Shakedown limit analysis of railway slab track foundations under train loading

Shakedown limit analysis is used to calculate the factor of safety of a structure subject to cyclic moving loading. It is a promising approach for railway slab track structural design because it can help identify the required layer thicknesses and material strength properties. However, the approach is based on an underlying assumption that the stress field in the train passage direction is invariant, which is violated for slab tracks in the vicinity of expansion joints. To address this issue, this paper proposes a novel shakedown limit analysis implementation that enables its use for slab tracks with joints. Firstly, a 3D finite element slab track model is developed to calculate the stress field profiles exerted on the subgrade surface. Analytical equations describing the shape of these profiles are then derived, considering locations along the slab track, including those near and far from expansion joints. Relationships are also derived to describe the stress field profile variation with depth, including both train-induced and geostatic stresses. Next, a lower-bound shakedown limit method is used to calculate the elastic shakedown limit based on the Mohr-Coulomb criterion using the computed stress fields. After the model is validated, shakedown limits are examined, considering various friction angles, cohesions, and Poisson's ratios. It is shown that the limit is reduced when the geostatic stresses in the ground are ignored. Furthermore, the shakedown limit is not always directly proportional to subsoil cohesion and increases with Poisson's ratio.