7.10) m clear distances The longitudinal wall thickness = 400mm The transversal wall thickness = 300mm The concrete cover = 40mm The load factor γq = 1.5 (variable load)

The factored hydrostatic pressure (Pw): Pw = γq * γw * h = 1.5*10* 7.1 = 106.5 kN/m2 h = the maximum water head during the flooding of one compartment.

Using (table (18) NEN6720) to get the forces: ly/lx = 7.55/5.55 = 1.36

2 Moment = Pl*lx /factor = 106.5*5.552 = 3280 kN- m/m/factor Shear force = Pl*lx /factor = 106.5*5.55 = 591 kN/m/factor

Checking the transversal wall thickness:

The concrete strength of C53/65 = 65 N/mm2 The concrete cover = 40 mm table (4-2) The maximum allowable compression strength fc’ = 0.6*65 = 39 N/mm2 The yield strength of the steel Feb 500 steel class fy = 500 N/mm2 fs = fy/ γ = 500/1.15 = 435 N/mm2 The strip depth of the transversal wall d = h – ϕ/2 – cover = 300 – 16/2 – 40 = 252 mm The width of the strip b = 1000 mm The maximum applied bending moment Md = 133.6 kN-m

Applying steel bar ϕ = 16mm @ 150mm: As = 1340mm2 Mu = 142.4 kN-m

Mu ≥ Md OK

2 Mbr,o = 6.12*(1000*300 )/6 = 91.8 kN-m 2 Mbr,∞ = 4.29*(1000*300 )/6 = 64.35 kN-m

Mu ≥ Mr OK

Checking for the maximum applied shear force:

The concrete shear resistance 1 = 0.4 * fc + 0.15* σ´bm

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2 σ´bm = F/Ap = 197950/(300*5500) = 0.12 N/mm 2 1= 0.4*0.7*(1.05+0.05*65)/1.4 + 0.15*0.12 = 0.88 N/mm 2 The maximum shear stress capacity 2 = 0.2 * fc’ = 0.2*39 = 7.8 N/mm The maximum applied shear force Vmax = 217.27 KN 2 The maximum applied shear stress d = Vmax/ b.d = 217270/252*1000 = 0.862 N/mm 1 ≥ d OK

No need for the shear reinforcement

Table (5-9) the internal – and external walls forces Internal wall External wall X = horizontal Factor units Hydrostatic Hydrostatic Wave Total Y = vertical pressure pressure pressure forces ly/lx 1.36 kN-m/m Mx fix-end 26.55 kN-m/m -123,54 -87,23 -76.5 -163.73 Mx span 66.8 kN-m/m 49,1 34,67 33.45 68.12 My fix-end bottom 24.55 kN-m/m -133,6 -94,34 -60.05 -154.39 My max 99 kN-m/m 33,13 23,39 14.26 37.65 My fix-end top 61.2 kN-m/m -53,59 -37,84 -60.05 -97.89 qx max shear x=0 3.32 kN/m ±178,01 ±126,20 62.61 188.81 qy max shear y=0 2.72 kN/m 217,27 154,04 85.13 239.17 qy max shear y=ly 9.695 kN/m -60,95 -43,2 -85.13 -128.33

5.2.3.2 The design of the External wall:

Given:

The element size (lx*ly) = (5.522*7.55) or (5.222*7.10) m clear distances The wall thickness = 400mm The external concrete cover = 50mm. The internal concrete cover = 40mm. The load factor γq = 1.5 (variable load) The wave pressure = (The extreme wave force / pontoon depth) = (191.87/8.0) = 23.98 KN/ m2

[The wave pressure can be considered as a uniform distributed load along the pontoon depth]

The current load = 0.644kN/ m2

The possible load combinations:

On the external wall, we can expect the most three critical load combinations:

1. Hydrostatic pressure on the whole pontoon depth + current load.

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2 Ptop = 0.644 , Pbottom = 10*8.0+0.644 = 80.644kN/m 2. Hydrostatic pressure on the draft distance (5m) + wave pressure of extreme storm+ current load. Ptop = 191.87/8 = 23.98kN/m, Pbottom = 10*5.0 + 23.98 + 0.644 = 74.63kN/m govern 3. Hydrostatic pressure on the draft distance (5m) + compression wind load of extreme storm + current load. Ptop = 36.05kN/m table (5-7) , Pbottom = 10*5.0 + 0.644 = 50.644kN/m

Using (table (18) NEN6720) to get the forces: ly/lx = 7.55/5.522 = 1.36 For the factored triangle distributed load (hydrostatic pressure + current load):

2 2 Moment = γq * Pbottom *lx /factor = 1.5*50.644*5.522 = 2316.4 kN-m/m /factor Shear force = γq *Pl*lx /factor = 1.5*50.644*5.522 = 419.5 kN/m /factor

For the uniform distributed load (wave load), we use table (18) of the Dutch norm NEN6720:

2 2 The moment = factor*0.001* γq *Pl *lx = 0.001*1.5*23.98*5.522 = 1.097 kN-m/m *factor Shear force = γq *Pl*lx = 1.5*23.98*5.522 = 198.6 kN/m

Figure (5-8) external wall load combinations

Using the interpolation to get the moment factors from the table (18) of the Dutch norm NEN6720 with dimension ratio of ly/lx =7.55/5.55=1.35 and case II:

Moment Mxv Mxs Myv Mys ax/lx ay/ly factor 30.5 69.75 13 54.75 0.19 0.1525 The depth of the strip d = 400 – 16/2 – 50 = 342 mm The width of the strip b = 1000 mm The maximum applied bending moment Md = 163.73 kN-m (table (5-8)): Applying steel bar ϕ= 16mm @ 150mm:

As = 1340mm2 Mu = 194.88 kN-m

Mu ≥ Md OK

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2 Mbr,o = 5.65*(1000*400 )/6 = 150.67kN-m 2 Mbr,∞ = 3.96*(1000*400 )/6 = 105.6 kN-m

Mu ≥ Mr OK

Checking for the maximum applied shear force:

The concrete shear resistance 1 = 0.4 * fc + 0.15* σ´bm

2 σ´bm = F/Ap = 73550/(400*5522) = 0.034 N/mm 2 1= 0.4*0.7*(1.05+0.05*65)/1.4 + 0.15*0.034 = 0.865 N/mm

2 The maximum shear stress capacity 2 = 0.2 * fc’ = 0.2*39 = 7.8 N/mm The maximum applied shear force Vmax = 239.17 kN 2 The maximum applied shear stress d = Vmax/ b.d = 239170/352*1000 = 0.699 N/mm 1 ≥ d OK

No need for the shear reinforcement

5.2.3.3 Design of bottom slab:

Panel size (lx x ly) = (5.555*5.522) Alternatively (5.255*5.222) clear distance Slab thickness = 500mm. The external concrete cover = 50mm. The internal concrete cover = 40mm. The load factor γq = 1.5 (variable load) The load factor γd = 1.2 (dead load) The concrete density (γc) = 24kN/m3

The maximum expected hydrostatic water pressure 2 Pw = 8.0*10 = 80kN/m (worst case) The dead load = γc*d = 24*0.5 =12 kN/m2

The possible load combination: 1. Hydrostatic pressure on the whole pontoon depth (8m) - slab weight The total factored DL (Pd) = 1.5*10*8.0 – 1.2*0.9*12 = 107 kN/m2 Govern [The dead load is against the hydrostatic pressure and it should be subtracted with reduction of 10%]

2. Hydrostatic pressure on the draft distance (5m) + wave pressure of extreme storm- slab weight. The total factored DL (Pd) = 1.5*10*5.0 + 1.5*(P5=25.86) – 1.2*0.9*12 = 100.83 kN/m2

For the uniform distributed load, we use table (18) of the Dutch norm NEN6720 case II:

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The moment = factor*0.001*Pd*lx2 = factor*0.001*107*5.5552 = factor*3.302kN –m/m The depth of the strip d = h – ϕ/2 – cover = 500 – 16/2 – 50 = 442 mm The width of the strip b = 1000 mm

Table (5-10) slab forces Factor units The value Fixed – end moment Msx 51 [kN-m/m] -166.4 Span moment Mvx 18 [kN-m/m] 58.73 Fixed – end moment Msy 51 [kN-m/m] -166.4 Span moment Mvy 18 [kN-m/m] 58.73 ly/lx = 5.55/5.522 1

The maximum applied bending moment Md = 166.4 kN-m (table (5-10)):

Applying steel bar ϕ= 16mm @ 150mm: As = 1340mm2 Mu = 253.2 kN-m

Mu ≥ Md OK

2 Mbr,o = 5.18*(1000*500 )/6 = 215.83kN-m 2 Mbr,∞ = 3.63*(1000*500 )/6 = 151.25kN-m

Mu ≥ Mr OK

Checking for the maximum applied shear force:

The concrete shear resistance 1 = 0.4 * fc + 0.15* σ´bm

2 σ´bm = F/Ap = 299360/(500*5522) = 0.108 N/mm 2 1= 0.4*0.7*(1.05+0.05*65)/1.4 + 0.15*0.108 = 0.876 N/mm

2 The maximum shear stress capacity 2 = 0.2 * fc’ = 0.2*39 = 7.8 N/mm The maximum applied shear force Vmax = [(166.4+58.73)*8/5.5222] *5.522/2= 162.25 kN 2 The maximum applied shear stress d = Vmax/ b.d = 162250/442*1000 = 0.367 N/mm

1 ≥ d OK No need for the shear reinforcement

5.2.3.4 Design of top slab:

Panel size (lx x ly) = (5.55 X5.522) m or (5.25X5.222) m clear distance Slab thickness (h) = 400mm. The external concrete cover = 65mm. The internal concrete cover = 40mm. The width of the strip b = 1000 mm The depth of the strip d = 400 – 16/2 – 65 = 327 mm (at the negative moment). The depth of the strip d = 400 – 16/2 – 40 = 352 mm (at the positive moment).

The applied loads:

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1. The slab self weight = γc*h = 24*0.4 = 9.6kN/m2 2. The traffic UDL = 2.5kN/m2. + (9-2.5) movable UDL 3. The axel load of (300X2) + (200X2) + (100X2) as define in section (4.1.7.1)

Figure (5-9) shear force and bending moment of the top slab

The maximum applied bending moment Md = 124 kN-m (figure (5-10)):

Applying steel bar ϕ = 16mm @ 150mm: As = 1340mm2 Mu = 186.13 kN-m

Mu ≥ Md OK

2 Mbr,o = 5.65*(1000*400 )/6 = 150.67kN-m 2 Mbr,∞ = 3.96*(1000*400 )/6 = 105.6 kN-m

Mu ≥ Mr OK

Checking for the maximum applied shear force:

The concrete shear resistance 1 = 0.4 * fc 2 1= 0.4*0.7*(1.05+0.05*65)/1.4 = 0.86 N/mm

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2 The maximum shear stress capacity 2 = 0.2 * fc’ = 0.2*39 = 7.8 N/mm The maximum applied shear force Vmax = 254kN 2 The maximum applied shear stress d = Vmax/ b.d = 254000/327*1000 = 0.749 N/mm

1 ≥ d OK No need for the shear reinforcement

Table (5 -11) the shear forces and stresses

) ) )

2 2 2 n

m o m m m d 1 b i t ´ m m m Vd b d F(kN)  

/ / / f f M M

c br,o br,∞ br,o br,∞ σ e N N N ( ( ( S 1 103 1000 327 0 0 0,315 0.86 5.65 3.96 150.67 105.6 3 -254 1000 327 0 0 -0,777 0.86 5.65 3.96 150.67 105.6 3 172 1000 327 0 0 0,526 0.86 5.65 3.96 150.67 105.6 5 -127 1000 327 0 0 -0,389 0.86 5.65 3.96 150.67 105.6 5 127 1000 327 0 0 0,389 0.86 5.65 3.96 150.67 105.6 6 -128.33 1000 342 73.55 0.033 -0,375 0.893 5.65 3.96 150.67 105.6 8 239.2 1000 342 367.75 0.166 0,699 1.026 5.65 3.96 150.67 105.6 9 -161.5 1000 442 299.36 0.11 -0,669 0.97 5.18 3.63 215.83 151.25 11 164 1000 442 299.36 0.11 0,674 0.97 5.18 3.63 215.83 151.25 11 -162.25 1000 442 299.36 0.11 -0,672 0.97 5.18 3.63 215.83 151.25 13 162.25 1000 442 299.36 0.11 0,675 0.97 5.18 3.63 215.83 151.25 13 -162.25 1000 442 299.36 0.11 0,675 0.97 5.18 3.63 215.83 151.25

Table (5 -12) the moment and the required steel reinforcement

Bar n r ) e o

i M h Ø d distance ω A M f M d m s u br,o r,o v t

o 2 2 c m

e (kN-m) (mm) (mm) (m) c/c (%) (mm ) (kN-m) (N/mm ) (kN-m) ( C s (mm) 1 97.9 400 16 65 327 150 0.41 1340 186.13 5.65 150.67 2 68.5 400 16 40 352 150 0.38 1340 200.7 5.65 150.67 3 124 400 16 65 327 150 0.41 1340 186.13 5.65 150.67 4 68.5 400 16 40 352 150 0.38 1340 200.7 5.65 150.67 5 115 400 16 65 327 150 0.41 1340 186.13 5.65 150.67 6 97.89 400 16 50 342 150 0.392 1340 194.9 5.65 150.67 7 37.65 400 16 40 352 150 0.38 1340 200.7 5.65 150.67 8 160.39 400 16 50 342 150 0.392 1340 194.9 5.65 150.67 9 160.4 500 16 50 442 150 0.305 1340 253.2 5.18 215.83 10 61.73 500 16 40 452 150 0.2965 1340 259 5.18 215.83 11 166.4 500 16 50 442 150 0.305 1340 253.2 5.18 215.83 12 58.73 500 16 40 452 150 0.2965 1340 259 5.18 215.83 13 166.4 500 16 50 440 150 0.305 1340 253.2 5.18 215.83

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Figure (5-10) shear force diagram of the ZY-direction section

Figure (5-11) the bending moment diagram of the ZY-direction section

5.2.4 The mooring system:

The mooring system is designed to introduce the sea wave entirely so that the designed horizontal force which carried by the mooring line should take the sea wave pressure on the bridge side which confined by the two mooring lines.

Given: The mooring line submerged weight (wsubmerged ) = 50 N/m The water depth (h) = 25m The horizontal sea wave force (F) = 191.9 KN per meter length The distance between two lines (lv) = 10m The horizontal force of the cable (H) = 191.9*10 = 1920 kN per cable

Table (5-13) mooring system parameters The parameter Static, inextensible Static, extensible The minimum length required (L) 1385.4 m

The horizontal force at the pontoon (H) 1919kN

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The horizontal scope distance (X) 1385.09 m

The vertical force at the pontoon (V) 69.27kN

The Tension force ( T ) 1920 kN

The value of ∆H is the mooring line resistance force when the pontoon moves (60mm) which represents the maximum operational horizontal displacement (X). By using the same method, we can determine the maximum design horizontal displacement (Xdmax) and the breaking horizontal displacement (Xmax). The 20-year windstorm wave force (82.620*10) kN in the table (4-6) will move the pontoon over (106mm) and 100-year wind storm wave force (191.9*10) kN will move the pontoon over (220mm). The breaking displacement is (289.6mm) which can apply a force larger than (8000kN) on the tensioned cable and break it.

Wind speed Wind speed Applied wave Applied Cable Horizontal details (km/hour) pressure (kN/m) force @10m stiffness displacement (kN) (kN/m/m) 1-year wind storm 39 39.5 395 654.8 60 Design tension force = 1920 kN 20-year wind storm 74 83 830 779.4 106 Horizontal distance =1385.1m Cable length = 1385.4 m 100-year wind storm 180 191.9 1919 972.1 220 Cable code = C4 Breaking load 8000 3060 283 Vertical force = 69.3 kN Water depth = 25 m Fetch =100 km

5.3 The Global design

5.3.1 Individual pontoon response method

Heave Motion

One of the approximation methods to determine the maximum expected response of the bridge that determine the Heave displacement of one individual pontoon due to a sea wave and consider it as a maximum response which it is in the reality much larger than the real response. By using the dynamics formulas in the chapter (2) ‘Mechanical calculations’ we can complete our calculations. We start with the following data:

The pontoon dimension (L.b.h) = 50x22.6x7.9 m The draft d = 5m The water depth h = 25m

Heave movement can be described as a damped linear mass-spring system with a spring constant [k] and a damping constant [c]. The mass of the body should be increased by the inertia of the water, as a result of the moved water particles. The total moving mass are called (m+ a) and [a] is called the added mass which depend on the body shape and the movement direction. The equation of motion is:

m  a X  c  X  k  X  F k = ρw.g.Aw = 1030 *9.81* 22.6 *50 = 11417859 N/m m = ρ.b.L.d = 1030*22.6*50*5 = 5819500 kg

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2 2   b  1030  .3 1416  22 6.  a=         206592 7. kg / m 2  2  2  2  a = 10329635.8 kg c  2 (m  a)  k  = 2*0.2√ ((5237550 + 10329635.8)* 11417859) = 5431590

F = F (t) = FA*sin (ω.t)

X t  Xˆ sint  

The Eigen frequency can be determined by equalizes the undamped equation of motion to zero:

2 k 2 gb g -1 o   o  2  = => wo = 0.8564 sec m  a   b  b bd    d  2  2  8

H b 2/ .3 62 11 3. Fˆ  Lg ekd cos kx dx  50 1030  .9 81  e  .0 06 .4 50 cos .0 06  x  dx  275312N HFK       2 b 2/ 2 11 3.

b / 2  2 H Fˆ  L  2 e kd cos kx dx HA  2    2 2 b / 2 2 11 3. .3 1416  50  2 .3 62  1030  .0 932  e  .0 06 5.4 cos .0 06  x dx  Fˆ  478608 8. N        HA 2  2  2 11 3.

ˆ ˆ ˆ F  FHFK  FHA = 275312 + 478608.8 = 753.920 kN

Fˆ 8423562 Xˆ   2 2 k  2 m  a  c 2 11417859 .0 63272 5819500103296358.   5431590 .0 63272 8423562 Xˆ   .1 397m 6027948

Table (5-14) waves forces and response of individual pontoon The parameter unit Extreme wind storm Normal wind Operational wind storm The wind speed km/h 180 74 39 FHFK kN 4676,2 2310,7 1189,2 FHA kN 3747,3 4055,2 4011,3 F kN 8423,6 6365,8 5200,5 X m 1.397 1,102 0,301

The Roll:

The roll movement separately likes the heave motion of a damped mass-spring system. There is no translation only rotation. In the context of ambiguity of the various movements, the same symbols are used. They must also fully aware that the units do not match.

The equation of motion:

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  m  a  X  c  X  k  X  F

The dynamic analysis of the roll motion by the corresponding equation of motion is equal to the dynamic analysis of the Heave motion. The method as described in the Heave motion can also be applied. In this framework it is sufficient to list below of relevant formulas (see figure (A-3) appendix A):

4 4 Ixx = 1649.66 m , Izz = 316.917 m

iy = 1649.66/34.46 = 6.9 , iz = 316.917 / 34.46 = 3.033

The mass inertia: 2 2 The floating object: m  m  iy  iz  = 5819500*(692+3.033) = 576446190 kg 2 2 2   b   d   d   The added mass: a  L      r             4   2   2   r =1.382 2 2 2  22 6.   5   5   a  50 1030  .3 1416   .3 618    6378248 6. kg          4   2   2   The roll-forces (moment round the rotation centre) are calculated according to the Froude-Krilov method that is defined in appendix A and listed in the table (5-15):

Fˆ Xˆ  2 2 2 k   m  a   c 

Table (5-15) waves forces and response of individual pontoon The parameter unit Extreme wind storm Normal wind storm Operational wind The wind speed km/h 180 74 39 FθFKS kN 11203,989 5536,174 2849,236 FθFKB kN 50326,01 24867,351 12798,181 FθAMS kN 4517,26 4888,388 4835,47 FθAMB kN 9654,563 10447,758 10334,659 F kN 75701,824 45739,671 30817,545 Xo Rad 0,217920064 0,212206746 0,058940034

The [r] in the above formula is the distance between the mass centre of the object and the water surface.

The spring constant: kθ = kθhydrostatic + kθgeometric = 485982138.6 + 63825831.8 = 549807970.4 N/m

3 b 3 kθhydrostatic  gL =1030*9.81*50*(22.6 /12) = 485982138.6 N/m 12  d  kθgeometric  gLbd  GK  =1030*9.81*50*22.6*5*(5/2-3.618) = 63825831.8 N/m  2 

Where: GK = distance from the object bottom side to the mass gravity point of the object.

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Damping coefficient: b  2 (m  a)  k = 2*0.2*((576446190+6378248.6)* 549807970.4) = 226430217.7

2 k For the Eigen frequency it is valid to use: o  = 549807970.4/ (576446190+6378248.6) m  a  = 0.943351 ===> ωo = 0.97126 sec-1

5.3.2 The total bridge static response

In the global design we will consider the whole bridge as several beam segments (pontoons) hinged end-to-end. The hinge can have a variable rotational stiffness Kt ranged from zero to EI (the pontoon flexure rigidity). In the Maple sheet, we use a factor fa to calculate a Kt where:

Kt = fa * EI (0 ≤ fa ≤ 1)

The beam flexure rigidity (EI) is calculated in the local design section. The global moment of inertia of the pontoon has to be considered in the flexure rigidity. The applied loads are three types:

4. The concentrated traffic load F: which represents passing vehicle axels (defined in section 2.5.3 in chapter (2)) on both carriageways at the same transversal line. This is simplified as a point load on the bridge.

F = (4*300 + 4*200 + 4*100) = 2400 kN

5. The traffic UDL [qmax ]: the applying of all UDL on both carriageways at the same time can be replaced by the following magnitude: qmax = 2*3*9 + (22.6-2*1.41-2*3) *2.5 = 54 + 34.5 = 88.5 kN/m

6. The sinusoidal wave load qwave (x): applying the extreme wind storm 180km/h as a critical case in the longitudinal direction of the bridge and the resulting sea wave is applied as sinusoidal distributed load which it has a maximum pressure :

Awave = ½ (Hs) * sea water density (ρw)* g* pontoon width (W) = ½*9.81*1030*22.6*Hs qwave (x) = Awave *sin( 2π x/Lwave) = 114.18*Hs*sin( 2π x/Lwave) kN/m

5.3.2.1 Heaving and pitching motion (XZ-plane)

The structural analysis bases on the static response determination by using equation (2-4). The water damping, the inertia force and all time depending terms have been neglected here. The bridge will be analyzed as a beam on elastic foundation and will be modeled as it shown in the figure (4-24). In this structural analysis, we will consider only the heave and pitching motion and by applying the above-mentioned loads in different cases, we can reach to the following results:

TU Delft 197 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

11. Applying the force F on the hinge every two pontoons (Kconnector = 0): the settlement of every hinge under this loading case, when there are no rotational resistance, shows an uplifting of the in between hinge. The maximum deflection is at the two ends.

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0;Lcharacteristic=426m no.1 N k

0 0 4

2 = F

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

12. Applying the force F on the hinge every two pontoons (Kconnector = EI): when the rotational resistance of the connections equal to the bending rigidity of the pontoon for the same loading case, we will notice a large reduction in the settlement of a uniform value for all hinges except the two ends.

18 2 Case Lpontoon=50m; EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector =EI; no.2 Lcharacteristic=426m N k

0 0 4 2 = F

e v r u c

n ) o i t m c e m l ( f e d

e h T

TU Delft 198 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

13. Applying the force F on the hinge every four pontoons (Kconnector = 0): it is necessary to study the maximum deflection under one individual axel load and its influence range when the connector stiffness = 0.

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0;Lcharacteristic=426m no.3 N k

0 0 4 2 = F

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

14. Applying the force F on the hinge every one pontoons with (Kconnector =0): applying the axle load on all hinges shows a uniform deflection except the two ends.

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0;Lcharacteristic=426m no.4

TU Delft 199 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge N k

0 0 4 2

= F

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

15. Applying the force F on the hinge every pontoon with (Kconnector = EI): the use of stiff connectors reduces the deflection at the ends only with a large internal moment reduction.

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector= EI; no.5 Lcharacteristic=426m N k

0 0 4 2

= F

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

TU Delft 200 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

e c ) r N o ( f

r m a a e r h g s

a i e d h T

16. Applying the force F and qmax on the hinge every pontoon with (Kconnector = EI):

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector= EI; no.6 Lcharacteristic=426m N k

N 5 . k

8 0 8 0 =

4 x 2 a

m = F q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

m

r a r a e g ) a h i s N

d (

e e h c r T o f

17. Applying the force F and qmax on the hinge every pontoon with (Kconnector = 0):

18 2 Case Lpontoon=50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0; Lcharacteristic=426m no.7 N k

N 5 . k

8 0 8 0 =

4 x 2 a

m = F q

e v r u c

n ) o i t m c e m l ( f e d

e h T

TU Delft 201 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

18. Applying the qwave on every pontoon with (Kconnector = EI) and wave length smaller than characteristic length: The sea wave loading is created by the extreme windstorm in the longitudinal direction of the bridge. Using Bretschnieder method to determine the wave characteristics with a fetch equal to the bridge length (2000m):

18 2 Case Lpontoon= 50m; EI=4.818×10 N/mm ;Kbuoyancy= 0.228N/mm/mm ; Kconnector= EI; Lcharacteristic= no.8 426m; Hs = 2.07m, Ts = 4.7 sec; windstorm = 180km/h

x

π 2 ( n i s 5 . 9 4 N 1 k

) = e

v e a v a w w L q / ) m m (

e v r u c

n o i t c e l f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

19. Applying the qwave on every pontoon with (Kconnector = 0) and wave length = pontoon length:

TU Delft 202 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

18 2 Case Lpontoon= Lwave =50m;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0; no.9 Lcharacteristic=426m N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

20. Applying the qwave on every pontoon with (Kconnector = 0) and wave length > pontoon length: Wave load wave length > pontoon length, rigid pontoon +free connector

18 2 Case Lpontoon= 50m < Lwave ;EI=4.818×10 N/mm ;Kbuoyancy=0.228N/mm/mm ;Kconnector=0; no.10 Lcharacteristic=426m N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T

TU Delft 203 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

5.3.2.2 Swaying and Yawing (XY-plane)

19 2 Case Lpontoon= Lwave =50 m; EI=2.341×10 N/mm ; Kmooring= 654.8 kN/m/m ; Kconnector= 0; no.1 Lcharacteristic= 485.9 m; Wind storm 1-year (39 km/h); wave force = 39.5 kN/m; wind force = 3.52 kN/s.m; ϕ= 90o e v a w - d n i w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

19 2 Case Lpontoon= Lwave =50 m; EI=2.341×10 N/mm ; Kmooring= 779.4kN/m/m ; Kconnector= 0; no.2 Lcharacteristic= 465.2 m; Wind storm 20-year (74 km/h); wave force = 82.6kN/m; wind force = 11.43kN/s.m

TU Delft 204 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

19 2 Case Lpontoon= Lwave =50 m; EI=2.341×10 N/mm ; Kmooring= 972.1kN/m/m ; Kconnector= 0; no.3 Lcharacteristic= 440.2 m; Wind storm 100-year (180km/h); wave force = 192kN/m; wind force = 67.65kN/s.m N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

TU Delft 205 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

e c ) r N o ( f

r m a a e r h g s

a i e d h T

19 2 Case Lpontoon= Lwave =50 m; EI=2.341×10 N/mm ; Kmooring= 872.1kN/m/m ; Kconnector= 0; no.4 Lcharacteristic= 426 m; Wind storm 100-year (180km/h); wave force = 192kN/m; wind force = 67.65kN/s.m; the extreme sea wave only on the middle pontoon N k

=

e v a w q

e v r u c

n ) o i t m c e m l ( f e d

e h T )

m t n m

e - m N o (

m

m e a r h g T a i d

e c ) r N o ( f

r m a a e r h g s

a i e d h T

5.3.3 The maximum moment capacity of the pontoon

5.3.3.1 The serviceability limit state

A plane deformation in the concrete and the prestressing steel should be considered to determine the cross sectional forces. The linear strain of the concrete should not exceed (1.75*10-3) while the maximum linear strain of the prestressing is (7.605*10-3). From those two conditions, we can determine the minimum elastic compression zone depth of the concrete (Xe) which leads to large concrete deflection within the elastic phase. The elastic deflection of the concrete structure can be reduced by increasing the concrete compression zone depth (Xe) which leads to increasing in the concrete force and the prestressing steel area. The minimum crack width and minimum deformation are the design requirements of the concrete pontoon which floating always on the water. Therefore, we shall choose a large concrete depth (Xe).

TU Delft 206 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

The horizontal forces equilibrium of the cross section can be determined the relation between the (Xe) and the prestressing steel area (Ap). Using the figure (4-33) to determine the relation between the (Xe) and the strain of the prestressing (ϵp) according to the following equations:

 d   X  ∆ϵ = '   p e  p c    X e    X  d '  '  e p  ∆ϵ’p =  c  X   e   X  t  ' '  e topflange   cof   c    X e   d  X  '  s e   s   c    X e  Where: ϵ’c = the concrete elastic strain = 0.00175. ϵ’cuf = concrete strain under the flange. ϵs = conventional steel strain. Ttopflange = top flange thickness. ∆ϵp = the strain of the tensile prestressing.

∆ϵ’p = the strain of the compressive prestressing. dp = the arm of the tensile prestressing steel at the positive moment = 8000 – 500/2 = 7750 mm. d’p = the arm of the compressive prestressing steel at the positive moment = X – 500/2.

The strain of the prestressed steel ∆ϵpmax is determined from the total elastic strain after subtraction of the prestressing strain (ϵpw) which is calculated on base of 15% shrinkage and relaxation losses from the initial prestressing force (Fpi).

9.0  f .0 85     pu  pi p max ptotal pw E E p p 9.0 1690 .0 851350    .7 605103  .5 7375103  .1 8675103 2105 2105

Substitution of this value in equation (4-34) determines the minimum compression depth of the concrete:

d p 7750 X e min   3  3749mm  p max .1 867510 1 3 1  'c .1 7510 The area of the prestressing steel is determined according to the chosen value of (Xe) which has to be more than (Xemin) and the chosen strand diameter and cable size. To increase the bending capacity of the pontoon, it is necessary to use large prestressing steel quantity.

Prestressing cable specification:

TU Delft 207 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

Type : 6-31 No. of strand : 31 Strand diameter : ϕ15.7mm Cross section area of strand : 150mm2 Cable total area : 4650mm2 Duct diameter : 130/137mm Min. anchor spacing c/c : 520mm Min. anchor edge distance c/c: 260mm The cables of the prestressing distributes around the pontoon shell to brace the flexure rigidity in both direction as it shown in the figure (5-14):

Figure (5-14) prestressing cable distributions

No. of cables at the flanges = 30 cable @750mm No. of cables at the external walls = 12 cable @571mm No. of cables at the internal walls = 6 cable @571mm The total used cables = (30)*2+12*2+2*6 = 96 cable The total prestressing area (Ap) = 96*31*150 = 446400mm2 ax = ay = 520mm rx = ry =260mm

The available information is satisfactory to determine the exact compression zone depth(X).

Given: fc’ = compression strength of the concrete = 65*0.6 = 39N/mm2 Ec = 38500N/mm2 FeP 1860: fpu = 1690N/mm2 Ac = 36600000 mm2 Izz =3.7545*10^14 mm4 Zo =4000mm Zb = 8000 – Zo = 8000-4000 = 4000mm Wo = Izz/Zo = 9.38625*1010mm3 Wb = Izz/ Zb = 9.38625*1010mm3 dp top = 500/2 = 250mm dpbottom = 8000 – 250 = 7750mm ds = 8000-50 – 16/2 = 7942mm Area of steel As = ϕ16mm@150mm =150*201 = 30150mm

TU Delft 208 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

Prestressing modulus of elasticity = 200000N/mm2 ' f c 39 2 The concrete elastic modulus of elasticity Ec'elastic    22285.7 N/mm  c .0 00175 The forces in the pontoon cross section can be determined from:

Figure (5-14)

1. The force of concrete is calculated from:

'  1 ' 1 '  N c  Ec'elastic    c  bpontoon  X e   cof bcompartment  X e  ttopflange   2 2   1 1  400   N '  22285   .0 00175  22600  X   .0 00175 1   4 5150  X  400  c  e    e   2 2  X e   10 ' 8 .6 426992 10 N c  .3 213497 10  38998 X e   1376570963N X e

2. The conventional steel tension force is calculated from:  7942    N s   s  E s  As  .0 00175   1  200000  30150  11678267 N  X e 

3. The conventional steel compression force is calculated from:  73  '   N s   s  Es  As  .0 00175  1   200000  30150  11678267 N  X e 

4. The tensile prestressing force in the bottom flange is calculated from:  7750  N p   p  E p  Ap  .0 00175  1  200000  (76  37 150)  155860795 7. N  Xe 

5. The tensile prestressing force in the walls is calculated from:

TU Delft 209 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

 .1 75 10 3  5   N p  walls    p  E p  Ap  2 10    150 * 37  X e 

6 [8000  X e  827  8000  X e 1404  8000  X e 1981]

 4 [8000  X e  2558  8000  X e  3135  8000  X e  3712 ]  32982467 N

6. The prestressing force relaxation in the top flange due to the compressive concrete is calculated from:

' '  ttopflange  N p p E A .0 00175 1  200000 76 37 150 137839974N     p  p             2 X e 

7. The prestressing force relaxation in the walls due to the compressive concrete is calculated from:  .1 75 10  3  5    N p  walls     p  E p  A p  2 10      X e 

(150 * 37 )  6  [X e  827  X e  1404  X e  1981 ]

 4  [X e  2558  X e  3135  X e  3712 ]  25868985 N

From the horizontal equilibrium we can determine the exact (Xe):

 Fx  0

Fpw  N'c N p  N' p  N pwalls   N pwalls  N s  N's  0

Xe = 4864.83mm > Xemin = 3744.9 the prestressing remain in the elastic phase.

The concrete compression zone depth (Xe) is known and the assumed prestressing steel area is checked and adjusted.

5.3.3.2 The ultimate limit states

The behaviour of concrete and the prestressing steel in the ultimate limit state converts totally or partially into the plastic deformation. The upper half of the concrete compression block deforms plastically and the strain reaches the maximum allowable concrete strain (3.5*10-3). The prestress steel takes another linear response stage. The maximum allowable stress is taken from the Dutch Norm NEN6720 and should not exceed (0.95*fpu). The maximum allowable strain is calculated as follow:

 f pu  9.0  f pu  1690 1521 2 E p2    6206 4. N / mm  pu   p.el.max   .0 035  .0 007609091

9.0  f pu  .0 95  f pu  9.0  f pu  1521 84 5.  p max    5   .0 02122 E p E p2 2 10 6206 4.

 9.0  f pu  pw   .0 95  f pu  9.0  f pu  373 5. 84 5.  p max    5   .0 01548 E p E p2 2 10 6206 4.

TU Delft 210 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

 d  X   7750  ∆ϵ = '   p u   5.3 103   1  p cu      X u   X u   X  d '   250  ∆ϵ’ = '   u p   5.3 103  1   p cu      X u   X u   X  t   500  ' '  u topflange  3    cof   cu    5.3 10 1    X u   X u   d  X   7942  '  s u  3    s   cu    5.3 10  1   X u   X u  The forces in the pontoon cross section can be determined from the following: 1. The force of concrete is calculated from:   X  X   N '    X  f '  b   u  t   u   f '  4  b  c  u c pontoon  topflange  c compartment    2  4  

2. The conventional steel tension force is calculated from:

N s  f s  As  435  30150  13115250 N 3. The conventional steel compression force is calculated from: ' N s  f s  As  435 30150  13115250 N 4. The tensile prestressing force in the bottom flange is calculated from:   d   N  9.0  f  A   '  p 1       E  A  p  pu p   cu    9.0 fpu pw  p2 p   X u     7750        9.0 1690   .0 0035 1   .0 00760909  .0 0057375  6206  (76 37 150)     Xu   

5. The tensile prestressing force in the walls is calculated from:  5.3 10 3  5   N p  walls    p  E p  Ap  2 10     150 * 37   X u 

6 [8000  X u  827  8000  X u  1404  8000  X u  1981 ]

 4 [8000  X u  2558  8000  X u  3135  8000  X u  3712 ] 

6. The prestressing force relaxation in the top flange due to the compressive concrete is calculated from:

' '  ttopflange  N p p E A .0 0035 1  200000 76 37 150     p  p             2 X u  7. The prestressing force relaxation in the walls due to the compressive concrete is calculated from:

N p  walls    p  E p  A p  5.3 10 3  5    2 10     (150 * 37 )  6 [X u  827  X u  1404  X u  1981 ]  X u 

 4 [X u  2558  X u  3135  X u  3712 ] 

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 Fx  0

F pw  N 'c N p  N ' p  N p  walls   N p  walls  N s  N ' s  0

Xu =3975.85mm The moment capacity is calculated from the moment equilibrium round the centriod of the pontoon cross section which is in most cases in the middle because of the symmetrical necessity of the pontoon section:  M  0  h  t   h  t   pontoon topflange   pontoon bottomflange  M u  N'c armNc  N p    N' p     N pwalls  armNp   2   2   h   h  N arm N d pontoon  N' d' pontoon    pwalls   N 'p  s  s    s  s    2   2 

Figure (5-16) the concrete compression forces

N  t  N  Xu  t  N  2  Xu hpontoon c1 2 c2  4 2 c3  3 armNc   2 N c1  N c2  N c3 Nc1 = t*hpontoon*f’c Nc2 = 5*twall*(Xu/2 - t)*f’c Nc3 = ½* 5*twall*(Xu/2)*f’c armnc = 8000/2-725.23 = 7274 mm

The maximum moment capacity Mu = 3275*634287225 + 213553232* (8000 - 500)/2 + 91509804*(8000 - 500)/2 + 113279416*(2098) + 2*(13108696*7942) + 29397050*(2098) Mu = 3.72883*1012 N-mm = 3.72883*106 kN-m

5.3.3.3 The shear strength of the pontoon

The concrete shear stress is determined from the equation (4-25): . . 1 ≤ 0.4 fc + 0.15 σ´bm (4-25) 6 σ´bm = Fpw/Ac = ((96*31*150)*0.85*1350) /36.66*10 =13.97 N/mm2

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1 = 0.4* 2.15 + 0.15* 13.97

Vd d = (4-26) b d Vd = 1 *b*d = 0.86* 5*400*8000 = 13760kN . . 2 = 0.2 f’c. kn k (4-27)

5.3.3.4 The pontoon connector rigidity

Figure (5-17) the pontoon connector details

2  w  w  w    2 1 3 (4-25) L

M connector  K connector  (4-26)

The connection between the pontoons represents a layer of cement mortal. The rubber fender of 200mm is used to form the mould to pour the cement mortal. The fender is fixed by the confine it between the two pontoons by some initial prestressing cables. This layer is deform under the compression force and should be limited in the linear behaviour. The tension force of the connector is taken by the prestressing cables that distributed along the cross section edges. The technical properties of C4:

 The rotation stiffness can be determined freely that enable us to get a spectrum stiffness value according to the design requirements.  The spherical connection gives a free space of rotation in both directions more than any conventional joints.  The pitching and yawing motion is allowable.  The existing of the spherical joint ensures the connections when the cables cutting off or fatigued.  The design ensures the cables replacement possibility after life time due to the fatigue without any special requirements or danger.  The symmetrical position of the cables maintains the righting moment in both direction.

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 The prestressing cables should be tensioned to the 55% of the linear behaviour zone of the prestressing cable (0.55*0.9*fp=718 Mpa).  The rotation of the connection should limit so that the stress in the cables not exceed the maximum linear stress (1.0*0.9*fp =1305Mpa) and not to be less than the minimum required stress to keep the cables anchorage (0.1*0.9*fp =130.5 Mpa).  The prestressing cables should be laid in the duct without injected mortar. The duct consists of two parts and each part embedded in a pontoon. The diameter of the duct is determined by the maximum allowable rotation.  The lifetime of the cables is determined by the fatigue calculations of the prestressing cables which depend on the range of the stressing variation.  The maximum allowable rotation is determined by the maximum allowable relative vertical displacement, the cable length, the pontoon length and the pontoon depth.  The connector C6 can be constructed in the midspan of the pontoon and completed in situ and used this pontoon as a flexible connection where is it required along the bridge.

The calculation assumptions:

 The maximum linear stress of the prestressing cable = 0.9*fp =1305 N/mm2  The initial stress of the prestressing cable = 0.55*0.9*fp=718 N/mm2

According to the stress- strain diagram of strand, the stress in the all cables should be ranged from (0.1*0.9*fp =130.5 N/mm2) to (1.0*0.9*fp = 1305 N/mm2) so that the maximum strain in the cables should not exceed the 0.653% and the minimum strain must be not less than 0.0653%. The mentioned strain limitation ensures the linearity in the strain – stress relationship.

5.3.3.5 Pontoon connector analysis

The analysis will be done in both the horizontal and the vertical directions. The maximum rotation will depend on the strand length of the top and bottom layer, which will provide a satisfactory elongation within the elastic phase. The maximum elastic strain of the strand is 7.605*10-3. The connector C4 (see section 2.3.3.1) is selected to use in this case.

The maximum rotation of the connector (θ) XZ- plane: The strand length = 3000+400+3000 = 6400mm 5 -3 The maximum elastic strain of prestressing ϵp.el = 0.9*fp/Ep = 0.9*1450/2*10 = 6.53*10 -3 The maximum strain variation ∆ϵp.el = 0.45* ϵp.el = 2.94*10

The maximum elongation of the strand ∆Lstrand = ∆ϵp.el * cable length = 2.94*10-3 *6400 = 18.8 mm -3 θxz = ∆Lstrand / strand arm = 18.8/ (8000/2-500-500/2) = 5.8*10

From figure (4-27c) log (fa) = -6.6 (the bridge will be considered as non-continuous beam), which will lead to the following connector stiffness:

-6.6 18 12 2 The connector stiffness K connector = fa* Kpontoon = 10 * 4.818×10 = 1.21*10 N/mm From figure (4-26) the maximum allowable relative vertical displacement will be as follow:

-3 w = θxz * Lpontoon = 5.8*10 *50000 = 290mm

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In comparison with the global analysis, we see the (w) is smaller than the expected response. That can we solve it by using longer pontoon or longer strand in the connector.

The maximum moment in the connector Mconnector = K connector * θxz = = 1.21*1012*5.8*10-3 = 7018 kN-m

Figure (5-18) connector C4 with details

The design of the connector:

The moment at the connection in the horizontal (equilibrium) stage is equal to zero because of the symmetrical distribution of the forces round the rotation centre (the forces cancel each other). The moment will arise only when the connection rotates and the moment will commensurate directly with the rotation. If the connection rotates, the cables in one side will be released and the other elongate. This cables deformation will change the forces in cables. These forces will arise the moment which can be calculated as follow:

Prestressing cable specification: F5 F4 Type : 6-1 F3 No. of strand : 1 F2 Strand diameter : ϕ15.7mm F1 Cross section area of strand : 150mm2 2 Cable total area : 50mm d1 d2 d3 d4 d5 Duct diameter : 30/35mm Min. anchor spacing c/c : 95mm Min. anchor edge distance c/c: 48mm

Due to the symmetry

ΔM connector = ∑ {(Fi +ΔFi)* di - (Fi-ΔFi)*di}

Figure (5-19)

= 2*{ΔF1 * d1 + ΔF2 * d2 + ΔF3 * d3 + ΔF4 * d4 +ΔF5 * d5 } when i =1, 2,3,4,5 Δ Fi = Δ σi * Ai , Δ σi = Ep * Δ ɛi , di = 8000/2-500-500/2 = 3250 mm -3 5 Δ Fstrand = 2.94*10 *2*10 *150 = 88.2 kN 6 No. of strand per layer = ΔM connector /2* Δ Fstrand * di = 7018*10 / (2*88200*3250) = 12.25 Try the no. of strand in each side = 13@1580mm

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The maximum rotation of the connector (θxy) XY- plane: -3 θxy = ∆Lstrand / strand arm = 18.8/ (22600/2-400-500/2) = 1.77*10

From figure (4-27c) log (fa) = -5.6 (the bridge will be considered as non-continuous beam), which will lead to the following connector stiffness:

The angle of rotation - moment relationship of the pontoon connector

9000

8000

7000 m - 6000 N k

t

n 5000

e Series1 m 4000 o m

e 3000 h t 2000

1000

0 0.0000 0.0020 0.0039 0.0058 0.0059 0.0079 rotation angle

Figure (5-20) pontoon connector in XZ-plane

-5.6 19 13 2 The connector stiffness K connector = fa* Kpontoon = 10 * 2.341×10 = 5.9*10 N/mm

From figure (4-26) the maximum allowable relative vertical displacement will be as follow: -3 w = θxz * Lpontoon = 1.77*10 *50000 = 290mm The maximum moment in the connector Mconnector = K connector * θxy = = 5.9*1013*1.77*10-3 = 104104.4 kN-m 6 No. of strand per layer = ΔM connector /2* Δ Fstrand * di = 104104.4*10 / (2*88200*10650) = 55.4 Try the no. of strand in each side = 56 @125mm

5.4 Evaluation

The results of the case study can be briefly summarized as follow:

 The deflection is inversely proportional to the wavelength.  The deflection increases linearly with the wave height.  Despite the length of pontoon is shorter than the characteristic length, the bridge segment (pontoon) behaves as an elastic beam. For low flexural rigidity, the deflection is limited locally and relatively small but when we use higher flexure rigidity; the deflection jumps to a higher level and spreads to a larger zone.  Rigid connectors reduce the deflection to a minimum and increase the internal forces to the maximum while the free connectors stiffness provide the maximum deflection value and decrease the internal forces.  Pontoon connector considers fully rigid when the ratio of its stiffness to the pontoon stiffness range from one to 1*10-3 and it considers free connector when this ratio less than 1*10-8.  The maximum deflection occurs at both free ends.  The superposition principles can be used in calculating the total deflection.  Large internal forces occur under the axel load or at both ends of UDL. Chapter VI: Conclusion .

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Content:

6.1 Summary 6.2 Conclusion 6.3 Recommendations

6.1 Summary

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The floating bridges have particular technical characteristics in comparison with the conventional bridges or other floating structures. Most of them can be briefly mentioned as follow:

 Takes advantage of the natural law of water buoyancy.  There is no need for the conventional piers or foundations.  Anchoring or mooring structural system is needed to maintain transverse and longitudinal alignments of the bridge.  It creates an obstacle for marine traffic; therefore, the navigational opening is required.  It need access bridge to connect the abutment because of the tide variation during the day and to reduce the undesirable cross sectional forces when it bases on the abutment directly.  Stability structural system at both ends of the bridge is required to reduce the amplified response of the free end wave’s reflection (that will be explained later).  The floating bridge is a cost-effective solution.  Multi-rigid body analysis has relatively advantage to be complied with the wave loads.

The reasons of selecting floating bridges must be investigated in economical and technical problems. Floating constructions are preferred to fix ones in the following conditions:

 In deep waters where making fixed foundation is very expensive or impossible.  In places with a very weak bed where making fixed foundations is impossible.  In remote places where it is difficult to build or perform a project. For this case the construction can be built in another place and then moved to the main location.  In those ports which have high tides, so there will be a large difference between the surface of the ship’s deck and the fixed jetty.  In military operations, in which there is time limitation for doing the project.  In seismic places where fixed foundations can be shaken severely.  In temporary projects and operations, after which the construction is not useful anymore.  In those projects in which environmental and biological conditions should not be changed a lot.  Smart solution when the conventional bridges are impossible.

6.2 Conclusion

Pontoons

The length of the reinforced concrete pontoons is determined by construction feasibility. In this project 50 m pontoons have been designed. The pontoon length has a substantial influence on the structural behaviour of the bridge, for example on the connection rotation. The pontoon width (22.6 m) follows from the number of road lanes that need to be supported. The pontoon depth is an important parameter that determines the draft (5 m) and freeboard (3 m) which determine the wave and wind loading and the bridge downtime in extreme winds. The pontoons have partitions for increased stiffness, for supporting the bottom and top slab, and for remaining buoyancy in case of a severe collision. The pontoon vertical wall thickness (0.4 m) and horizontal slab thickness (0.5 m) are designed to avoid shear reinforcement,

TU Delft 218 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge assure crack control, and contain prestressing ducts. The force flow due to truck axial load has been determined by linear finite element analysis.

Pontoon connections

In this project several pontoon connections have been studied. The most suitable connection consists of prestressing cables; cement mortal and a rubber water proofing system (see Section 2.3.3 connection C4). The connection stiffness has a large influence on the bridge response. In turn, the bridge response has a large influence on the connection moments and rotation. A good design approach starts by deriving the allowable connection rotation from the length of the cables, thickness of the mortar. Subsequently, the required connection stiffness can be derived from the structural analysis. For this design, graphs have been developed (Figure (4-26)). From the required connection stiffness the number of cables and mortal details can be determined.

Mooring system

The lateral position of a floating bridge is fixed by a mooring system. Often piles are not suitable because of the seabed depth and soil conditions, therefore, cables are used. The mooring system is a nonlinear spring, which includes an anchor, a catenary and a dashpot. From an initial mooring design a linearized horizontal spring stiffness can be derived, which has been used in the structural analysis of the bridge horizontal response due to extreme wind and waves. It is shown that large moments and shear forces occur at both ends of the bridge. This is caused by the fixed position of both ends. Therefore, it is recommended to use extra cables near the bridge ends or build wave breakers at the bridge ends. The mooring system details can be designed from the allowable bridge displacement (acceleration) and the allowable horizontal rotation of the pontoon connections.

Parameter study

From many structural analysis performed the following observations have been made. The ratio connection stiffness over pontoon stiffness is very important for the bridge structural behaviour. When this ratio is smaller than 10-8 the bridge behaves as rigid bodies connected by hinges. When this ratio is larger than 10-3 the bridge behaves as a continuous elastic beam.

Unlike conventional bridges, the moments and shear forces in a floating bridge occur due to changes in the loading. For example when a distributed loading of some length (small traffic jam) is applied, large moments occur at the beginning and the end of this loading.

A moving point load gives a displacement under the load. This displacement is small when the load is in the middle of a pontoon and large when it is above a connection. In extreme cases the difference in displacement can be as much as 0.1 m. This can cause serious problems for fast moving vehicles. The connector stiffness has a large influence on this differential displacement.

The largest deflections, moments, and shear forces occur in the ends of the bridge. Additional supports, masses, or dampers at these ends can reduce these moments and forces strongly.

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6.3 Recommendations

Further optimization of the pontoon length is recommended. Fatigue of the prestressing steel and the concrete are shown to be critical and need to be further investigated. Lateral movement (sway) of the pontoons will reduce the wave forces. This has not been taken into account in this project. It is recommended to develop a method to include this effect.

References

1. N.D.P.Barltrop , “Floating Structures: a guide for design and analysis “ volume one 2. N.D.P.Barltrop , “Floating Structures: a guide for design and analysis “ volume two 3. Wai-Fah Chen, Lian Duan , “Bridge Engineering Handbook “ 4. G. de Rooij , master thesis:” very larger floating terminer” 5. Master thesis report of “Floating foundation “by: Maarten Kuijper. 6. NEN6720 7. Euro code (NVN-ENV 1991-3). 8. Walraven, J.C. Prestressing concrete lecture note of ct4160 and ct3150. Delft University of Technology, the Netherlands 9. Spijkers, J.M.J.& Vrouwenvelder, A.W.C.M. & Klaver, E.C. (2004) Structural Dynamics, CT4140. Delft University of Technology, The Netherlands. 10. W.F.Molenaar,Dr.S.van Baars, H.K.T.Kuijper , “Manual Hydraulic structures”(2008) lecture note of course CT3330 11. Angelo Simone, AN INTRODUCTION TO THE ANALYSIS OF SLENDER STRUCTURES, lecture note of course CT3110 12. http://www.vsl.net/Portals/0/vsl_techreports/PT_Floating_Concrete_Structures.pdf FLOATING CONCRETE STRUCTURES EXAMPLES FROM PRACTICE SECOND PRINTING JULY 1992 13. http://www.jodc.go.jp/info/ioc_doc/JCOMM_Other/WMO702.pdf Guide to the wave analysis and forecasting second edition 1998 14. http://www.issc.ac/img/r16.pdf VERY LARGE FLOATING STRUCTURES volume 2 Issc 2006 15. http://www.andrianov.org/thesis/Thesis.pdf HYDROELASTIC ANALYSIS OF VERY LARGE FLOATING STRUCTURES by: Alexey Andrianov 16. http://mehr.sharif.edu/~scientia/v12n2%20pdf/seif1.pdf Floating Bridge Modelling and Analysis by: M_S_ Seif_ and R_T_ Paein Koulaei 17. http://www.iwwwfb.org/Abstracts/iwwwfb16/iwwwfb16_19.pdf REDUCTION OF HYDROELASTIC RESPONSE OF FLOATING PLATFORM IN WAVES by: T.I. Khabakhpasheva and A.A. Korobkin 18. http://www.seattleasce.org/committees/hh/LaceyBridgeReport.pdf Major Floating Bridges around the World 19. www.ntnu.diva-portal.org/smash/get/diva2:124757/FULLTEXT02 Efficient Prediction of Dynamic Response for Flexible and Multi- Body Marine Structures, by: Reza Taghipour 20. http://en.wikipedia.org/wiki/Main_Page . 21. http://en.structurae.de/structures/stype/index.cfm?ID=1051 . 22. http://www.cesos.ntnu.no/activities/workshops/vlfs/presentations_web/VLFS(Ohmatsu).pdf 23. http://www.lankhorstropes.com/bestanden/Image/Products/Gama98.pdf mooring cables specifications. 24. http://www.eng.nus.edu.sg/core/Report%20200402.pdf VERY LARGE FLOATING STRUCTURES: APPLICATIONS, ANALYSIS AND DESIGN –by: E. WATANABE, C.M. WANG, T. UTSUNOMIYA and T. MOAN 25. http://ce.sharif.edu/~taghipour/publication/OMAE-28343.pdf MOORING SYSTEM DESIGN AND OPTIMIZATION FOR FLOATING BRIDGE OF URMIA LAKE –by: M. Daghigh / R.T. Paein Koulaei/M.S.Seif1 26. http://www.wsdot.wa.gov/NR/rdonlyres/5077880C-AF1A-4252-B60A-01FD6A6A456A/0/HCB 2ndQReport06 .pdf mooring line pontoon connection. 27. http://www.wsdot.wa.gov/NR/rdonlyres/BB05779A-C59A-4A5A-998E-BB45EC55D2A3/0/Bridge _Design_Concepts.pdf floating bridges models.

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28. Dutch norm (ROA & RONA) [Richtlijnen ontwerpen voor / (niet) auto-snelweg]. 29. NEN-1994 30. http://www.wsdot.wa.gov/research/reports/fullreports/558.1.pdf elastomer. 31. http://hbo-kennisbank.uvt.nl/cgi/hu/show.cgi?fid=10960 32. www.designcommunity.com 33. Dr. ir. Cor van der Veen, Concrete Bridges lecture note of ct5127. Delft University of Technology, the Netherlands 34. http://www.fdn-engineering.nl/publicaties 35. (ROA & RONA) [Richtlijnen ontwerpen voor / (niet) auto -snelweg] 36. http://www.wsdot.wa.gov/NR/rdonlyres/5077880C-AF1A-4252-B60A- 01FD6A6A456A /0/HCB2ndQ Report06.pdf 37. Prof. dr. ir. J. Blaauwendraad, lecture note of CT5141, theory of Elasticity direct method. 38. NEN 6723 VBB (1995)

Appendixes

Appendix A

A.1 Dynamic analysis of an individual pontoon

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Before we start with the analysis of the floating body, it is important to define some principles. The hydrodynamics is so complex and comprehensive that simplifications are necessary to achieve the desired result: a simple calculation method for the analysis of a floating object for assessment and verification of the movements.

 principles :

• We consider a rectangular floating platform. In practice, floating platforms are often a rectangular shape. In the case of different forms the basis for calculating is justified to use rectangular shapes.

• We assume a rigid body. For a relatively small floating surface, this simplification is justified. For large surface areas, the elasticity does affect the movements.

• We consider the situations of wave propagation in x or y direction. In the case of vertical current in x direction will pitch, yaw and surge prevention. If there is current in y-direction will be the platform Heave, roll and sway motions. In short current perpendicular to decouple the movements in 2 times 3 coupled movements. Because there is a rectangular platform, it is possible for both directions only heave, roll and sway movements consider.

• In addition we assume that the floating body, we want to design, movements in the horizontal plane (x, y) will prevent sustainable. Movements in the horizontal plane for both floating bridges and floating building are not permissible. The movement restriction will result dynamic loads on the mooring system. We will consider that through the application of a factor to the static load due to the movement of water particles. According to t this assumption, we consider only the roll and heave movements.

• It is assumed that the mooring system practices no any influence on the heave and roll movement. Actually, the mooring system practices an influence only on the roll motion. When the rotation angle of the body is small, we can neglect its influence.

• We have fully decoupled movements. This allows us to treat the individual movements. For a manual calculation is justified.

A.1.1 Heave motion

Heave movement can be described as a damped linear mass-spring system with a spring constant [k] and a damping constant [c]. The mass of the body should be increased by the inertia of the water, as a result of the moved water particles. The total moving mass are called (m + a) and [a] is called the added mass which depend on the body shape and the movement direction.

The equation of motion is:

m  a X  c  X  k  X  F

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Figure (A-1)

The Eigen frequency of the system is an important quantity. The Eigen frequency is the frequency with which a structure will vibrate when there is no external load. An equilibrium state in any structure, which is then released to vibrate in its Eigen frequency, is so-called free vibration. Excitation in the Eigen frequency should be avoided as this may lead to resonance. The Eigen frequency can be determined by equalizes the undamped equation of motion to zero:

m  a X  k  X  0

The external wave force [F] is a function of the wave frequency: F =FA*sin (ω.t) We assume that the body responses with the same frequency: X t  Xˆ sint   If we substitute this equation in the undamped equation of motion we obtain:

 m  a 2  k Xˆ sint    0

This equation can only be zero at any time when the term in brackets equal to zero. The frequency of free vibration can be identified as [ωo]: k  2  o m  a

We will simplify this expression for the case of a rectangular cross section. From the definition of spring force (F = k* x) is easy to derive that [k] is equal to the buoyancy force per unit depth: k = ρw . g . Aw

Aw = the project area of the body on the water = L*b or (= b if we consider it per unit length) 2   b  a = the add mass (for heave motion) =   per unit length of the body. 2  2  b = the body dimension in the wave direction.

By using the Archimedes law to calculate the body mass: m = ρ.b.L.d or = ρ.b.d per unit length

If we substitute all these parameters in the Eigen frequency equation we obtain:

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2 gb g o  2    b  b bd    d  2  2  8

Figure (A-2) the added mass definition of Heave and Sway motion [ref.1]

The Eigen frequency for the heave motion is known. In addition to its Eigen frequency, we need to predict the maximum amplitude of the movement. In the previous section we discussed how to determine the 'wave spectrum Sξ(ω) from the fetch length, water depth and wind speed at 10meters from the significant wave height and peak period. The response spectrum of surface structure Sr(ω) could be found by Sξ(ω) by the Response Amplitude Operator (RAO) in the square. In formula it is:

2 ra S r     S   a

Where:

Sζ(ω) = wave spectrum Sr(ω) = response spectrum 2 r a   ROA- function  a

Based on a Raleigh distribution, we can translate the response spectrum in the significant deflection of the structure:

r  2 m  2RMS a 1 0r 3

For the amplitude in 2% of the cases will be found valid: ra0.02 = 2.79RMS

The standard deviation [σ] (Root Mean Square (RMS)) of the series we can determine by:

N 1 2 RMS      ra,n N 1 n1

ROA- Function:

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We return to the previously treated damped mass spring system:

m  a X  c  X  k  X  F

The load on the construction is time dependant sinusoidal force with an angular frequency equal to the wave frequency:

F = F (t) = FA*sin (ω.t)

We assume that the structure responses with a harmonic motion with the same angular frequency.

X t  Xˆ sin t 

When we substitute these expressions in the equation of motion we find, after some manipulations that the amplitude of the response [x] is equal to: Fˆ Xˆ  2 k   2 m  a  c 2

The dynamic load consists of a wave with the frequency varying pressure on the underside of the structure: the so-called Froude-Krilov added strength and a force caused by the accelerations of water particles in the vicinity of the construction: the added mass force. The Froude-Krilov force when the wave is perpendicular to the longitudinal direction is: H b / 2 Fˆ  Lg e kd cos kx dx HFK    2 b / 2

The force, due to the added mass effect, is: b / 2  2 H Fˆ  L  2 e kd cos kx dx HA  2    2 2 b / 2 ˆ ˆ ˆ F  FHFK  FHA  (k) is the wave number. Since the scope is limited to shallow waters: k  gh The spring constant (k) and added mass (a), as earlier deals, equal to: k = ρw g Aw 2   b  a =   2  2 

The damping coefficient is: c  2 (m  a)  k It is [ξ] the damping ratio. For ships often held the value 0.1 for rectangular structures, the damping higher. It is possible to validate the damping on the basis of computer models (e.g. DELFRAC).

A.1.2 The Roll motion [ref.5]

TU Delft 225 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

The roll movement separately likes the heave motion of a damped mass-spring system. There is no translation only rotation. In the context of ambiguity of the various movements, the same symbols are used. They must also fully aware that the units do not match.

The equation of motion:

  m  a  X  c  X  k  X  F

Figure (A-3) the added mass concept of rolling motion [ref.1].

The dynamic analysis of the roll motion by the corresponding equation of motion is equal to the dynamic analysis of the Heave motion. The method as described in the Heave motion can also be applied. In this framework it is sufficient to list below of relevant formulas:

The mass inertia: 2 The floating object: m  m  iy  iz  2 2 2   b   d   d   The added mass: a  L      r             4   2   2  

The roll-forces (moment round the rotation centre):

1 The Froude-Krilov force at the side face: H 0  b  F  2g L e kz z  r dz sin 2 FKS      2 d  2 

2 The Froude-Krilov force at the bottom face:

H b 2/  y  F  g Le kz sin 2 ydy FKB    2 b 2/    3 The force due to the added mass at the side face: 2 d 1 2 H  k d   B  F  d2L e 2 r sin 2 AMS  2      2     2   2 

4 The force due to the added mass at the bottom face:

TU Delft 226 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

2 1  B  5 B  2 2H   B  F     L ekd sin 2 AMB    2    2  4  4 2     4 

F  FFKS  FFKB  FAMS  FAMB

The [r] in the above formula is the distance between the mass centre of the object and the water surface.

The spring constant: kθ = kθhydrostatic + kθgeometric

b3  d  kθhydrostatic  gL kθgeometric  gLbd   GK  12  2 

Where: GK = distance from the object bottom side to the mass gravity point of the object.

Damping coefficient: b  2 (m  a)  k

2 k For the Eigen frequency it is valid to use: o  m  a  After substitution:

 b 2 d  gbd    KG  12d 2   2    0 2 2 2 2  b   d   d   bd i  i       r   y z          4   2   2  

For the using of a simple formula, the added mass can be sometimes neglected. The usual used formula is the following equation:

g  h  2  m 0 j 2

We call to remind that the term between brackets (in the complete formula for the own frequency) the expression for the metacentre height (hm) for rectangular con instructions. Also we know that the polar radius of inertia (j) is equal to the sum of the inertia of the cross and rays. iy and i z .

Both expressions are (under neglect of the added mass) so similar. In the same way as the Heave motion we can determine the RAO. The term will be so big and complex that an explicit expression no added value.

TU Delft 227 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge Appendix B

Table (B-1) summary of the wave characteristics according to the linear wave theory. [ref.10] Relative Shallow water Transitional water Deep water Depth d/L < 1/25 1/25 < d/L < 1/4 d/L > 1/4 Wave profile H  2 2  Same as > x,t   sin  t  x < same as 2  T L  Wave L L gT  2d  L gT velocity C   gd C   tanh  C  C   T T 2  L  o T 2 Wave length 2 2 gT gT  2d  L  L   C T L  T gd  T C L  tanh  o 2 o 2  L  Group  4d  velocity 1  L  1 gT C  C  gd Cg  1 C C  C  g 2  sinh 4d  g 2 4   L Water particle  2d  H gT cosh2 z  d / L H   velocity: H g u  cos u  e L  cos (a)Horizontal u  cos 2 L cosh2d / L T 2 d  2d  H gT sinh2 z  d / L H   H  z  w  sin  L  w  1 sin 2 L cosh2d / L w  e sin (b)Vertical T  d  T

Water particle 2  2d  gH cosh2 z  d / L     acceleration: H g a  sin a 2H e L  sin a  sin x x     (a)Horizontal x 2 d L cosh2d / L T   gH sinh 2 z  d / L 2  2d  2           z ay  cos a  2H e L  cos L cosh2d / L y   (b)Vertical ay 2H  1 cos T  T  d

Water particle  2 z  d  cosh   displacement:  HgT 2 L    2d  (a)Horizontal  HT g   sin    4L  2d   H  L  x  sin cosh   x  e sin 4 d  L  2  2 z  d  2 sinh    HgT  2d  (b)Vertical H  z   L      cos  H  L   y  1 cos 4L  2d    e cos 2  d  sinh   y 2  L 

Subsurface cosh2 z  d / L  2d  pressure p  g  gz   p  g  z cosh2d / L  L  y  ge gz

The definitions of the symbol: d = the water depth L = the wave length L o = the wave in the deep water H = the wave height (the distance between the crest and trough) T = the wave period C = the wave velocity

TU Delft 228 M.Sc. thesis: Ali Halim Saleh Final report Mega Floating Concrete Bridge

Co = the wave velocity in deep water Cg = the group velocity u = the horizontal velocity of the water particle w = the vertical velocity of the water particle z = the distance between the surface water level to any point in the wave profile ax = the horizontal acceleration of the water particle az = the vertical acceleration of the water particle p = the subsurface water pressure ξ = the water particle displacement η = the water surface profile

TU Delft 229 M.Sc. thesis: Ali Halim Saleh