THE DEFINITIVE PUBLICATION FOR BRIDGE PROFESSIONALS WORLDWIDE | ISSUE NO. 72 | THIRD QUARTER 2013 | WWW.BRIDGEWEB.COM

HIGH-SPEED HELPER

DESIGN OF THE ALMONTE BRIDGE

50 www.bridgeweb.com Bd&e | ISSUE 72 | 2013

� SPECIALIST SOFTWARE

Construction is just beginning on the main structure of what will be the world’s longest high-speed railway arch bridge when it opens in 2015. The 384m-long main span structure, which is close to Cáceres in the western side of Spain, will carry high-speed trains travelling from the capital Madrid to Extremadura on the Portuguese border.

The Almonte River Bridge designed by Arenas & Asociados is 996m long and will carry trains across the Alcantara Reservoir on an arch structure. As well as being the longest high speed railway arch it will be the third longest concrete arch bridge in the world. Its design and construction incorporate many special features which required demanding and complex analysis; this was carried out using bridge engineering software Midas Civil.

The high speed rail system has undergone rapid expansion in Spain in the last two decades and last year became the second largest network in the world, with some 2,900km already in use and 1,500km under construction. The particular features of high speed rail bridges that make them so demanding to design include heavier loads than road bridges, dynamic effects, signifi cant horizontal loads, fatigue considerations, and functional considerations such as the smaller permissible defl ections, accelerations and limited length that relate to rail expansion joint capacity and track-structure interaction. Given these peculiarities, spans longer than 100m are unusual for high speed rail, render-ing this structure even more challenging.

The arch bridge deck has a typical span of 45m over the total deck length of 996m and the 14m-wide deck, which consists of a 3.1m-deep box girder, will be constructed using a movable scaffolding system. The arch will be built using a cantilever method with form travellers and temporary stays tied back to two temporary steel towers. Over the

arch section of the bridge, the spans are reduced to 42m. The main challenges in the analysis of the structure included calculation of the anti-

funicular shape of the arch, taking into account construction stages, non-linear analysis for the service limit state and ultimate limit state, dynamic analysis and track-structure interaction. Special studies included wind tunnel testing and non-linear behaviour.

The 384m-long concrete arch structure has an octagonal cross-section with a depth that varies from 4.2m at the key section to 6.3m at the end sections. The width at the central key section is 6m, increasing towards the end sections. Beyond the central 220m, the arch splits into two separate sections that diverge to a maximum overall width of 19m. This provides the necessary lateral stability against wind loads and addresses the global instability phenomena stemming from the narrow deck and the heavy railway loads. The arch will be built of 80MPa self-compacting concrete.

The typical deck section is a 3.1m-deep prestressed concrete box girder. Its 14m width is typical of high speed rail bridges and can accommodate two railway tracks and all the functional elements such as the railway platform, communications ducts, ballast, electrifi cation catenary posts, service paths, barriers and so on.

The concrete arch staged erection forms the basis for predicting the real static state of the structure and carrying out all other calculations such as non-linear analysis, anti-funicular curve analysis, cable stay tensioning forces and so on.

The arch will be erected using the cable-stayed cantilever method; its total length is divided into 66 segments which will be cast in situ, 33 on each side of the bridge.

In order to ensure that they stay within the allowable stresses and that the optimum geometry of the arch is maintained, the segments will be supported by temporary

Designing an arch bridge to carry high-speed trains is a complex and demanding process. Guillermo Capellán and Juan José Arenas explain how software can help

HIGH-SPEED HELPER

Midas model for construction stage analysis of the Almonte River Bridge

52 www.bridgeweb.com Bd&e | ISSUE 72 | 2013

n SPECIALIST SOFTWARE

stay cables during the construction.

A total of 26 cables will be used on each side with corre-

sponding back stays; cables one to eight will be anchored to piers six and

15, while the anchorages for the remaining cables will be placed on temporary steel towers

that will be built on the piers. Cable forces will be adjusted during the construction process, and some

cables will be released at intermediate construction stages in order to avoid excessive stress. Once the arch

structure has been closed, the piers on top of the arch and the deck structure will be erected.

For the concrete arch erection using temporary stays and steel towers, a Midas model was used for stage analysis. The calculation process was divided

into a series of steps, the fi rst one being to carry out non-linear analysis for every construction stage right up to the permanent load situation. Geometrical imperfections were considered for every stage.

Secondly, non-linear – material and geometric – long-term analysis was carried out for creep and shrinkage due to member forces resulting from the fi rst step of the process.

The third step was to carry out non-linear (material and geometric) analysis for thermal actions, followed by incremental non-linear analysis to the ultimate limit state starting with the geometry and member forces resulting from the third step.

Permanent loads are divided into fi ve steps, from the characteristic to factored values. Live loads are also stepped in fi ve increments, so the ultimate limit state values were reached at the same step for both type of loads. At every step, the section stiffness was re-calculated to comply with the strain-stress EC-2 models, both for concrete and steel. This way, concrete cracking was considered for every step.

Analysis took into account the effects of cracking on concrete, creep and shrinkage of concrete, non-linear relationships σ-ε steel and concrete, and the construction stage

infl uence for the fi nal safety of the fi nished structureSecond order effects were studied considering the impact of existing

imperfections on the initial arch geometry. It was considered as a defor-mation homothetic with the fi rst buckling mode, which was introduced as a different model of initial geometry for each load combination.

As previously described, permanent and variable loads achieve their ultimate limit state at the same load step. For permanent loads, values from characteristic to factored were divided into fi ve steps and live loads were also stepped in fi ve increments. For every step, the section stiffness was re-calculated according to the stress-strain relationships given by EC-2 for concrete and reinforcement steel, properly considering concrete crack-ing. This was an incremental, iterative process.

Firstly, no cracking was considered, and this assumption was checked for member forces obtained at each calculation step, considering sectional moment-curvature diagrams. Secondly, the section stiffness was modifi ed according to EC-2 stress-strain diagrams, and new member forces were calculated.

Finally, checking was carried out if the considered stiffness matched the tension lev-els achieved. This process was repeated until there was no signifi cant variation between the stiffness considered for the member force calculations and the one obtained on the moment-curvature diagram. In this incremental calculation procedure, the stiffness was obtained as the tangent to the moment-curvature diagram at the point corresponding to the previous load step.

Given the long span and the structure’s slenderness, it is necessary to take into account the aeroelastic phenomena in the bridge analysis, covering all the oscillatory effects induced by the wind-structure interaction. This is not only because IAPF-2007 specifi cations require this type of study for spans longer than 200m, but also the fact that the structure’s main modal vibration frequencies are very low – below 0.3Hz – indi-cates that the structure may be sensitive to these effects.

A complete wind analysis study was carried out including wind tunnel sectional aerodynamic response analysis and aeroelastic studies in the wind tunnel with a scaled model for the bridge at the fi nal state and construction cantilever stages. The tests were carried out in the Limit Layer II Wind Tunnel at Western Ontario University in Canada. These studies validated the structure’s behaviour in service and construction stages and also underlined the importance of using aerodynamic sections for the arch from an early design stage.

Construction of the bridge began in 2012 and when Bd&e went to press, all the founda-tions, piers and most of the deck outside of the arch had been completed. Arch erection was just starting and is due to continue through 2014, using the temporary stay system. The arch piers and deck are due to be fi nished by the summer of 2015 n

Guillermo Capellán is technical director and Juan José Arenas is president of Arenas & Asociados

Owner: ADIF (Spanish Railway Infrastructure Administrator)Project design: Arenas & AsociadosConstruction: FCCProject management: Arenas & Asociados, IDOM

Piers for the bridge under construction in June this year

Midas model for stage analysis