Shakedown analysis is a robust approach for solving the strength problem of a structure under cyclic or repeated loading, e.g. railway structures subject to rolling and sliding traffic loads. Owing to the traffic loads, which are higher than the “shakedown limit”, railway structures may fail due to the excessive permanent deformation. This paper develops the analytical shakedown solutions based on Melan’s shakedown theorem, which is then applied for the evaluation of the strength and bearing capacity of multilayered railway structures. The shakedown solutions utilize the elastic stress fields obtained from the fully three-dimensional finite/infinite model, and calculate the shakedown multiplier for each layer of railway structures by means of a self-equilibrated critical residual stress field. The shakedown limits are then determined as the minimum shakedown multiplier among all layers. Parametric studies are also conducted, which indicate how the frictional coefficient, strength and stiffness of the materials, and the thickness ratio of ballast to subballast influence the shakedown limit and the stability condition of railway structures. The critical points of shakedown occur at the rail for low values of rail’s yield stress and large frictional coefficient, while they occur at the ballast layer when the frictional coefficient is relatively small. The shakedown limits are found to decrease with the increase in the strength and thickness of the ballast for a relatively small frictional coefficient. For the engineering design, there is an optimum combination of material properties and layer thickness, which provides the maximum bearing capacity of the railway structure based on this research. The results obtained from this study can provide a useful reference for the engineering design of railway structures.
Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling
