This paper discusses the propagation of surface waves in a stratified half space, which consists of an elastic granular upper layer that rests on a half-infinite elastic substratum. For the upper layer the effect of particle translation and particle rotation are incorporated via a second-gradient continuum formulation and a Cosserat continuum formulation, respectively. Consequently, additional surface wave modes emerge, which cannot be described by a classic elastic formulation. After a general discussion of the surface wave dispersion curves, the critical behaviour of the stratified medium under a moving vibrating load will be examined. Here, the adjective `critical' designates that the wave energy that is generated by the moving load has the same velocity as the load itself, which results in resonance phenomena. The model parameters in this study are chosen to be representative for conditions in a high-speed railway track. The critical load velocities will be determined for several cases, where the effect by the ballast particle size, the ballast layer thickness, the load velocity and the sleeper distance will be analyzed.