Keywords: discrete element method, finite element method, ballasted track, vibration analysis, wave propagation.

Modelling techniques were developed for use in three-dimensional finite element studies of a ballasted railway track to clarify the transmission characteristics from low frequency up to high frequency with respect to a dynamic load within the ballast layer. The results obtained using the technique were for the evaluation of the dynamic behaviour of ballast aggregate and wave propagation inside the ballast grains when they were affected by impact loads. Explanations of the analyses using an integrated approach combining finite element modelling and discrete element modelling are also given.

For individual ballast grains and the ballast aggregate structure, the author performed finite element normal mode analysis. All normal modes for individual ballast grains were identified in the very-high-frequency domain of more than 11 kHz. Application of finite element normal mode analysis for the ballast aggregate structure yielded a set of normal modes related to the ballast aggregate. The normal frequency of the first-order normal mode, which represents the vertical motion of the entire aggregate, is 1715 Hz, which is much lower than the normal frequency of the individual particles. An actual ballast structure is larger than this model, but the results indicated that the actual ballast in the lower frequency domain will have a similar normal mode to that of the analytical result.

Next, inputting measured train loads into the ballast aggregate model clarified that the dynamic stress of the ballast induced by a passing train was not distributed uniformly throughout the ballast aggregates. Rather, large stresses concentrated locally around specific contact points. Moreover, the author, using only elastic body analysis which does not incorporate material nonlinearity, numerically reproduced the mechanisms which reduce the wave propagation velocity inside a ballast layer and which greatly decreased wave motion inside a ballast layer. These newly developed techniques are beneficial for analyzing three-dimensional ballast motion induced by passing trains.

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