Three-dimensional shakedown analysis of ballasted railway structures under moving surface loads with different load distributions

Shakedown of ballasted railway structures was analyzed based on Melan's shakedown theorem, in which the wheel/rail contact was approximated by Hertz (circular and elliptical contact areas), uniform and trapezoidal load distributions, separately. The shakedown solutions incorporating to the three-dimensional finite element model calculated shakedown multiplier by means of a self-equilibrated critical residual stress field. The shakedown multiplier for multi-layered ballasted railway structure was determined as the minimum one among all layers. The results showed that elliptical Hertz and uniform load yielded the largest and smallest shakedown limits, respectively, with the maximum difference of approximately 64%. The shakedown limits always occurred at ballast layer for relatively small frictional coefficient, whilst occurred at rail for low rail's yield stress with large frictional coefficient. As expected, the shakedown limits decreased as the ballast stiffness and thickness increased, especially for relatively small frictional coefficient; while increased with raising rail's yield stress. The material properties and thickness should therefore be optimally designed so as to provide a maximum resistance to the structure failure and reduce the material costs.