Modelling railway ballasted track settlement in vehicle-track interaction analysis

The geometry of a ballasted railway gradually deteriorates with trafficking, mainly as a result of the plastic settlement of the track-bed (ballast and sub-base). The rate and amount of settlement depend on a number of factors, and for various reasons are difficult to predict or estimate analytically. As a result, various empirical equations for estimating the rate of development of plastic settlement of railway track with train passage have been proposed. A review of these equations shows that they (i) do not reproduce the form of settlement vs number of load cycles relationships usually seen in the field; (ii) do not reflect current knowledge of the behaviour of soil subgrades in cyclic loading; and (iii) are often critically dependent on the curve fitting parameters used, which in turn depend on the circumstances in which the calibration data were obtained. To address these shortcomings, this paper develops a semi-analytical approach, based on the known behaviour of granular materials under cyclic loading, for the calculation of plastic settlements of the trackbed with train passage. The semi-analytical model is then combined with a suitable vehicle-track interaction analysis to calculate rates of development of permanent settlement for different initial trackbed stiffnesses, vehicle types and speeds. The model is shown to be able to reproduce recursive effects, in which a deterioration in track geometry causes an increased variation in dynamic load, which feeds back into a further deterioration in track geometry. The new model represents a significant improvement on current empirical equations, in that it is able to reproduce observed aspects of railway track settlement on the basis of the known behaviour of soils and ballast in cyclic loading.