Earth seismology and earthquake engineering

environ-Herein the seismic behaviour of the Rion-Antirion cable-stayed Bridge, Greece, is studied bymeans of computer analyses employing the finite element method.. State of Research on

and Earthquake Engineering

CableStayed Bridges Earthquake Response and Passive Control

CableStayed Bridges Earthquake Response and Passive Control

Supervisors: Professor A S Elnashai, Professor G M Calvi

Engineering Seismology and Earthquake Engineering Section

Department of Civil EngineeringImperial College of Science, Technology and Medicine

London SW7 2BU

I would like to express my deep gratitude to my two supervisors for this dissertation Firstly mythanks must go to Professor A S Elnashai for his help and guidance throughout the year Hislectures have laid a sound foundation for the work on this project and his constant support evenduring my stay in Italy is greatly appreciated.

Equally important, I would like to thank Professor G M Calvi from the Structural MechanicsSection of Università di Pavia Through him I had the opportunity to work on a fascinatingproject and to experience a beautiful country and a lovely town at the same time His generosity

in taking time to discuss the progress of my work and his support in organising my stay wereessential for my completing the work in time

The comments of Professor N Priestley and the help of the other people at San Diego are alsogratefully acknowledged

Finally and most importantly, I would like to thank my parents who are always there for me

I am grateful for their encouragement and unending support

1.2.2 The trans-European transport network 7

2.1 Configuration of Cable-Stayed Bridges 11

4.4 Calibration investigations on the piers 42

5 CHARACTERISTICS OF THE RION-ANTIRION BRIDGE 44

5.1 Static characteristics - special considerations 44

in the overcoming of barriers that had split people, nations and even continents before.

Figure 1: Normandie Bridge, France

It is evident that they are an important economical factor as well By cheapening the supply ofgoods they contribute significantly to economical prosperity

Cable-stayed bridges, in particular, have become increasingly popular in the past decade in theUnited States, Japan and Europe as well as in third-world countries This can be attributed toseveral advantages over suspension bridges, predominantly being associated with the relaxedfoundation requirements This leads to economical benefits which can favour cable-stayedbridges in free spans of up to 1000m

Many of the big cable-stayed bridge projects have been executed in a seismically active ment like Japan or California However, very few of them have so far experienced a strongearthquake shaking and measurements of seismic response are scarce This enforces the need foraccurate modelling techniques Three methods are available to the engineer to study thedynamic behaviour: forced vibration tests of real bridges, model testing and computer analysis.The latter approach is becoming increasingly important since it offers the widest range of possi-ble parametric studies However, testing methods are still indispensable for calibration purposes

environ-Herein the seismic behaviour of the Rion-Antirion cable-stayed Bridge, Greece, is studied bymeans of computer analyses employing the finite element method A framework of performancecriteria is set up and within this different possible structural configurations are investigated.Conclusions are drawn regarding the effectiveness of deck isolation devices

1.2 Significance of long-span bridges

1.2.1 Impact of bridges on economy

Roads and railways are the most important means of transport in all countries of the world Theyact as lifelines on which many economic components depend Naturally rivers, canals, valleysand seas constitute boundaries for these networks and therefore considerably confine theunopposed supply of goods They cause significant extra costs because goods have to bediverted or even shipped or flown These extra costs can exclude economies from foreignmarkets

It is evident that in this situation bridging the gap is worth considering Cable-supported bridgesoffer the possibility to cross even very large distances without intermediate supports Hence, it isonly since their development, that people can consider crossings like the Bosporus (Istanbul -Anatolia, completed 1973 and 1988), Öresund (Denmark - Sweden, to be completed 2000), theStrait of Messina (mainland Italy - Sicily, design stage finished), the Strait of Gibraltar (Spain -Morocco) or the Bering Strait (Alaska - Russia)

Of course infrastructure projects like these are costly Countries take up high loans to affordthese road links Cost-benefit analyses are inevitable as proof for banks However, the number

of already executed major projects emphasises that even the exorbitant costs can be worthwhile.The bridges become an important factor for the whole region and can significantly boost theindustry on both sides of the new link

Furthermore and equally importantly, those bridge projects can become a substantial factor inthe cultural exchange among people

1.2.2 The trans-European transport network

The European Parliament has on the 23 July 1996 introduced plans for the development of a

"trans-European transport network" ([29]) This project comprises infrastructures (roads,railways, waterways, ports, airports, navigation aids, intermodal freight terminals and productpipelines) together with the services necessary for the operation of these infrastructures.Investments of about 15 billion Euro per year in rail and road systems alone underline theremarks made in the previous section regarding the importance of transport networks and thelinks within them

The objectives of the network were defined by the European Parliament as follows:

- ensure mobility of persons and goods;

- offer users high-quality infrastructures;

- combine all modes of transport;

- allow the optimal use of existing capacities;

- be interoperable in all its components;

- cover the whole territory of the Community;

- allow for its extension to the EFTA Member States, countries of Central and EasternEurope and the Mediterranean countries

Introduction Page 8

Some of the broad lines of Community action concern:

- the development of network structure plans;

- the identification of projects of common interest;

- the promotion of network interoperability;

- research and deve lopment,

with priority measures defined as follows:

- completion of the connections needed to facilitate transport;

- optimization of the efficiency of existing infrastructure;

- achievement of interoperability of network components;

- integration of the environmental dimension in the network

It is apparent that the connections as means of interoperation between sub-networks are one ofthe most important components within the network Many of the currently planned majorbridges in Europe are therefore part of the network and supported by the EU Among them arethe Öresund and Rion-Antirion Bridges which are discussed subsequently

1.3 Recent cable-stayed bridge projects

1.3.1 Öresund Bridge, Sweden

The £1.3 billion Öresund crossing will link Denmark and Sweden from the year 2000 on Itcomprises an immersed tunnel, an artificial island and a bridge part of which is a cable-stayedbridge (Figure 2)

Figure 2: Öresund Bridge, Sweden

For a combined road and railway cable-stayed bridge the center span of 490m (8th largest stayed bridge in the world) is remarkable A steel truss girder of dimensions 13.5x10.5m was

cable-employed to accommodate road and railway traffic on two levels The concrete slab is 23.5mwide and provides space for a 4 lane motorway.

The structurally more difficult harp pattern (see section 2.1.2.1) was chosen for aestheticreasons It should be mentioned that the struts of the girder were inclined according to the angle

of the cables which is favourable from the structural as well as pleasing from the aesthetic point

of view

The money for the project was borrowed on the international market and jointly guaranteed bythe governments of Denmark and Sweden It will be paid back from the toll fees introduced.Being part of the trans-European transport network the link will be one of the most importantEuropean Structures carrying railway and at least 11,000 vehicles per day

More information on the Öresund project can be found in [91]

1.3.2 Tatara Bridge, Japan

Upon completion in 1999 the Tatara Bridge will be the cable-stayed bridge with the longest freespan in the world It is shown in Figure 3, an elevation is given in section 2.1, Figure 5 Thecenter span is 890m, supported by a semi-fan type cable system Compared with this the sidespans with 270 and 320m are extremely short and asymmetric so that intermediate piers andcounterweights needed to be applied there

Figure 3: Tatara Bridge, Japan

The girder is a steel box section with a streamlined shape to decrease wind forces It is 31mwide and only 2.70m deep To act as counterweight the deck in parts of the sidespans is made ofconcrete At the towers the girder is kept free because of high temperature induced forces in thecase of a fixing

In model tests it was found to be necessary to install additional damping devices for the cables.Particularly the upper ones (the longest one having a length of over 460 m - the longest staycable ever) were found to be prone to wind and rain induced vibration Additional ropes

is 7.2s being associated with a longitudinal sway mode.

All information about the Tatara Bridge were taken from [33]

1.3.3 The Higashi-Kobe Bridge, Japan

The Higashi-Kobe Bridge in Kobe City, Japan, is one of the busiest bridges in the world As part

of the Osaka Bay Route it spans the Higashi-Kobe Channel connecting two reclaimed land areas(Figure 4)

Figure 4: Higashi-Kobe Bridge, Japan

The bridge's main span is 485m with the side span being 200m each The main girder is aWarren truss with height a of 9m It accommodates 2 roads at the top and bottom of the trussrespectively Both of these have three lanes, the width of the truss being 16m

For the cable system the harp pattern was chosen The steel towers are of the H-shape and have

a height of 146.5m These are placed on piers which are founded on caissons of size 35 (W) x

32 (L) x 26.5 (H) m

An important feature of the bridge is that the main girder can move longitudinally on all itssupports This results in a very long fundamental period which was found to be favourable forthe seismic behaviour

On 17 January 1995 Kobe was struck by an earthquake of magnitude 7.2 Although the Kobe Bridge performed well in this earthquake, certain damage did occur which was reported in[44] Important information about the soil behaviour could be obtained from this event becausethe bridge was instrumented These will be further discussed in section 2.3.3

Higashi-2 STATE OF RESEARCH ON CABLE-STAYED BRIDGES

2.1 Configuration of Cable-Stayed Bridges

In this section a brief overview of the structural configuration and the load resisting mechanisms

of cable-stayed bridges is given This is necessary because they are in many ways distinctlydifferent from beam-type bridges and these differences strongly affect their behaviour understatic as well as dynamic loads It has to be noted that herein only the current trend of design can

be described An outline of the evolution of cable-stayed bridges and more elaborateinformation can be found elsewhere: [50], [87]

Figure 5: Tatara Bridge, Japan, elevation

It is apparent from the picture that the close supporting points enable the deck to be very slim.Even though it has to support considerable vertical loads, it is loaded mainly in compressionwith the largest prestress being at the intersection with the towers This is due to the horizontalforce which is applied by each of the cables This characteristic also distinguishes the cable-stayed bridge from the suspension bridge because necessary provisions for anchoring cables aremuch more relaxed Often cable-stayed bridges are even constructed as being self-anchored.The particular components of this bridge type will now be discussed in more detail However, ifmore comprehensive information are sought the reader is referred to [50] and [87]

State of Research on Cable-Stayed Bridges Page 12

- harp system and

- modified fan system

These are depicted in Figure 6 All of these patterns can be used for single as well as for doubleplane cable configurations

Figure 6: Cable patterns in cable-stayed bridges ([50])

In the fan system all cables are leading to the top of the tower Structurally this arrangement isusually considered the best, since the maximum inclination of each cable can be reached Thisenables the most effective support of the vertical deck force and thus leads to the smallestpossible cable diameter

The fan system causes severe detailing problems for the configuration of the anchorage system

at the tower The modified fan system overcomes this problem by spreading the anchoragepoints over a certain length If this length is small, the behaviour is not significantly altered.The stay cables are an important part of the bracing system of the structure It was found thattheir stiffness is highest when the cable planes are inclined from the vertical This favours A-shaped towers with all the cables being attached to one point or line at the top

In the harp system the cables are connected to the tower at different heights and placed parallel

to each other This pattern is deemed to be more aesthetically pleasing because no crossing ofcables occurs even when viewing from a diagonal direction (in contrast see Figure 1) However,this system causes bending moments in the tower and the whole configuration tends to be lessstable However, excellent stiffness for the main span can be obtained by anchoring each cable

to a pier at the side span as was done for the Knie Bridge, Germany ([87])

Most of the recent cable-stayed bridges, particularly the very long ones, are of the modified fan

type with A-shaped pylons for the discussed reasons However, there are still many variationsregarding the configuration of the abutments, piers and towers and their respective connectionwith the stiffening girder These problems will be discussed subsequently in the light of thedynamic behaviour.

2.1.2.2 Types of cables

The success of cable-stayed bridges in recent years can mainly be attributed to the development

of high strength steel wires These are used to form ropes or strands, the latter usually beingapplied in cable-stayed bridges

There are 3 types of strand configuration:

- helically-wound strand,

- parallel wire strand and

- locked coil strand

Figure 7 shows these arrangements

Figure 7: Helically-wound, parallel wire and locked coil cable strands ([50])

The first two types are composed of round wires Helically-wound strands comprise a centrewire with the other wires being formed around it in a helical manner They have a lowermodulus of elasticity than their parallel counterparts and furthermore experience a considerableamount of self-compacting when stressed for the first time

Locked coil strands consist of three layers of twisted wire The core is a normal spiral strand It

is surrounded by several layers of wedge or keystone shaped wires and finally several layers ofZ- or S-shaped wires The advantages of this type of cable are a more effective protectionagainst corrosion and more favourable properties compared with the previous arrangements.First, the density is 30% higher, thus enabling slimmer cables which are less sensitive to windimpact Second, their modulus of elasticity is even 50% higher compared with a normal strand

of same diameter Third, they are largely insensitive to bearing pressure because of a betterinteraction of the individual wires

The vast majority of modern cable-stayed bridges use galvanised locked-coil wire strands Theseare assembled to the large diameter cables, which are usually parallel strand cables

State of Research on Cable-Stayed Bridges Page 14

2.1.2.3 Anchorage of cables

Cables need to be anchored at the deck as well as at the towers For each of these connectionsnumerous devices exist depending on the configuration of deck and tower as well as of thecable Exemplary, some arrangements for tower and deck are shown in Figure 8 and Figure 9respectively

Figure 8: Devices for cable anchorage at the tower ([87])

Figure 9: Devices for cable anchorage at the deck ([50])

Cable supports at the tower may be either fixed or movable They are situated at the top or atintermediate locations mainly depending on the number of cables used While fixed supports areeither by means of pins or sockets, movable supports have either roller or rocker devices

Connections to the deck are by means of special sockets Their configuration strongly depends

on the type of cable used Usually these sockets are threaded and a bolt is used to allowadjustments on the tension of the cable

2.1.3 Stiffening Girder

The role of the stiffening girder is to transfer the applied loads, self weight as well as trafficload, into the cable system As mentioned earlier, in cable-stayed bridges these have to resistconsiderable axial compression forces beside the vertical bending moments This compressionforce is introduced by the inclined cables

The girder can be either of concrete or steel For smaller span lengths concrete girders areusually employed because of the good compressional characteristics However, as the span

increases the dead load also increases, thus favouring steel girders The longest concrete bridgethat has been constructed is the Skarnsund Bridge, Norway, with a main span of 530 m ([58]).Also composite girders have been extensively used, entering the span range above 600 m.

The shape of the stiffening girder depends on the nature of loads it has to resist In the design ofvery long-span bridges aerodynamic considerations can govern the decision These are beyondthe scope of this work but brief account of this issue will be given It was shown in [41], thatbluff cross sections which have a higher drag coefficient, experience considerably highertransverse wind forces than less angular sections Specially designed streamlined sections canalso avoid the creation of wind-turbulence at the downstream side, a phenomenon referred to asvortex-shedding Considerable affords are therefore made to account for these circumstances.For the Tatara Bridge these were reported in [33]

There are three types of girder cross sections used for cable-stayed bridges:

- longitudinal edge beams,

- box girders and

Figure 10: Girder cross-sections: a) simple beam arrangement (Knie Bridge,

Germany), b) box section (Oberkasseler Bridge, Germany),c) truss (Öresund Bridge, Sweden) ([50])

State of Research on Cable-Stayed Bridges Page 16

Beam arrangements consist of a steel or concrete deck which is supported by either a steel or aconcrete beam The beams carry the loads to the cables where they are anchored Although easy

to construct and generally efficient, beam-type girders have only a small torsional stiffnesswhich can be undesirable depending on the structural system

Box sections possess high torsional stiffness and can be formed in a streamlined shape thusshowing best behaviour under high wind impact However, there are numerous possible shapesand the choice depends on the distances between the supports, the desired width of the section,the type of loading and the cable pattern

Trusses have been used extensively in the past They possess similar torsional stiffnesses as boxsections The aerodynamic behaviour is generally good Trusses are of steel and thus thestiffness is high with respect to the weight However, the high depth of the section can becriticised for aesthetic reasons Trusses are unrivalled if double deck functionality is desired Inthis case the railway deck can be accommodated at the bottom chord

2.1.4 Towers

The function of the towers is to support the cable system and to transfer its forces to thefoundation They are subjected to high axial forces Bending moments can be present as well,depending on the support conditions It has already been pointed out that the towers in harp-typebridges are subjected to severe bending moments Box sections with high wall widths generallyprovide best solutions They can be kept slender and still possess high stiffnesses

Towers can be made of steel or concrete Concrete towers are generally cheaper than equivalentsteel towers and have a higher stiffness However, their weight is considerably higher and thusthe choice also depends on the soil conditions present Furthermore, steel towers haveadvantages in terms of construction speed

The shape of the towers is strongly dependent on the cable system and the applied loads butaesthetic considerations are important as well Possible configurations are depicted in Figure 11

Figure 11: Tower configurations: H-, A- and λ-shapes ([50])

While I- and H-shapes are vertical tower configurations and therefore support vertical cableplanes, A- and λ-shaped towers correspond to inclined cable planes The influence of thesepatterns on the overall stiffness of the structure have been discussed earlier As far as thestiffness of the tower itself is concerned, A- and λ-shapes are preferable However, theirstructural configuration is significantly different from the I- and H-shape which can haveadverse effects on the ductility (cf section 5.1.2).

Cable-stayed bridges often need to be founded in water In this case caisson foundations areused The caisson acts as a block and can be placed either on the sea bed or, again, on piles

2.2 Nonlinearities in Cable-Stayed Bridges

Cable-stayed bridges have an inherently nonlinear behaviour This has been revealed by veryearly studies and shall be discussed in detail here because the nonlinearity is of greatestimportance for any kind of analysis

Nonlinearities can be broadly divided in geometrical and material nonlinearities While the latterdepend on the specific structure (materials used, loads acting, design assumptions), geometricnonlinearities are present in any cable-stayed bridge

Geometric nonlinearity originates from:

- the cable sag which governs the axial elongation and the axial tension,

- the action of compressive loads in the deck and in the towers,

- the effect of relatively large deflections of the whole structure due to its flexibility([1], [4], [9], [50], [52], [73], [74], [75], [87], [88])

It is well known from elementary mechanics that a cable, supported at both ends and subjected

to its self weight and an externally applied axial tension force, will sag into the shape of acatenary Increasing the axial force not only results in an increase in the axial strain of the cablebut also in a reduction of the sag which evidently leads to a nonlinear stress-displacementrelationship The influence of the cable sag on its axial stiffness has first been analyticallyexpressed by Ernst ([34]) If an inclined cable under its self weight is considered, an equivalentelastic modulus can be calculated as follows:

State of Research on Cable-Stayed Bridges Page 18

( )3 2

12

1

σ

E l w

E

E e

⋅+

where: E e is the effective modulus of elasticity of the sagging cable,

E is the modulus of elasticity of the cable which is taut and loaded vertically,

w is the unit weight of the cable,

l is the horizontal projection of the cable length and

σ is the prevailing cable tensile stress

This relationship can be easily implemented in nonlinear computer codes

It is interesting to note that the above described cable behaviour leads to an increase in thebridge stiffness if the forces are increased This is depicted in Figure 12 and clearly distin-guishes cable-supported structures from standard structures They can be classified as being ofthe geometric-hardening type ([2], [4], [5])

Generalized Displacement

Figure 12: Nonlinearities in cable-stayed bridges

Today most finite element programs offer nonlinear solution algorithms With these it ispossible to take the above mentioned characteristics of cable-stayed bridges into account Thenonlinear cable behaviour can be either treated utilising Ernst's formula or applying multi-element cable-formulations This issue will be further discussed in section 2.3.1

The nonlinear behaviour of the tower and girder elements due to axial force-bending momentinteraction is usually accounted for by calculating an updated bending and axial stiffness of theelements Detailed descriptions of nonlinear element formulations can be found in [32], [57],[107] and elsewhere

The overall change in the bridge geometry as third source of nonlinearity can be accounted for

by updating the bridge geometry by adding the incremental nodal displacements to the previousnodal coordinates before recomputing the stiffness of the bridge in the deformed shape ([74])

2.3 Dynamic behaviour and earthquake response

2.3.1 General dynamic characteristics

Long-span cable-supported bridges, due to their large dimensions and high flexibility, usuallyhave extremely long fundamental periods This distinguishes them from most other structuresand strongly affects their dynamic behaviour However, the flexibility and dynamic charac-teristics depend on several parameters such as the span, the cable system and the supportconditions These will be discussed in detail here

The dynamic behaviour of a structure can be well characterised by a modal analysis The linearresponse of the structure to any dynamic excitation can be expressed as superposition of itsmode shapes The contribution of each mode depends on the frequency content of the excitationand on the natural frequencies of the modes of the structure

The results of modal analyses of cable-stayed bridges can be found in most of the researchpapers dealing with their seismic behaviour In Figure 13 the first modes obtained by Abdel-Ghaffar for a model bridge in [1] are shown The first modes of vibration have very long periods

of several seconds and are mainly deck modes These are followed by cable modes which arecoupled with deck modes Tower modes usually are even higher modes and their coupling withthe deck depends on the support conditions between these The influence of different supportconditions on the mode distribution has been investigated by Ali and Abdel-Ghaffar in [9] It isapparent from the resulting diagram shown in Figure 14 that movable supports lead to a moreflexible structure, thus shifting the graph towards longer periods As an example, in [44] it wasmentioned by Ganev et al that the Higashi-Kobe Bridge has been deliberately designed withlongitudinally movable deck in order to shift the fundamental period to a value of low spectralamplification The decision upon the support conditions of the deck is usually governed byserviceability as well as earthquake considerations A restrained deck will avoid excessivemovements due to traffic and wind loading and may thus be preferred However, in the case of

an earthquake a restrained deck will generate high forces which are applied to the pier-pylonsystem It is thus a trade-off and often intermediate solutions are sought Elaborate investiga-tions on possible damping solutions are discussed subsequently in this report

Usually the modes obtained are classified in their directional properties Thus, vertical,longitudinal, transverse and torsional modes are distinguished and the order of these wellcharacterises the bridge behaviour without the need to depict the individual mode shapes As anexample the first 25 modes of the Quincy Bayview Bridge, US, are given in Table 1 They havebeen identified experimentally as will be discussed later

State of Research on Cable-Stayed Bridges Page 20

Figure 13: First six computed mode shapes (considering one-element cable

discretisation) ([1])

Figure 14: Effect of support conditions on the natural periods ([9])

Typical for cable-stayed bridges is a strong coupling (such as bending-torsion coupling) in thethree orthogonal directions as can also be seen in Table 1 This coupled motion distinguishescable-stayed bridges from suspension bridges for which pure vertical, lateral and torsional

motions can be easily distinguished This also implies that three-dimensional modelling isinevitable for dynamic analyses.

The importance of the cable vibration for the overall response of the bridge was pointed out byAli and Abdel-Ghaffar in [2], Abdel-Ghaffar and Khalifa in [9] and Ito in [56] They concludedthat appropriate modelling of the cable vibrations is necessary For this purpose multi-elementformulations for the cables are suggested Only if the mass distribution along the cable ismodelled and associated with extra degrees of freedom the vibrational response of the cablescan be obtained In [2] a modal analysis was performed modelling the cables with multi-elementcable discretization It was pointed out that there is coupling between the cable and deck motioneven for the pure cable modes which suggests not to solely rely on analytical expressions fornatural frequencies of a cable alone In [9] it was found that the natural frequencies of the cablesare strongly dependent on the cable sag as can be seen in Figure 15

Figure 15: Effect of the sag-to-span ratio on the natural frequencies of a cable,

analytical and experimental results ([9])

An analytical method for calculating natural frequencies of cable-stayed bridges has beendeveloped by Bruno and Colotti in [18] and Bruno and Leonardi in [19] Prevailing trussbehaviour and small stay spacing have been assumed and on this basis diagrams showing themain natural frequencies depending on geometric parameters were developed These werecompared with results from numerical analyses and a good agreement was found

For existing bridges the modes can be obtained from vibration measurements Ambientvibration measurements of the Quincy Bayview Bridge, US were undertaken by Wilson et al.The dynamic response of the bridge to wind and traffic excitation was measured The resultsobtained were reported in [94] and the mode shapes are depicted in Table 1

State of Research on Cable-Stayed Bridges Page 22

Table 1: Experimentally identified Modes of the Quincy Bayview Bridge

([94])

It should be mentioned here, that a response spectrum analysis on the basis of a performedmodal analysis is highly questionable although differently stated in some older papers (e.g.[92]) Firstly, modal superposition is only possible for linear structural behaviour, which isusually not the case for cable-supported bridges as explained in section 2.2 Secondly, even iflinearity could be presupposed, the superposition procedure must be based on reasonableassumptions and methods like the SRSS procedure are only valid for well-spaced modes which

is, again, not necessarily the case for cable-supported structures Hence, the level of safetyreached would not be assessable

2.3.2 Damping characteristics

Cable-stayed bridges have inherently low values of damping It is therefore even more important

to have accurate information about the level of damping reached by the structure Research onthis issue has shown that generalisation of damping values is difficult because dampingcharacteristics vary significantly depending on the configuration of the bridge Sources ofenergy dissipation in cable-stayed bridges are: material nonlinearity, structural damping such asfriction at movable bearings, radiation of energy from foundations to ground and friction withair

There are essentially two ways in which damping is considered in most past investigations.Firstly, energy dissipation by elastic-plastic hysteresis loss can be considered This requiresconducting a nonlinear analysis with the application of material nonlinearity and is mostimportant when special energy absorption devices are to be modelled Secondly and mostcommonly, an equivalent viscous damping can be introduced in the system in the form of a

damping matrix C Damping in cable-stayed bridges is undoubtedly not viscous However, it is

an easy to implement and reasonable treatment of the problem as explained by Abdel-Ghaffar in[9] Usually the damping matrix is established using a linear combination of mass and stiffnessmatrix This is called Rayleigh damping and enables satisfying damping ratio exactly for 2modes as shown by Clough and Penzien ([27]) An established estimate of viscous dampingratio seems to be 2% for cable-stayed bridges According to Abdel-Ghaffar ([1]) values of thislevel have been found in many measurements Damping ratios of 2-3% have in the past been

employed by many investigators in their analyses without further discussion ([1], [2], [4], [5],[9], [10], [31], [38] , [66], [73]).

Dynamic testing of two bridge models of 3.22m length was conducted by Garevski and Severn([47], [48]) Shaking table tests were performed as well as excitation by means of electro-dynamic shakers The results obtained are shown in Table 2 It is important to note that thedamping ratio notably depends on the mode under consideration This is due to the differentmode shapes and the different member contributions in these On the other hand it is obviousfrom the differences between the testing methods that experimental results should also be usedwith caution

Frequency (Hz)

Damping (%)

Frequency (Hz)

Damping (%)

Frequency (Hz)

Damping (%)

Table 2: Experimentally measured damping (Garevski and Severn, [48])

Several studies on damping characteristics of cable stayed bridges were conducted byKawashima et al and reported in [60], [61], [62], [63] and [64] Model oscillation tests weredone in which the damping ratio was computed from the averaged decay over 13 cycles Apicture of the model, which represents the Meiko-nishi Bridge, Japan, is given in Figure 16

Figure 16: Experimental Bridge Model, Kawashima et al ([64])

In the tests the damping ratio was found to be dependent on the amplitude of excitation and themode shape (cf Figure 17) as well as on the cable pattern Damping ratios for the fan-typebridge were in the range between 0.6-0.8% while the harp-type structure had damping ratiosbetween 1.2 and 1.5%, the higher values being for higher amplitudes of oscillation Higherdamping ratios of the harp configuration can be attributed to larger flexural deformations of thedeck in vertical direction which leads to a higher energy dissipation

State of Research on Cable-Stayed Bridges Page 24

Figure 17: Experimentally measured damping (Kawashima and Unjoh, [61])

Because damping ratios vary with structural types, Kawashima suggested an approach in whichthe energy dissipation capacity is evaluated for each structural segment ([60], [64]) From thisthe overall damping can be calculated The structural segments in which energy dissipation isconsidered uniform are referred to as substructures These could be deck, towers, cables andbearing supports Material nonlinearity is considered to be the prevailing mechanism for energydissipation Kawashima et al reduced the problem to applying so called energy dissipationfunctions for the substructures which can either be obtained by experiments or taken from theirwork

Kawashima and his co-workers also investigated the damping activated under earthquakeconditions In [62] it is stated that in an earthquake considerably higher damping values arefound than the ones usually obtained from forced vibration tests Hence, strong motion datarecorded at the Suigo Bridge, Japan, during 3 earthquakes were used to estimate dampingratios These are found to be 2% and 0-1% of critical in longitudinal and transverse direction,respectively, for the tower, and 5% in both directions for the deck

From their model tests of the Quincy Bayview Bridge (already mentioned in 2.3.1) Wilson et al([94]) also obtained an estimate for the range of damping of the bridge They found the upperand lower bound of the damping ration for the first coupled transverse/torsion mode to be 2.0-2.6% and 0.9-1.8% respectively

2.3.3 Influence of soil conditions and soil-structure interaction effects

It is well established that the soil that a structure is founded on has a significant effect on theearthquake response of this structure This is due to three main mechanisms that are referred to

as soil amplification, kinematic interaction and inertial interaction Firstly, amplitude andfrequency content of the seismic waves are modified while propagating through the soil.Secondly, kinematic interaction means the influence that the soil would have on the movement

of a massless, rigid foundation embedded in the soil Thirdly, inertial interaction describes theeffect that the inertia of the moving structure has on the deformation of the soil Thesecomponents cannot be further discussed here However, brief account shall be given ofinvestigations on the importance of soil-structure interaction on the behaviour of cable-stayedbridges and possible treatments of the problem

Well established for modelling the soil-structure interaction is the substructure approach,described by Betti et al in [16] It deals with each part of the system (soil, foundation,superstructure) separately The main advantage is that the analysis of each subsystem can beperformed by the analytical or numerical technique best suited to that particular part of theproblem: e.g finite element method for the superstructure, continuum mechanics analysis forthe soil The individual responses are combined so as to satisfy the continuity and equilibriumconditions.

The other modelling approach comprises the so called direct methods Here, the soil is included

in the global analysis model Different element formulations and properties can be used for soiland structure but the problem is solved as one This imposes great importance on the boundaryconditions to be used in the model For further treatment of this problem reference is made tothe publications by Wolf: [95], [96]

Zheng and Takeda in [106] investigated the applicability of soil-spring models for foundationsystems Analyses on a 2-D finite element model of the soil were compared with those of thesimplified model It was found that the simplified model shows good agreement with reality forlow frequency input motions while the errors increase for higher frequencies In Figure 18transfer functions for both horizontal and vertical motions are shown These results suggest that

a mass-spring model would be a good approach for the analysis of long-period structures likecable-stayed bridges However, the contribution of higher modes could be underestimated

Figure 18: Transfer functions for horizontal and vertical component of effective

input acceleration at top of foundation computed by 2-D FEM andmass-spring model ([106])

Elassaly et al in [31] presented results of a case study investigating the effects of differentidealisation methods for a pile foundation system on the earthquake forces acting on thestructure Two cable-stayed bridges were studied in this context Firstly, a so called Winklerfoundation making use of spring and damper elements was employed Secondly, a discretization

of the surrounding soil with plain strain elements was used as shown in Figure 19

State of Research on Cable-Stayed Bridges Page 26

Figure 19: Modelling approaches for soil-pile interaction; top: Winkler model,

bottom: plain strain finite element modelling ([31])

It should be emphasised that, in contrary to other investigations, the bridge superstructure wasmodelled entirely, too This is deemed to be important, since it significantly contributes to theinteraction between soil and foundation It could be shown in time-history analyses, thatneglecting the effects of local soil conditions and the soil-structure interaction results in a greatunderestimation of displacements of the superstructure particularly for soft soils Under-estimation mainly occurs if the soil site has a fundamental frequency close to the one of thestructure In terms of simplified approaches it was stated that fixed base modelling approachescan only be justified for structures founded on rock On the other hand, the accuracy ofemploying an "equivalent stiffness" strongly depends on the conditions of the case in questionand the way in which this stiffness has been evaluated

Betti, Abdel-Ghaffar et al ([16]) investigated the influence of both soil-structure interactioneffects and the different seismic waves on the response of a cable-stayed bridge Analyses werecarried out using a fixed structure and a structure with the soil interaction modelled using thesubstructure method Most interestingly it was found that inclined incoming waves, in-plane aswell as oblique, cause a rocking motion of the foundations This behaviour underlines theimportance of including soil-structure interaction effects since a rocking motion of thefoundations has a great effect on the behaviour of the bridge piers and thus of the wholestructure

Investigations on the response of the Higashi-Kobe Bridge (see also section 1.3.3) and thesurrounding soil during the Hyogoken-Nanbu Earthquake have been undertaken by Ganev et al([44]) Time-histories that were recorded by the downhole soil accelerometer and the surfaceaccelerometer showed clear evidence of liquefaction Because the acceleration at the surface issmaller than the one at 34m depth and exhibits longer period motions, it was concluded that thesurface soil layers which consist of loose saturated sands had actually been liquefied during theearthquake The measurements from the instrumented bridge could also be employed to validatenumerical approaches for analysis of soil-structure interaction Extensive analyses usingdifferent computer codes have been conducted in this context In the present case one of themost important issues associated with interaction analysis is the degradation of the soil stiffness.Three factors are considered to have the largest effect on this: non-linear stress-strain

dependence of the soil material, separation of soil from the structure and pore-water pressurebuildup For explanations on the modelling approach used to take these into account the reader

is referred to the paper mentioned above Good correlation between the instrumentation data andthe numerical analyses could be achieved as can for example be seen in Figure 20

Figure 20: Simulation of the earthquake response to the 1995 Hyogoken-Nanbu

Earthquake ([44])

2.3.4 Structural control

The field of vibration control has experienced an immense evolution in the past years.Fundamentally different techniques have been developed and many different devices areavailable For extensive descriptions of these reference is made to publications like [72] and[42] Herein, only a broad overview can be given

Control of dynamic response can be either active or passive While active control is dependent

on external power supply, passive devices are not Active control is essentially based onavoiding the impact of forces by modifying the vibration in a favourable way, e.g additionalmasses are controlled so as to counteract the inertial forces of the structural members For cable-stayed bridges special solutions like "active tendon control" (Achkire et al [6], Warnitchai et al[90]) have been developed In this, sensors near the lower anchorage of the cables detect thegirder motion Passed through a linear feedback operator the resulting signals are fed toservohydraulic actuators fixed at the cable ends These actuators change the cable tension,therefore providing a time-varying force upon the girder This mechanism is depicted inFigure 21

Results of investigations on the effectiveness of active tendon control can be found in [84], arecent paper by Schemmann et al

State of Research on Cable-Stayed Bridges Page 28

Figure 21: Active tendon control of a cable-stayed bridge ([90])

Although active control can be highly effective, the costs are obstructive and for an emergencysituation like an earthquake the dependence on electrical power is deemed to be unfavourable.Passive control is based on energy dissipation in special devices These devices are placed atcritical zones such as the deck-abutment and deck-tower connections to concentrate hystereticbehaviour in these specially designed energy absorbers Inelastic behaviour in primary structuralelements of the bridge can therefore be avoided, assuring the serviceability after an earthquake

An extensive study on possible applications of energy dissipation devices on cable-stayedbridges has been conducted by Ali and Abdel-Ghaffar ([10]) Recent applications have beenintroduced and modelling guidelines for lead-rubber bearings proposed This paper makes clearthat particularly for cable-stayed bridges no standardised passive control solutions can bedeveloped Many solutions are generally possible and their applicability depends on thebehaviour characteristics of the bridge as well as on the design aim However, it is stated thatthe new trend in cable-stayed bridge design is to have the main deck fixed to neither towers norpiers but to support them elastically by means of dampers, cables and links The use of theseelastic supports makes it possible to control the natural period of vibration, and accordingly arevery effective in reducing the dynamic forces and, consequently, the size of the towers and thefoundations

3 THE RION ANTIRION BRIDGE

3.1 Introduction to structure and site

The Rion-Antirion Bridge will cross the Gulf of Corinth near Patras in western Greece It is part

of the country's new west axis, a major national transport project This highway will connectKalamata in the south, Patras, Rion, Antirion and Igoumenitsa in the north Being linked withtwo other major axes it forms part of a new high-performance transport network which is also apart of the trans-European network described in section 1.2.2 The objective is to establish directaccess of all major urban centers of Greece (Patras, Athens, Lamia, Larissa, Thessaloniki) fromthe developing neighbouring countries in the Balkan region, the other European countries andthe east Vital is also the connection of the major harbours to the network

The main bridge of the Rion-Antiron crossing is a cable-stayed bridge It is located in anexceptional environment consisting of high water depths and rather weak soil deposits as will befurther discussed in 3.2.5 Additionally, the seismic activity in the area is severe which makesthe design even more challenging The final solution will be described in detail subsequently

3.2 Description of the structure

The main part of the Rion-Antirion Bridge is a continuous multi-cable-stayed bridge, supported

by four large pylon/pier structures named M1, M2, M3 and M4 resting on the sea bed Doublecantilevers are built from each of the pylons Final junctions are then made between the centralcantilevers and the outer parts are extended towards the transition piers so that the final spanlengths are 286, 3x560 and 286 m The transition piers are connected to approach viaducts.The bridge has two 9.50m wide carriageways, separated by a 0.50m wide central separator with

a double safety fence and bounded by lateral crash barriers

The main structural configuration can be seen in Figure 22

Figure 22: Rion-Antirion Bridge, elevation of main bridge ([81])

The Rion Antirion Bridge Page 30

3.2.1 The deck

The bridge deck is a composite steel-concrete structure (depicted in Figure 23) consisting of:

- two main longitudinal steel girders, 2.20m high, spaced at 22.10m These beams areI-shaped plate girders with variable sections, the maximum width of the lowerflange being 2.00m

- Transverse I-shaped plate girders spaced at 4.06m Both longitudinal and transversebeams include stiffeners to avoid local buckling of the steel plates

- A top reinforced concrete slab connected with the girders by steel studs Theconcrete grade is C60/75 The slab thickness is generally 25cm, increased to up to40cm above the girders

The overall slab width is 27.20m including two 1.95m wide cantilevers The central partbetween the main steel girders is precast to ensure best concrete quality

Figure 23: Rion-Antirion Bridge, deck cross section ([81])

The deck is supported by steel stay cables These are anchored directly above the web of themain girders

It should be noted that the deck is only supported by the stay cables at the main pylons Nobearings are provided to the deck by the piers However, isolation and dissipation devices areplanned to be placed between the deck and the pylon base in transverse direction These are tolimit the relative displacements between the deck and the piers in the case of a severeearthquake

3.2.2 The pylons and piers

The four pylons, providing the anchorage for the stay cables, are composed of four reinforcedconcrete legs, joined at their top level to a composite steel-concrete pylon head The bases of thelegs are rigidly restrained in a prestressed concrete pylon base The total height of the pylons is113m above the 3.50m thick pylon base

The pylon legs are square shaped concrete box girders, the outer section of these being 4.0x4.0mand the minimum wall thickness being 60cm The pylon head is 35.0m high and has a squarehollow section of 8.0x8.0m

The pylon base is composed of four prestressed concrete beams, 3.50m high and 6.00m wide.These beams form a square grid of 40.0x40.0m They provide a structural junction between thepier head and the pylon legs and also constitute the anchorage for the isolating devices betweendeck and pier

An elevation of the pylon/pier system is shown in Figure 24

Figure 24: Rion-Antirion Bridge, tower ([81])

The Rion Antirion Bridge Page 32

The main piers are reinforced concrete structures, consisting of the following parts:

- the "pier head": a spatial structure of height 15.28m and varying thickness, joiningthe square pylon base to the octagonal pier shaft,

- the "pier shaft" with its base 3m above mean sea level Because of the variableheight of the deck the length of this pier shaft is different for the four piers

- The "cone" allows the adaptation to the actual soil level at each pier site Hence, thelength of the cones varies for the certain piers They have an external diameter of26.0m at the top and of 38.0m at the base

- The roughly cylindrical "footing" consists of a system of walls and slabs for stabilityreasons and has a diameter of 90m The external wall is cylindrical and has athickness of 0.80m

The footing and the very first meters of the cone are constructed in a dry dock and towed out to

a wet dock where the cone walls are completed The pier shaft slab and the upper pier arecompleted on site after the base has been immersed to its final position The various compart-ments of the stiffener ring as well as the hollow central part are filled by a concrete or a gravelpier ballast adjusted to ensure the stability of the pier at any time

3.2.3 The transition piers

The transition piers act as junction between the high bridge and the approach bridge Theirdesign has not been finalised yet However, the following conditions will apply:

- vertically, the deck lays on fixed bearings with anti-lifting devices,

- longitudinally, sliding bearings are provided,

- in the transverse direction, the conditions of the main piers are likely to be adopted.Isolation and energy dissipation devices are provided for improving the earthquakebehaviour

3.2.4 The stay cables

The two planes of stay cables are arranged in the semi-fan pattern Each of the spans issupported by 4 sets of 23 cables The horizontal spacing of cables along the deck is 12.174m.The cables have increasing numbers of parallel strands towards the mid-span Each strand has anarea of 150mm2

At the pylon head the cables are anchored with typical threaded anchorages that permitadjustment if required

3.2.5 The foundation

The bridge is founded on a deep soil strata of weak alluvions, the bedrock being approximately800m below the sea bed level It was therefore found to be necessary to reinforce the top soillayers with steel inclusions consisting of driven 25m long steel tubes of 2m diameter and 20cmthickness as explained in [28]

The bridge also has to accommodate possible fault movements which lead to horizontaldisplacements of one part of the bridge with respect to the other The tectonic movement and thethus caused expansion has been discussed in a paper by Ambraseys and Jackson ([13]) Usingrecords of earthquakes in Central Greece since 1694 they found an average extension rate of theGulf of Corinth of 11mm/year

Finite Element Model of the Bridge Page 34

4 FINITE ELEMENT MODEL OF THE BRIDGE

4.1 Introduction

For purposes of static and dynamic analysis a finite element model of the Rion-Antirion Bridgewas set up for use in the program system ADINA ([7]) It is depicted in Figure 25 As summary,Table 3 lists the mass distribution within the model

Figure 25: Rion-Antirion Bridge, finite element model

M1[kt]

M2[kt]

M3[kt]

M4[kt]

Table 3: Mass distribution of the bridge

The bridge was modelled in full taking into account all major structural components and theircharacteristics Since the properties could be taken from design documents the bridge modelreflects an actual structure designed to all code requirements which was not the case for allearlier investigations on cable-stayed bridges

The accuracy of finite element analyses naturally depends on the assumptions made for setting

up the model A description of the model and these assumptions will thus be givensubsequently

4.2 Description of the finite element model

4.2.1 The deck

As described in 3.2.1 the deck of the Rion-Antirion Bridge is a composite member consisting ofsteel girders and a concrete slab It had to be modelled such as to behave correctly in bendingand torsion on one hand and to resemble the inertia effects correctly on the other hand

The finite element model of the bridge deck is depicted in Figure 26

Figure 26: Finite element model of the deck

A modelling approach suggested by Wilson and Gravelle in [93] was utilised This comprisesintroducing a single central spine of linear elastic beam elements that has the actual bending andtorsional stiffness of the deck These stiffnesses were evaluated by establishing an equivalentsteel cross section, thus taking into account the concrete contribution The cross section of thedeck is not uniform along the bridge which was taken into account while setting up the deckspine elements The torsional stiffness is the most difficult one to evaluate The deck will haveboth pure and warping torsional stiffnesses As an approximation, the deck cross section (shown

in Figure 23) was considered to be a thin-walled open C-shaped section

Each of the spine beam elements has a length of approximately 12m, spanning from one cableanchor location to the next At these nodes two rigid links were placed on either sideperpendicular to the spine to attach the cable elements, thus achieving the proper offset of thecables with respect to the centre of inertia of the spine Using the rigid link option allows thedisplacements of the "slave" node to be expressed in terms of the displacements of the "master"node, thus not introducing additional degrees of freedom into the model

Since the spine beam does not allow for the torsional inertia effects of the real bridge additionallumped masses were attached on either side of the central spine By placing these below thelevel of the spine the difference between the centre of stiffness and the centre of mass can beaccounted for This produces coupling between the torsional and the transverse motions of thedeck

The modelling approach for the deck is shown in Figure 27

Finite Element Model of the Bridge Page 36

4.2.2 The cables

As has already been mentioned in 2.2 and 2.3.1 the modelling of the cables is a difficult issuebecause nonlinearities arise from the cable sag The stiffness therefore changes with the appliedload However, in this study one linear truss element without stiffness in tension was employedfor each of the cables as shown in Figure 28 Taking into account the cable sag and thusnonlinear cable behaviour by means of an equivalent stiffness would have been extremelytedious since every cable would have had to be associated with a different force-displacementrelationship because of the changing inclination and length of the cables This would have alsoconsiderably increased the computation time as would have done utilising multi-elementdiscretisation because of introducing new degrees of freedom

It should be mentioned that linear elastic elements have also been used by Wilson et al in [93].Even though the authors suggested that the error is not significant it is clear that this approachcan lead to considerable inaccuracies

F

d

Figure 28: Employed cable behaviour

A prestress was applied to all the cables in order to ensure small deformations of the deck whenthe self weight is applied The bridge was modelled picking up the geometry from the designdrawings Since these show the as-built configuration the application of the self-weight to thestructure has to be taken into account In reality the cables are prestressed according to a priorcalculation so that the final shape is correct Accordingly, in the present study the prestress wasadjusted so as to have as small as possible a deflection when the self-weight is applied

4.2.3 The pylons and piers

Modelling of the pylons and piers was by means of beam elements As an example, the model ofpylon M3 is shown in Figure 29

The piers were modelled with a single set of beam elements The change in the cross-sectionalong the cone was taken into account However, in preliminary studies the stiffness of thecantilever was found to be inaccurate and a calibration analysis using a refined model wasconducted as described in section 4.4

The pylon legs have been connected to the piers using rigid links This was done because thepier head was deemed to be extremely stiff in terms of relative rotations between the pier topand the base of the pylon The pylon legs unify at the pylon head which was divided into beamelements as long as the distance between the cable anchorage points, thus readily allowing forthe connection of the cable elements

Figure 29: Finite element model of a pylon

An important feature for the present study was the damping system connecting the deck and thepylon base To accommodate these, rigid links were placed between the top of the pier andpoints at the level of the deck on either side of it This enabled the damping devices only to act

in the transverse direction because they have no component in longitudinal and vertical direction

as can also be seen in Figure 29

4.2.4 The foundations and abutments

The interaction between soil and structure was modelled using linear damped springs in thevertical direction and nonlinear undamped springs in the horizontal directions Nonlinear springswere also applied for the bending rotational degrees of freedom

As was already mentioned in 3.2.5, the Rion-Antirion Bridge is to be built on very weak soildeposits Extensive investigations on the soil properties were conducted by the designers andequivalent spring stiffnesses, including the contribution of the piles, were available from these

To retain the advantage of having a model close to reality it was decided to make use of theseproperties As will be explained subsequently, there was also concern that the nonlinearities inthe soil could play an important role in the behaviour of the bridge, thus making it necessary totake them into account As an example, the characteristics of the nonlinear springs at pier M3are shown in Figure 30 The linear spring's properties are:

- vertical stiffness: k v=23⋅108 N/m2

- torsional stiffness: k t=51⋅108 Nm/rad

Finite Element Model of the Bridge Page 38

Pier M3, Force-Displ x,y

0 100

Figure 30: Characteristics of nonlinear soil springs at pier M3

The modelling approach employed for the base of the piers is depicted in Figure 31 Asexplained, nonlinear springs with the behaviour adopted from design documents were applied inhorizontal direction These were identical in both directions at each pier, but different from pier

to pier In vertical direction linear springs were applied The rotational springs, not shown inFigure 31, have nonlinear behaviour and are the same for the two bending and different for thetorsional degree of freedom

Figure 31: Modelling of the foundation

To the end point of the translational springs the accelerograms were applied, thus exciting thestructure via the ground springs

4.3 Accelerograms

Synthetic accelerograms have been used in the present study that were derived from actualearthquake records using a special procedure to fit them to a predefined spectrum These spectrathat are referred to as KME spectra have been agreed upon with the client, the Greekgovernment

The spectrum compatible accelerograms have been derived by the designers and are for thepurpose of structural analysis The real earthquake records that have been used as basis are listed

in Table 4

No Reference/name PGD

[m]

PGV[m/s]

PGA[g]

Table 4: Basis earthquake records for KME spectrum

The last column shows the A/V ratio This is a good measurement for the demand of the record.Records with low A/V ratios (smaller than unity), as have all of the ones used here, tend to havehigher spectral accelerations in the long period range Hence, the records can be expected toimpose high demand on a long period structure like a cable-stayed bridge

The records obtained were scaled so as to represent a return period of 2000 years, thus imposing

a very high demand on the structure This means that a design earthquake was considered which

is only appropriate for a very important structure

The accelerograms and their response spectra are shown in Figure 32 through Figure 37 It isapparent from the response spectra that the records impose a high demand on a long periodstructure

Finite Element Model of the Bridge Page 40

Accelerogram h1 (longitudinal direction)

-6.00 -4.00 -2.00 0.00 2.00 4.00 6.00

Figure 32: Accelerogram, longitudinal direction (PGA=0.44g)

Response spectrum, h1 (longitudinal dir.)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

Figure 33: Response spectrum, longitudinal direction

Accelerogram h2 (transverse direction)

-6.00 -4.00 -2.00 0.00 2.00 4.00 6.00