A Railway Track Deflection Model Based on Nonlinear Discrete Support

Abstract

A nonlinear deflection model for railway tracks is developed for static or semistatic loads. The model is motivated by the fact that the load-deflection curve for a railway track is often, if not always, nonlinear with a hardening response. Hence a Winkler foundation is not appropriate as this represents a linear model - the beam on elastic foundation model. Euler-Bernoulli beam elements are used to model the rails, and the sleeper support is modelled by discrete nonlinear springs. The spring response is modelled by a simple power function with two parameters, thus providing a nonlinear behaviour. The analysis is based on measuring the rail deflection for two different load levels. A back-analysis using the nonlinear load-deflection relationship measurements is then carried out, which will give the numerical values of the two parameters in the nonlinear spring model. The rail deflection, rail bending moment and the rail seat loads can now be calculated. Assuming a hardening behaviour, the new model predicts a somewhat more extended deflection basin as compared with the beam on elastic foundation model with the same max imum deflection. Also, the maximum rail bending moment is somewhat smaller, while the maximum rail seat load attains a somewhat larger value. Thus, the new model can be said to give a stiff track response near the load application point and a softer response farther away from the load as compared with the beam on elastic foundation model.