An evolution in track-structure dynamic analysis

Think of a music box. Hold it in your hand and the melody it produces is only just audible. But place it on a box lid or tabletop, and the sound is amplified. The same thing happens when trains cross bridges and culverts, which can act as large-scale resonators, amplifying the vibration of wheel on rail.

This matters for environmental, safety and user comfort reasons: HS2 aims to be a good neighbour, so minimising noise is important. Uncontrolled vibration can cause structural damage and ultimately risk of failure. And vibration can feed back into the train, causing passengers to feel motion sick.

Design codes have been developed to control the vibration, or ‘dynamic excitation’ of railway structures. But high speed trains require special treatment.

HS2’s unique challenges

Controlling dynamic excitation isn’t only about designing bridges and culverts for a train’s top speed. Resonance is set off when the frequency of wheel-rail vibration harmonises with the frequency of the structure itself. Just like a musical instrument, there may be several frequencies where the harmonics match. So designing ‘quiet’ structures (that will resist excitation) requires multiple analyses to be carried out over a full range of speeds.

It gets more complex: HS2 may be used for conventional rolling stock as well as high speed trains, all with different axle configurations and imposing different loads. And HS2 is being designed for longer trains than run on the rest of the UK rail network. Structural excitation builds over time. Shorter trains may pass before resonance builds to a significant level. But longer trains increase the chance for the resonant response to build and pass acceptable thresholds. This had to be modelled too.

For extra challenge, the bridges and culverts on Phase 1 North came in a wide range of configurations, each requiring bespoke dynamic analysis.

The Curzon No.2 Viaduct required dynamic analysis

Turning dynamic analysis on its head

Dynamic analysis has traditionally been considered a validation process – confirming a structure as safe and serviceable at the end of the design process. Modelling all the variables is time-consuming and can cause over-design of structures to prevent the possibility of re-work. But on this project we’ve turned the sequence on its head through digital innovation, simplifying and radically reducing the time needed to analyse multiple dynamic response scenarios – and enabling analysis to inform design.

Ben Gough is principal consultant in Mott MacDonald’s ‘special services’ team, working across civils structures and transportation infrastructure. His team are finding new ways to use data and technology, bringing engineers together with data scientists and programmers who have expertise in machine learning and artificial intelligence.

This has seen the team develop our pioneering validation software Mabel, now Mabel 2.0, to rapidly analyse the dynamic response of a structure, far faster than has previously been possible. It’s also allowed for the efficient integration of the design and validation processes.

“Mabel is a digital dynamic analysis tool we developed in-house around 20 years ago,” says Ben. “To address emerging challenges on projects like HS2, we rebuilt it to massively expand its capabilities, and added a really good user interface while we were about it.”

90% time saving

Principal engineer Juan Trueba has been heavily involved in producing Mabel 2.0. “Bringing engineering and digital skillsets together has allowed us to push Mabel to the edge of the possible in the field of dynamics,” he says. Mabel 2.0 can simultaneously analyse the dynamic response of a structure for each of the 20 different trains being considered for HS2, at 50 different speeds for each.

20 train types factored into analysis

Simultaneous modelling is a huge leap forwards, since using the original version required a separate analysis and software configuration for each train, taking weeks of repetition by experienced engineers.

The ability to analyse so much so fast, with a single mouse click, enables dynamics analysis to be carried out in tandem with design iterations, resulting in more efficient structural designs. This has been helped by some special services coding expertise that has linked the Midas finite element analysis (FEA) software used by bridge engineers with Mabel 2.0, enabling on-the-fly validation.

90% faster computational speed

Other benefits: Mabel 2.0’s huge computational time saving – up to 90% for more complex scenarios – frees experienced engineers from repeated dynamic analyses, so that they can deploy their expertise more beneficially elsewhere. And the outputs are both user-friendly and save gigabytes of data.

“Post-analysis information is distilled into eight critical, transparent and accessible metrics, while allowing engineers to drill down into the results to verify the detailed dynamic behaviours,” says Ben.

Time saving track-structure interaction analysis

Another area where we’ve set a new bar is track-structure interaction (TSI), which examines the long-term effects of track stress. Technical principal for bridges and structures Stuart Moore explains: “Our scope is to understand the interaction between the track and bridges. Structures move – decks deflect when trains pass along them, and they elongate and contract with temperature variations. This can stress the rails, and the longer the structure, the greater the movement and potential stress can be.

“Rail design has to limit stresses to ensure the track is within its performance parameters, avoiding the risk of rail breaks and minimising the requirement for additional maintenance and rail replacement.”

Until now engineers have had to build TSI models manually, which soaks up engineering time and requires checking for human error. Our special services team addressed these challenges by linking bridge design and TSI models with a string of bespoke code.

Bridge designers use Dynamo, a ‘low code’ software package that defines parameters such as bridge length, span, depth, width and skew, track alignment, structural support, stiffness and articulation. This parametric data is structured and fed into a TSI modelling and analysis tool. This rapidly automates the generation of very complex models and can establish any possible track-structure interaction concerns.

“We put together our engineering and coding experience and expertise to create a system that takes the outputs from a structural design, generates a non-linear finite element analysis parametric model, and then performs a TSI analysis,” says Juan. “The first time we did a track-structure interaction analysis on a complex structure it took almost six weeks to complete, but the techniques we’ve developed can turn these around inside one week.”

Better solutions, faster delivery

Design optimisation is being carried out across every aspect of HS2. But every design change has knock-on effects requiring reanalysis of the dynamic response and TSI.

Our advances in both these areas mean we can accommodate design iterations swiftly to keep the project on track. Even within tight programme constraints, improved efficiency in both fields has allowed a limited team of specialists to deliver the quantity of analyses required, in a timely manner, across the project.

Moreover, reducing the amount of time engineers spend building and checking models allows them to look for opportunities for optimisation earlier in the design process. Because of this, we've been able to achieve more structurally efficient long-span bridges, which save on materials, without additional TSI risks.

Happier people, better value

An important benefit of these modelling and analysis efficiencies is the positive impact on our colleagues. Time previously spent ‘cranking the handle’ to complete a process can now be focused on engineering excellence that results in improved whole-life performance and value of the structures being designed.

The advances in modelling and analysis have made the processes themselves consistent and easy to understand. And this has made it easier and quicker to train new staff. It’s rapidly expanding the pool of specialists we can field to undertake this work – giving our clients greater access to the highest standards.