AJ Reis NT Lopes D Ribeiro Abs

Track-Bridge Interaction on High-Speed Railways 1

TRACK-STRUCTURE INTERACTION IN LONG RAILWAY BRIDGES

A. J. REIS

Technical. University of Lisbon Technical Director

GRID S.A. Lisbon - Portugal

N. T. LOPES Civil Engineer


D. RIBEIRO Civil Engineer


ABSTRACT The concept design for long railway bridges shall take into consideration the need to balance imposed deformations of the deck, due to thermal effects, shrinkage and creep in concrete and composite structures and induced stress effects in the rails. The need to reduce the number of rail expansion devices requires moderate lengths of continuous superstructures and so the introduction of expansion joints in the deck. In seismic zones, the concept design of the bridge shall balance the advantage of short continuous lengths of the superstructure, to reduce track-structure interaction effects, with the inconvenient of transferring the seismic forces to a limited number of piers. The bridge design shall take into consideration a variety of other variable actions inducing stresses in the rails due to longitudinal displacements, namely associated to braking forces and vertical actions. Due to the continuity of the rails on the structural expansion joints, the deformations of the deck induce stresses in the rails that need to be checked. The main design criteria are now specified in Eurocode 1 – Part 2. The concept design for two long railway bridges, located in seismic zones, is discussed in the present paper. Prestressed concrete and steel-concrete composite superstructures are considered. To check track-structure interaction, a numerical model based on EC1-Part 2 and UIC 774-3 was developed and results are presented for one of these viaducts. 1. INTRODUCTION In concept design of long railway bridges (above 400 m) one of the main constrains is the track-structure interaction, i.e. the concept design of the track itself.

2 Track-Bridge Interaction on High-Speed Railways

The ballasted continuous track is very popular among the track owners, since they can avoid introduction of rail expansion devices, and so, reduce track maintenance costs. On the other hand, the maintenance of ballasted tracks is a very well known problem and track owners have large experience on dealing with it. Although, this concept applied to long viaducts raises several problems regarding the track-structure interaction, namely the effect of structural deformations on rail stresses. This is not a specific problem of the High Speed Railway bridges, so from this point of view, there is no difference between HSR bridges and conventional railway bridges. Generally, regular bridges without special constraints, can be conceived for continuous ballasted track, adopting short spans and as many structural expansion joints as needed, but when other important structural constraints are imposed, such as topographical, geotechnical and seismic constraints, the structural design may prevail. This paper focus particularly on the design of two solutions for long railway bridges in similar environment, but with two different solutions to solve the track-structure interaction problem. The bridges are inserted in the same track stretch of the Portuguese south railway line, linking Lisbon to Algarve, but have slightly different ground conditions, and both are implanted in a seismic area. In this stretch, the design speed is 220 km/h. One of the design solutions was adopted in both approach viaducts – North and South – to the new bridge over river Sado, at Alcácer do Sal. The other solution refers to the São Martinho viaduct, a few kilometres towards north from the Sado crossing.

Table 1: General features of the bridges (in meters) ________________________________________________________________________________ Access Viaducts São Martinho _______________________________ North South Viaduct ________________________________________________________________________________ Length 1115 1140 852 Span distribution 35+6×37.5+ 17×45+ 30×28.4 +19×45 +10×37.5

Maximum Height 22.5 22.0 13.5 Number of rail 2 2 none expansion devices

Continuous segments 260+45+765+45 45+720+37.5+337.5 7×113.6+56.8 ________________________________________________________________________________


2. BASES OF DESIGN 2.1 São Martinho Viaduct São Martinho river is one of the most important tributaries of Sado river’s north bank. The location of the new railway viaduct, with the same name, is not far from the estuary of Sado, and is included in its Natural Reserve, an important sanctuary of birds. The viaduct is now under construction and has a prestressed concrete deck, composed of two main girders connected by the railway platform concrete slab. It is a ballasted double track solution with continuous rail.

Figure 1: São Martinho Viaduct Cross-Section

The crossing of São Martinho valley has required a long viaduct with more than 800 m, as the geotechnical conditions did not allowed an earthfill solution. There were not many constraints to piers implantation, so it was possible to establish a very regular distribution of spans; with 30 consecutive 28.4 m spans and a viaduct total length of 852 m. With 28.4 m spans, it was possible to divide the bridge length in a total of 8 continuous segments, 7 with 4 spans and 113.6 m length, and 1 last (south side) with 2 spans and 56.8 m length.


Figure 2: São Martinho Viaduct. Prestressed Concrete Deck, with 852 m (30 × 28.4 m) total

length. Double-beam section with diaphragms at supports. Total width: 13 m, for double track


A significant part of the total length of the viaduct was implanted over very thick alluvial deposits, imposing deep pile foundations (20-30 m). Despite the high deformability of the foundations, it was possible to maintain the continuity of the rail track without any expansion device, mobilizing a total of 4 stiff piers in each viaduct segment, that are responsible to control structural deformations and ensure track safety requirements.

Figure 3: São Martinho Viaduct. Typical 4-span Viaduct Segment 2.2 Approach viaducts to new bridge over Sado River The two approach viaducts to the new railway bridge over Sado River have basically the same solution, with steel-concrete composite decks and concrete piers. Like in São Martinho Viaduct, it is a double track ballasted deck. The cross section is composed of two plate girders 2.6 m high, supporting a concrete slab with variable thickness (30-40 cm). For many reasons, but mainly because of the simplicity and low intrusive process, the constructive solution was the incremental launching method, where steel girders present many advantages. This part of the Sado river valley is inside the Natural Reserve of the Sado estuary, and here, as in São Martinho River, there is a large area of alluvial deposits, where all piers should be founded. The incremental launching of steel girder imposes, for economical reasons, 40-50 m spans, and the adopted solution combines few 37.5 m spans with the typical 45 m span. Considering the spans, the piers height (over 20 m) and the poor geotechnical conditions, a fractioned superstructure like São Martinho it wasn’t feasible, therefore, the adopted solution included expansion rail devices, already foreseen in the bridge over Sado, where the structure is continuous along 480 m extension.


Figure 4: Approach Viaducts Cross-Section

The viaducts superstructure was divided in two continuous parts with a single simply supported span in the middle, where the rail expansion devices should be implanted. The distribution of continuous superstructure segments is presented in Table 1, and consists in a main long segment of 720 or 765 m length, between the bridge and the simply supported span, and a second long segment with 260 or 337.5 m length, fixed in the abutments. The transition to the bridge has also expansion rail devices (both sides) implanted in a simply supported span. In order to control longitudinal deformations and to face longitudinal horizontal forces, such as braking and acceleration, that for this continuous length totalize 7000 kN, the main continuous segments were fixed not to one single pier but to as much piers as allowed by thermal effects. The concentration of forces in one single very stiff pier was considered uneconomical, as regular piers, with some additional reinforcement, proved to be adequate for that purpose. This solution is more favourable for the foundations design as well. To face the seismic action, controlling the global deformation, some additional piers need to be mobilized, adopting special sliding bearings with dampers, fixing the pier under seismic action. For the second continuous segment, the superstructure is fixed at the abutment.


Figure 5: Approach Viaducts to the New Bridge over Sado River (South). Composite Steel-

Concrete Deck, approx. 1100 m total length. Double plated steel girders section, with tubular diaphragms. Total width varying between 13 m and 15.7 m. Double track


3. SEISMIC DESIGN 3.1 São Martinho viaduct

Seismic design of São Martinho Viaduct has faced a particular problem, as some localized sands occurring in the south part of the alluvial deposits reveal to have high liquefaction potential. The general solution consists on fixing each segment of 113.6 m, on its own piers, including the transition pier, as presented in Figure 3. In the design it was left enough clearance between adjacent segments, to prevent the risk of shock during seismic action. The last three segments, implanted over one layer of sands with high liquefaction potential were connected with dampers, between each other and at the abutment, to reduce the seismic impact to the foundations (see Figure 6).

Figure 6: Particular Solution for south part of São Martinho Viaduct. Connections with dampers 3.2 Approach viaducts to New Bridge over Sado River The seismic design of the approach viaducts, as previously described, considers two types of force transmission, as the viaducts are divided in two continuous segments. The continuous segment adjacent to the abutments is fixed at one point – the abutment itself. The main continuous segments, with 720 or 765 m long, are continuously fixed for seismic action along a set of 8 piers, 4 of them with special sliding bearings, provided with dampers, that are only fixed under seismic actions.


The single supported stretches are fixed at the transition piers.

Figure 7: Approach viaduct (North) seismic design. Dampers and bearings distribution


4. TRACK-BRIDGE INTERACTION 4.1 Introduction Continuous tracks when crossing support discontinuities, such as embankment-bridge transitions, or structural expansion joints, transmit horizontal forces directly applied to the support, which have a stiffness discontinuity, producing stresses concentration in the rails. In the same way, where continuous rails restrain the free movement of the bridge deck, deformations of the bridge deck (e.g. due to thermal variations, vertical loading, creep and shrinkage) produce longitudinal forces in the rails and in the fixed bridge bearings. The effects resulting from the combined response of the structure and the track to variable actions shall be taken into account for the design of the bridge superstructure, fixed bearings, the substructure and for checking load effects in the rails. The next specifications, based on section 6.5.4 of EN 1991-2:2003 are valid for conventional ballasted tracks, which is the design case to be discussed. 4.2 Combination of actions The following actions shall be taken into account:

− Traction and braking forces: For double track bridges the braking force in one track must be considered with the traction forces in the other track.

− Thermal effects in combined structure and track system: Temperature variations in the bridge should be taken as ΔTN (uniform temperature variation), with γ and ψ taken as 1,0.

− Classified vertical traffic loads (including SW/0 and SW/2 where required). Associated dynamic effects may be neglected.

− Other actions such as creep, shrinkage, temperature gradient etc. shall be taken into account for the determination of rotation and associated longitudinal displacement of the end sections of the decks where relevant.

When determining the combined response of track and structure to traction and braking forces, the traction and braking forces should not be applied on the adjacent embankment unless a complete analysis is carried out considering the approach, passage over and departure from the bridge of rail traffic on the adjacent embankments to evaluate the most adverse load effects. 4.3 Tensions on the track For rails on the bridge and on the adjacent abutment the permissible additional rail stresses due to the combined response of the structure and track to variable actions should be limited to the following design values:

– Compression: 72 N/mm²;


– Tension: 92 N/mm². The above given limiting values are valid for tracks complying with:

– UIC 60 rail with a tensile strength of at least 900 N/mm²; – Straight track or track radius r ≥ 1 500 m; – For ballasted tracks with heavy concrete sleepers with a maximum spacing of 65 cm or

equivalent track construction; – For ballasted tracks with at least 30 cm consolidated ballast under the sleepers.

In the viaducts to be discussed, all the above criteria are satisfied. When any of the criteria is not satisfied special studies should be carried out or additional measures provided. 4.4 Deformation of the structure 4.4.1 Longitudinal displacement: Due to traction and braking δB shall not exceed the following values:

– 5 mm for continuous welded rails without rail expansion devices or with a rail expansion device at one end of the deck,

– 30 mm for rail expansion devices at both ends of the deck where the ballast is continuous at the ends of the deck,

– Movements exceeding 30 mm shall only be permitted where the ballast is provided with a movement gap and rail expansion devices provided,

where δB is:

– The relative longitudinal displacement between the end of a deck and the adjacent abutment or,

– The relative longitudinal displacement between two consecutive decks. Due to vertical traffic actions up to two tracks loaded with load model LM 71 (and where required SW/0) δB shall not exceed the following values:

– 8 mm when the combined behaviour of structure and track is taken into account (valid where there is only one or no expansion devices per deck),

– 10 mm when the combined behaviour of the structure and track is neglected, where δB [mm] is:

– The longitudinal displacement of the upper surface of the deck at the end of a deck due to deformation of the deck.

4.4.2 Vertical displacement The vertical displacement of the upper surface of a deck relative to the adjacent construction (abutment or another deck) δV due to variable actions shall not exceed the following values:

– 3 mm for a Maximum Line Speed at the Site of up to 160 km/h, – 2 mm for a Maximum Line Speed at the Site over 160 km/h.


5. TRACK-BRIDGE INTERACTION MODELATION 5.1 Principles For the determination of load effects in the combined track/structure system a model based upon Figure 8 (from EC1, part 2: EN 1991-2:2003) was used.

Figure 8: Model of track-structure system

The longitudinal load/displacement behavior of the track or rail supports may be represented by the relationship shown in Figure 9 (from EC1, part 2: EN 1991-2:2003) with an initial elastic shear resistance [kN/mm of displacement per m of track] and then a plastic shear resistance k [kN/m of track].

Figure 9: Variation of longitudinal shear force with longitudinal track displacement for one

track


The diagrams (4) and (6) were adopted, with the following values (from UIC 774-3):

Loaded track (4): k = 60 kN, u0 = 2 mm Unloaded track (6): k = 20 kN, u0 = 2 mm

For the design case to be discussed there will be a change in the future from one way/track to two way/track use. Hence all cases are taken in account. For the calculation of the total longitudinal support reaction FL and in order to compare the global equivalent rail stress with permissible values, the global effect is calculated as follows:

liiL FF ∑ψ= 0 (1)

with:

Fli the individual longitudinal support reaction corresponding to the action i; ψ0i for the calculation of load effects in the superstructure, bearings and

substructures the combination factors defined in EN 1990 A2 shall be used; ψ0i for the calculation of rail stresses, ψ0i shall be taken as 1.0.

When determining the effect of each action, the non-linear behaviour of the track stiffness shown in Figure 9 is be taken into account. The “k” value depends if the track is loaded or unloaded. This means that for each loading, a different computer model has to be calibrated, according to the loaded and unloaded positions of the track. The longitudinal forces in the rails and bearings resulting from each action may be combined using linear superimposition. 5.2 Model description The track/structure interaction model developed for the viaduct was a global frame model, with bar elements to simulate:

- deck; - piers; - piles; - track.

The computer model simulates the entire viaduct and also an additional of 300 m (from each side of the viaduct) of track in the ground, above the backfill. All the 7 independent frames were included in the computer model (7×4×28.4+1×2×28.4 = 852m), according to the general principles of modelation and the global structural model. The connection between the track and the structure was modelated by elements with nonlinear response (as defined above), and each frame element has 1m length, in general. When we have a ballasted track, according to UIC 774-3, we may take:


- u0 = 2 mm, - Track-structure plastification force:

Loaded track (4): k = 60 kN, Unloaded track (6): k = 20 kN,

The track and the nonlinear modelation were extended to both sides of the structure of the viaduct, to take into account the track on the ground, admitting the soil rigid, as defined in EC1. On Figure 10, one show the analysis model, between the piers P1 and P5, where are modelated:

- the foundations, - the track over the deck, - the track over de terrain.

In this section, there are already discontinuities between the deck and the abutment (where the structure begins) and over the pier P4 (with doubling of nodes on top), being the track, and his connections, continuous.

Figure 10: Track-structure analysis model, including the backfill of the north abutment and the first 5 spans

Four braking positions and six traction positions were modelated, with the purpose of investigating the most unfavorable position for these actions. It was concluded that the most unfavorable effect for the tracks occur where discontinuities in the structure exist, due to differential displacements. There are differential displacements imposed to the structure that the track has to follow, and the load positions try to maximize this effect. The actions in the modelations were (following EC1-part2):

i) Traction loads: Qlak = 33 [kN/m] × La,b [m] ≤ 1000 [kN] ii) Braking loads: Qlbk = 20 [kN/m] × La,b [m] ≤ 6000 [kN] iii) Average temperature in structure: 20 ºC with ΔTcon = -16 ºC e ΔTexp = +22 ºC iv) Vertical loads: Load Model 71

In Figure 11 are shown the traction and braking position forces adopted. 6. ANALYSIS OF THE RESULTS In Table 2 one list the most unfavorable stresses obtained for two critical sections of the track: near the abutment (at the expansion joint) and at the expansion joint between two different


frame decks (at the intermediate piers). The safety check of the track is made according to EC1-2 for the maximum additional compression stress in the track, due to this action (Table 3). For the deformation check of the structure, due to traction and breaking actions, this type of analysis, based in a track-structure interaction, allows to check the limit defined in EC1-2 of 5 mm. On Table 4 one presents the results for each loading case and also the combined value of the displacement.

Table 2: Track verification: Axial force _____________________________________________________________________________ Action Abutment Joint Pier Joint ________________ ______________ kN kN _____________________________________________________________________________ Braking 886 831 Temperature (22ºC) 1121 1306 LM71 – Vertical < 10 < 10 Total 2017 2147 _____________________________________________________________________________

Table 3. Track verification: Security Check (4 rails -> 550 × 4 = 2200 kN) _____________________________________________________________________________ Security Check Abutment Joint Pier Joint ________________ ______________ kN kN _____________________________________________________________________________ ΔN Allow. – Comp. 72 MPa 2200 2200 Rail security check 0.917 0.976 _____________________________________________________________________________


Figure 11: Track-structure interaction model: localization scheme: traction actions (Axx) and

breaking actions (Fxx)


Figure 12: Track axial force diagram due to temperature (structure heating)

Figure 13: Track axial force diagram due to braking (maximum stress near the abutments)

Figure 14: Track axial force diagram due to braking (maximum stress near intermediate pier)

1121 1306

886

831


Table 4: Deck displacements due to traction and braking actions _______________________________________________________________________________________________ Zone f1 f2 f3 f4 a11 a12 a21 a22 a31 a41 máx.f máx.a d.máx ____________________________________________________________________________________ mm _______________________________________________________________________________________________ Abut. N 2.1 0.0 0.1 0.0 0.8 0.0 0.0 0.0 0.0 0.1 2.1 0.8 2.9 P04 – N 2.2 0.0 0.1 0.1 0.6 0.0 0.0 0.0 0.0 0.1 2.2 0.6 2.8 P04 – S 2.5 0.0 0.3 0.5 0.2 0.2 0.0 0.0 0.0 0.3 2.5 0.3 2.7 P08 – N 2.4 0.0 0.4 0.6 0.1 0.2 0.0 0.0 0.0 0.3 2.4 0.3 2.7 P08 – S 1.8 0.0 1.6 2.2 0.0 0.8 0.0 0.0 0.0 0.8 2.2 0.8 3.0 P12 – N 1.6 0.0 1.7 2.2 0.0 0.8 0.0 0.0 0.0 0.7 2.2 0.8 3.0 P12 – S 0.4 0.2 2.6 2.6 0.0 0.2 0.0 0.1 0.2 0.2 2.6 0.2 2.8 P16 – N 0.3 0.2 2.6 2.5 0.0 0.1 0.0 0.1 0.2 0.1 2.6 0.2 2.7 P16 – S 0.1 0.9 2.7 2.1 0.0 0.0 0.0 0.4 0.8 0.0 2.7 0.8 3.6 P20 – N 0.1 1.0 2.7 2.0 0.0 0.0 0.0 0.5 0.9 0.0 2.7 0.9 3.6 P20 – S 0.0 2.4 0.7 0.4 0.0 0.0 0.0 0.8 0.4 0.0 2.4 0.8 3.2 P24 – N 0.0 2.4 0.6 0.4 0.0 0.0 0.0 0.7 0.3 0.0 2.4 0.7 3.1 P24 – S 0.0 2.4 0.1 0.1 0.0 0.0 0.1 0.2 0.1 0.0 2.4 0.2 2.6 P28 – N 0.0 2.3 0.1 0.1 0.0 0.0 0.1 0.1 0.1 0.0 2.3 0.1 2.4 P28 – S 0.0 0.3 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.3 0.1 0.5 Abut. S 0.0 0.2 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 ______________________________________________________________________________________________ 7. CONCLUSIONS A discussion on track-structure interaction for long railway bridges was presented. The problem of imposed deformations and seismic actions were discussed taking into consideration the need to “balance” the continuity of the structure with the requirements for minimum track expansive joints. A design case was presented according to the Eurocodes, namely in terms of actions and in terms of structural safety verification. The stress analysis allows concluding that the limit stress on the rail is almost reach out, for compression, being, in general, the piers joints the most unfavorable. Although, the braking force produces higher stresses near the abutment joint, due to absorption of this force in the backfill of the abutments. Besides, for compatibility of displacements, the temperature generates higher stresses on the track near the piers joint (there is a higher displacement amplitude). The vertical forces, in this model, were not critical, and induce very low stress amplitude.


The displacement limit of 5 mm, was also verified with some clearance. In conclusion, the track interaction analysis allowed to check the track safety, in terms of Eurocodes criteria, for a joint distance larger than 90 m, although in this situation, the length of 4 × 28.4 = 113.6 m is almost at the allowable limit for stress verification. ACKNOWLEDGEMENTS Thanks are due to REFER for allowing the publication of some results of specific studies developed for the design of the new stretch of the Portuguese south railway line, near Alcácer do Sal, that includes the New Sado River railway crossing. REFERENCES [1] EN1991-2, Actions on structures – Part 2: General actions – Traffic Loads on Bridges,

European Committee for standardization, CEN (2003). [2] UIC Code 774-3-R, “Track/bridge interaction – Recommendations for calculations”, 2nd

edition, October 2001, Union International des Chemins de Fer, UIC, 2001.

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AJ Reis NT Lopes D Ribeiro Abs