Keywords: dynamic, interaction, settlement, roughness, pothole.

This paper describes a numerical model to calculate subgrade settlement in railway tracks as a result of repeated dynamic loading. The vehicle is modelled as a ten degree-of-freedom, lumped mass multi-body system comprising the carriage body mass and its moment of inertia, two bogie masses and their moments of inertia, and four wheel unsprung masses. The railway track is divided into Euler-Bernoulli beam elements of finite length resting on three layers of elastic foundation. The three layers of discrete springs and dampers represent the elasticity and damping effects of the rail pads, the ballast, and the subgrade. A condensation technique is used to improve the computational efficiency of the finite element model.

Permanent deformation of the subgrade layer is calculated on the basis of a power law assumption proposed by Li and Selig [1], i.e., permanent deformation is proportional to relative stress raised to a power, multiplied by the number of repetitions raised to another power. Dynamic interaction causes patterns of dynamic force on the track which, after many repetitions, result in subgrade settlement. The settlement changes the excitation displacements applied to the train which, in turn, changes the pattern of the applied dynamic force.

Patterns of dynamic forces are calculated initially for a perfectly smooth track. The contact force peaks shortly after the wheel passes the relatively stiff supports provided by the sleepers. A second lesser peak occurs between sleepers arising from an interference effect. The dynamic increment is modest relative to the static weight.

The train is also passed over a track with an initial 'pothole' in the subgrade, i.e., a local subsidence feature. The equation for the Gaussian (normal) statistical distribution is used to generate a bell shaped depression for this purpose. The calculation is repeated to determine the changes in the subgrade settlement with repeated loading, i.e., the pattern of forces cause permanent deformation in the subgrade layer, which leads to changes in the pattern of applied forces and so forth. Over many cycles of load, the pattern of forces changes and the deformations increase.

The pothole is found to grow with repeated loading and to change the pattern of applied force. However, the growth is modest and its rate of growth diminishes over time.

1

D. Li, E.T. Selig, "Cumulative plastic deformation for fine-grained subgrade soils", Journal of Geotechnical Engineering, ASCE, 122(12), 1006-1013, 1996. doi:10.1061/(ASCE)0733-9410(1996)122:12(1006)

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