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 the country, will carry high-speed trains travelling from the Spanish capital Madrid to Extremadura on the Portuguese border.

The Almonte River Bridge has a total length of 996m and will carry trains across the Alcantara Reservoir on an arch structure designed by Arenas & Asociados. 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 which 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, significant horizontal loads, fatigue considerations, and functional considerations such as the smaller permissible deflections, 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, rendering 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 faced in the analysis of the structure included the construction stage, 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, electrification 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 nonlinear 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 stay cables during the construction.

A total of 26 cables will be used on each side with corresponding 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 first 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 first 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 five steps, from the characteristic to factored values. Live loads are also stepped in five 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 influence for the final safety of the finished structure.

Second order effects were studied considering the impact of existing imperfections on the initial arch geometry. It was considered as a deformation homothetic with the first 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 five steps and live loads were also stepped in five 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 cracking. 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 modified 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 levels achieved. This process was repeated until there was no significant variation between the stiffness considered for the member force calculations and the one obtained on th