New Evolutions for High Speed Rail Line Bridge Design Criteria and Corresponding Design Procedures

CHAPTER 1 New evolutions evolutions for high speed rail line bridge design criteria and corresponding design procedures D. Dutoit Systra, Paris, France

ABSTRA ABSTRACT: CT: The high speed rail lines bridges bridges have alwa always ys had specific design criteria. criteria. NeverNevertheless, with the new development of the analysis of rail stresses due to rail structure interaction, some of the initial criteria used in France can be replaced by limitation of the rail stresses, as described for instance in the Eurocode. This can lead to significant savings, especially in highly seismic zones.

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MAIN SPECIFIC SPECIFIC FEA FEATURE TURES S OF HSR HSR BRIDGES BRIDGES PROJEC PROJECTS TS Typefont, typesize and spacing

Histo Historic ricall ally y, the deve develop lopem ement ent of the High High Speed Speed Lines Lines in Franc Francee has been been done done step step by step. step. Based Based on actual measurements made of stress concentrations in the rail done on real sites, and based on the experience of track stability and safety, rules were set-up to restrain specific features of the supporting structures within empirial limits in order to provide for the track safety. Usually, and as described today in Eurocode, UIC and present SNCF standards, the structures carrying the long welded rails for high speed trains have specific limitations due to 3 sets of phenomena: • Long

Welded rail  Rail structure interaction ◦ Additional rail stresses stresses brought by R.S.I. – Temperature variation maximum distance between based points – Deck end rotations – Braking & acceleration forces: maximum displacement under braking and acceleration forces ◦ This controls – The location of expansion joint – The girder stiffness – The support stiffnesses stiffnesses (piers, foundations, bearings) • High speed vehicle  Structure dynamic response The high speed rail supports vehicles travelling at high speed. This involves the analysis of the structures dynamic response to address the following items ◦ Control of vertical load (impact at resonance) resonance) ◦ Control of acceleration at deck level level – Track stability: acceleration at deck level – Rail/wheel Rail/wheel contact: acceleration at deck level – Rolling stock stability: acceleration at deck level – Passenger Passenger comfort: vertical acceleration in the cars 1 © 2009 Taylor & Francis Group, London, UK

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Track-Bridge Interaction on High-Speed Railways

Limit fatigue stresses. Rules of • Seismic environment  High speed track geometry and stresses In the case of seismic areas, there is the need of additional analysis for the safety of the traffic during a potential earthquake. ◦ Problematic: Find the limits of rail deformation and stresses compatible with the rain full speed operation under earthquake ◦ Steps of the analysis – Life safety analysis (full speed operation compatible with which Service earthquake Peak Ground acceleration?) – Risk analysis (which track stresses and deformation criteria combined with other concomitant sources of stresses?) – Translated that into practical and simple High Speed Serviceability earthquake structure design criteria ◦ Consequence on High Speed Operation Train switch off at certain level of earthquake ◦

6 1 0 2 h c r a M 1 3 0 2 : 4 0 t a ] a i l a r t s u A s r e e n i g n E [ y b d e d a o l n w o D

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EVOLUTION USING RAIL STRESSES COMPUTATIONS

In order to address the concerns described above, specific design criteria had been developed by several national codes. These specific criteria involved: • A

limitation of maximum distance between bridge expansion joints when using a continuous welded rail, in order to limit the additional stress in the rail due to the difference of displacement between the structure and the rail. • A maximum rotation at bridge ends in order to limit the additional stress in the rail due to bridge end displacement and the corresponding force transmitted by the elasticity of the ballast or of the rail supports in the case of slab track and to ensure the stability of the ballast. This may control the deck rigidity. • A maximum displacement of the bridge when the maximum braking and acceleration force is applied: this may control the foundation, pier and bearing design. In the new evolution, instead of controlling the additional stresses in the rail by the above mentioned limitations, a complete analysis of the additional stresses in the rail due to the bridges supporting the track is limited to the followings N/mm2 compression (Risk of track buckling in compression) Ballasted track 2 • 92 N/mm tension



• 72

Slab track 92 N/mm2 tension and compression. In addition, in case of the ballast track, other criteria shall be satisfied in order to ensure the stability of the ballast (relative displacement of the deck under braking and acceleration, maximum relative displacement of the expansion joint between two bridges under live loads, . . . ). This calculation is done by computing, on a computer model describing a significant length of the line on each side of the considered structure: • The

foundations and the corresponding elasticities due to the soil – foundation interaction • Pier flexibilities • The bearings (fixed, sliding or its elasticity) • The bridge superstructure • The tracks, with the rail stiffnesses and the elasticities (horizontal) of the support between the rail and the deck (ballast and ties, slab track, elastomeric pads underneath the rail) • The rail expansion joints

© 2009 Taylor & Francis Group, London, UK

New evolutions for high speed rail line bridge design criteria

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• The

environmental conditions (temperature variations, gradients, . . . ) • The train characteristics Based on the corresponding analysis, the piers and foundations can be optimized when compared to the conventional HSR criteria (see example in part 4.1.). In addition, it is also possible to identify critical points on the line where there are concentrations of forces on the bearings and design the sub-structures in order to reduce this unfavourable effect (see example in 4.2.). This cannot be done by using the simplified approach (without the rail interaction analysis). This new computerised method is therefore more economical and safer the simplified one. 3


MAIN CONSEQUENCES

These new design procedures can induce a significant saving in the substructures (foundation, piers). These savings may be magnified in seismic areas. Since the loads applied by a given earthquake increase with the substructure rigidity, the additional elasticity of the substructure due to the new HSR service load criteria will also induce a significant saving in the seismic analysis of the structure. 4

EXAMPLES OF RAIL-STRESSES COMPUTATION

The following examples show that the simplified method (no track structure interaction modelled) used to avoid computerised calculation (track structure interaction modelled) is generally too conservative and cannot identify the critical points on the line where very high bearing reactions can occur. In the following examples, we compare the simplified method and the computerised method on a simple case: • Train

type UIC 71 • Ballasted track • Straight track • Double track • Rail type UIC 60 • Succession of 30 m simply supported spans. 4.1

Comparison between the simplified method and the computerised method – optimisation of the pier and foundation

(a) Simplified method: In the case of a succession of simply supported spans, the braking and acceleration forces applied on one span are fully transmitted to the bearings of the span. In the case of a 30 m simple span, the longitudinal braking and acceleration forces are: F = 33 kN/m × 30 m + 20 kN/m × 30 m = 1590 kN

(1)

The bearing reaction under temperature effect is calculated using the formula 8 × L (L is the length of the span). It can be estimated at 8 kN/m × 30 m = 240 kN. The maximum allowable relative displacement under braking and acceleration forces between two decks is δ = 5 mm. Therefore, the minimum stiffness of the pier and foundation is: K =

F δ

=

318000 kN/m

Each pier and foundation shall have a stiffness higher than 318000 kN/m.


(2)

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(b) Computerised method (including rail structure interaction): 25 spans are modelled. The pier stiffness is the one calculated using the simplified method (see above). We study here the span located at the center of the computer model. The results of the calculations are the following. 25 Spans (30 m long)


Figure 1.

Scheme of the computer model.

Figure 2.

Stresses in the rails under Temperature, braking/acceleration and live loads.

The stresses in the rail is between

Figure 3.

−25 MPa

and +30 MPa.

Relative displacement between two decks under braking/acceleration.


New evolutions for high speed rail line bridge design criteria

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The maximum relative displacement between two decks is below 2 mm.


Figure 4.

Bearing reactions under braking/acceleration and live loads.

The maximum bearing reaction is 1019 kN. This represents only 64% of the value given by the simplified method (1590 kN). It can also be noticed that the bearing reaction under temperature effect is almost zero compared to 240 kN calculated by the simplified method. (c) Analysis of the results: The table below shows the results of the computerised calculations. Table 1.

Tensile stress Compression stress Relative displacement

Results

Allowable limits

Ratio

25 MPa 30 MPa 2 mm

92 MPa 72 MPa 5 mm

27% 42% 40%

In addition, the bearing reaction under temperature, braking/acceleration and live loads is only 56% of the value given by the simplified method. (d) Conclusion: It is therefore possible to optimise the piers and foundation. Additional calculations show that even if the pier stiffness is reduced by more than 2, the safety of the track is still ensured. The bearing reactions calculated by the computerised method are also around half of the value calculated by the simplified method. 4.2

Comparison between the simplified method and the computerised method – Identification of the critical points on the line

Due to the link between adjacent girder created by the track, a force applied on one span is transmitted to the adjacent spans.


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In some case, where there is a sudden variation of pier stiffness, a bearing reaction may be higher than the one calculated using the simplified method (see 4.1.a). The simplified method is, in these cases, too favourable. The case studied here is the same than the previous one (pier stiffness equal to 318000 kN/m), but one pier has a stiffness much higher than the other (due for example to a sudden variation of the ground level). We study in detail the bearing reactions on this pier under braking and acceleration forces. 25 span (30 m)

Very stiff pier


Figure 5.

Scheme of the computer model.

Figure 6.

Maximum bearing reactions under braking/acceleration and live loads.

The maximum bearing reaction is 2036 kN. Conclusion The maximum bearing reaction is 2036 kN, which is 128% of the value calculated using the simplified method (1590 kN – see 4.1.a). Additional calculations shows that, in case of slab track, it is even more unfavourable. The maximum bearing reaction is then 155% of the value calculated using the simplified method. The new computarised method allows therefore a better identification of the overstressed areas, and allows to make the required changes necessary to have a safer track.


New Evolutions for High Speed Rail Line Bridge Design Criteria and Corresponding Design Procedures

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