Shakedown limits can be used to predict different long-term responses of geo-structures under repeated moving loads. Based on lower-bound shakedown theorems, static and dynamic shakedown limits were obtained respectively for slab substructures under train loads of various speeds. The determination of the dynamic shakedown limit is relatively complicated due to the calculation of stable dynamic elastic stresses in the substructures. It was found the change of the dynamic shakedown limit from the corresponding static one is highly dependent on soil friction angle and a velocity factor (train speed over critical speed of the substructure). A simple relation between the dynamic shakedown limits at various speeds and the static one is then proposed which can serve as an efficient approach to estimate the influence of the train speed on the long-term performance of substructure.