Keywords: trackbed, ballast, settlement, prediction, under-sleeper pads.

It is widely reported that one of the benefits of under-sleeper pads (USPs) is a reduction in ballast deformation and therefore a reduction in the rate of track profile deterioration. This paper describes an approach to trackbed modelling that takes account of the slight tilt that each sleeper undergoes as an axle load passes over. The relevant assumptions and equations are explained and presented and it is deduced that the maximum stress experienced beneath the edge of a sleeper is slightly larger than the maximum stress on its centre line. This therefore implies that the unloaded shape of the ballast surface beneath a sleeper will theoretically become slightly curved in the longitudinal direction and that the stress distribution at the sleeper-ballast interface will be non-uniform. The implication of a contact between a flat rigid sleeper soffit and a curved ballast surface is that each axle pass will induce localised plastic deformation, the magnitude of which depends on the degree of sleeper tilt, which is a function of several track parameters including the stiffness of rail seat pads. It also depends on ballast strength. Predicted track settlement rates are given for selected cases, illustrating the effect of sleeper tilt.

The paper continues by presenting laboratory results from vertical load tests on a sleeper section with and without USPs of two different stiffnesses. The results indicate that even under purely vertical load USPs can still have a significant effect and that this is dependent on the stiffness of the pad; in these tests the stiffer pad performed better and this is theorised to be because the softer pad allowed too much lateral freedom to the upper layer of ballast stones. However, the point is made that the real effect of USPs is likely to be considerably greater than these tests reveal because of the importance of sleeper tilt. If the postulated tilting mechanism is accepted then the clear conclusion is that USPs could potentially prevent localised plastic strain from occurring by maintaining a contact with the ballast that follows the slightly curved shape of the ballast surface. An optimised USP would therefore be soft enough to achieve this but not so soft that it allowed excessive movement of the upper layer of ballast stones. No prediction method for track settlement including USPs is given at this stage because of the complexity of the problem.

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