Even More Track Structure Interaction
Welcome to the third, and thankfully final, part of this series on Track Structure Interaction (TSI for all of you who had the first album). Since the 1950s we’ve been using continuously welded rail in the UK, and with the introduction of the Eurocode we’re finally being made to consider the effect this has on our structures. If you want a reminder take a look back to parts one and two– don’t worry, this post will still be here when you get back.
Loading The Structure
A good case for the reduced (1.1) geotechical alpha value can be argued given the dependence on soil properties.
TSI considers only the loading which relies on the interaction between track and structure. Being a two-dimensional, primarily longitudinal, analysis the most prominent of these is traction and breaking. In the UK, at least, the NA breaking load, which inherits from BD 37/01, is always the worst case; however the unrestricted length is arguably unrealistic and there is potential to agree a 300m limit, in keeping with the unadjusted Eurocode loading. You are limited, however, to loading a maximum of two tracks at any one time, and the ballast springs must be updated to reflect this.
You also need to consider vertical loading (LM71 for short spans, SW/0 for long spans), as the bending deflection causes end rotation and shortening. Note that TSI is a global SLS analysis, and therefore doesn’t require partial or dynamic factors. Network Rail do, however, still specify the use of the future (α) factor; however a good case for the reduced (1.1) geotechical value can be argued given the dependence on soil properties.
As well as traffic actions the relative change in temperature between rail and structure leads to a transfer of stress as one restricts the other. The magnitude of this action depends on the fixity of the rail; with different generic ranges given for tracks with and without expansion joints (35o and 20o respectively). The effects resulting from thermal actions arguably develop over a long duration, and although not explicitly stated, I believe it would be hard to justify using anything but unloaded ballast stiffnesses for this loadcase.
The aim of TSI is to check relative movements between structures and the stresses in the rails. As a general guide applying horizontal load to the full length of the structure, and positioning vertical load to effect the largest bending moment will result in the worst case condition; thermal load should always be applied to the complete structure, and loads should not extend into the approach lengths (see the previous article for boundary conditions). Consideration of the distribution effects suggests that, for deflection, a good starting point is to use the lowest foundation stiffness with the highest ballast stiffness; and the reverse is true for rail stress. The complicated analysis, however, means that it is always worth checking all cases.
Doing A TSI Analysis
The non-constant stiffness of the ballast springs used in TSI makes it a second-order analysis. Although the Eurocodes do provide a hand calculation method (based on empirical relationships), the strict qualification requirements mean that most of the bridges suitable for such a check do not actually require the analysis, and in addition it does not consider the additional ballast stiffnesses included by Network Rail. The alternative is to use a finite element model, which the original documentation from the UIC provides some guidance for: notably that the maximum discrete element length should be limited to 2m and that linear superposition is allowable. It should be noted, at this point, that the likes of LUSAS already comes with a TSI module.
The criteria for TSI are two fold. The relative movements of structures due to traffic loading (laterally, vertically and rotationally) must be within the tight limits imposed by the Eurocodes, and the stresses in the rails due to traffic and thermal loading cannot exceed the tensile and compressive restrictions provided, once again, by the Eurocodes. There are, however, a few missing criteria. The limits noted in the Eurocodes are only correct for UIC 60 Rail on straight (radius less than 1500km), ballasted, track on heavy concrete sleepers spaced at 650mm intervals. There is some guidance on concrete fixings in the original research; but curvature has yet to be commented on.
The view of Network Rail appears to be that the radii limitation can be relaxed, with agreement, if there is additional lateral restraint (in the form of dagger boards, etc.), however its effect on the analysis is still unclear.
At A Glance
Typically the uncertainty surrounding geotechnical properties means that more detailed GI may reduce conservatism in values, thus reducing movement.
|Expansion Device on One Side||70%|
|Expansion Devices on Both Sides||100%|
You should never undertake an analysis without a good idea of what the answer should be. To this effect the ‘restraint coefficients’ provided in the Eurocode hand calculation method provide a simplified suggestion: apply a proportion of the total breaking load to the fixed pier, as shown in the above table. From the lateral load and moment, and an estimated ground spring, you can get a ballpark figure for the movement expected in the TSI analysis. The following rules of thumb can also give you a feel for the answer before you start:
- Expansion joints are required for steel bridges longer than 60m
- Concrete bridges longer than 90m will need expansion joints
- These spans can be doubled for centrally fixed bridges
- Medium span consecutive bridges with shorter start/end spans perform well
- Movement of tall bridges will be dominated by the pile design
- Movement in short bridges will be dominated by surface ground properties
If the bridge fails there is not a lot that can be done, structurally, to resolve the issue (remember the first thing I said in this series was: do the TSI first). Typically the uncertainty surrounding geotechnical properties means that more detailed GI may reduce conservatism in values, thus reducing movement. Similarly changes to articulation and span (note the rules of thumb above) can help rescue a failing structure. It is often conservative to apply to rules of linear superposition to a TSI analysis and, for close-cases, it may be worth building a stress history/combined loadcase approach into the model.
And so ends my series on Track/Structure Interaction; it’s been fun, and I’ve learnt a lot putting it all together. Let’s hope next time I have to do some heavy research it’s into something more interesting!
Note that the bare facts of these articles are quoted from Network Rail (typically NR/L3/CIV/020) and research by the UIC (774-3R). The rest is interpretation and notes from a graduate’s experience. As always, your attention is drawn to the disclaimer at the bottom of every page.