Dynamic Modelling of Train-Induced Ground Vibrations

Dynamic modelling of train-induced ground vibrations encompasses the numerical representation of the complex interaction between rolling stock, track structures and underlying soil. These models simulate how wheel–rail contact forces generate elastic waves in ballast, subgrade and surrounding ground and predict their propagation over distance and through varied geological layers. Approaches range from time-domain multibody methods, which resolve detailed vehicle and track dynamics, to frequency-domain formulations based on wavenumber–frequency analysis, capable of rapid prediction across broad frequency bands. Key phenomena include the onset of critical velocity, at which train speed matches wave propagation in the track-soil system, leading to amplified responses, and the influence of soil stratification on wave attenuation and resonance. Modern dynamic models inform the design of vibration mitigation measures—such as ballast mats, floating slabs or periodic pile barriers—and support environmental impact assessments, infrastructure planning and the optimisation of ground improvement strategies. The global significance of this work lies in its capacity to safeguard sensitive installations, improve passenger comfort and reduce community disturbance alongside the relentless expansion of high-speed and urban rail networks.

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Dynamic Modelling of Train-Induced Ground Vibrations publication trend

The graph below shows the total number of articles in dynamic modelling of train-induced ground vibrations across all publications each year (not limited to Nature Index journals).

Technical terms

Dynamic finite element model: A numerical representation dividing track or soil into discrete elements to solve wave propagation and structural response under time-varying loads.
Multibody modelling: A computational framework that simulates mechanical interactions of vehicle components and track elements through rigid and flexible bodies connected by joints.
Wavenumber–frequency domain: A spectral analysis approach that represents vibration fields as functions of spatial wavenumber and temporal frequency to predict propagation in layered media.
Critical velocity: The train speed at which the phase velocity of generated ground waves equals the train’s speed, causing resonance and peak vibration amplification.
Insertion loss: The reduction in vibration or noise level achieved by a mitigation measure, expressed in decibels, between source and receiver.
Free-field vibration: The ground-borne vibration measured in open soil away from structures, serving as input for building-vibration and human-comfort assessments.

References

1. Modelling the Environmental Effects of Railway Vibrations from Different Types of Rolling Stock: A Numerical Study. Shock and Vibration (2015).
2. Prediction of railway induced ground vibration through multibody and finite element modelling. Mechanical Sciences (2013).
3. Railway ground vibration and mitigation measures: benchmarking of best practices. Railway Engineering Science (2022).
4. Simple and fast prediction of train-induced track forces, ground and building vibrations. Railway Engineering Science (2020).
5. Vehicle–track–tunnel dynamic interaction: a finite/infinite element modelling method. Railway Engineering Science (2021).
6. Control of Metro Train-Induced Vibrations in a Laboratory Using Periodic Piles. Sustainability (2020).