A model for the stochastic prediction of track support stiffness

Abstract

As well as guiding the train, one of the key aims of a railway track system is to provide support to the train at the wheel–rail interface that is of near-uniform compliance. Of the various components that make up this compliance, the contribution of the trackbed (ballast and subgrade) is the most difficult to understand and control. This paper presents data from field measurements of the track support system stiffness for a continuous run of 209 sleepers on a high-speed ballasted railway. The data indicate a level of variability, even on a highly engineered and well-maintained route. Statistical analysis of the data is used to demonstrate the dependence of the trackbed modulus at an individual sleeper on the modulus of the sleeper immediately preceding it, and that in statistical terms the effect of sleepers further away is due to correlation between the intermediate sleepers. An optimum trackbed stiffness, close to the overall mean, at which the standard deviation is a minimum is demonstrated for a particular site. As the trackbed stiffness moves away from this optimum value, the likely variation from sleeper to sleeper increases. A framework for implementing a stochastic approach for predicting the variation in track support stiffness from one sleeper to another, based on a Markov model and appropriate probability distribution functions, is then proposed. This framework may be used for the quantitative comparison of different sites and for simulating the plausible values of track stiffness in the vehicle–track interaction analysis.