INFLUENCE OF BALLAST ON WAVE STEEPENING IN TUNNELS

The strength of micro-pressure waves emitted from railway tunnels is strongly dependent upon the steepnesses of wavefronts arriving at tunnel portals after travelling along the tunnel. The steepnesses are themselves dependent upon the ability of phenomena such as skin friction to resist inertial steepening. In this paper, the influence of air pockets in ballast track is investigated. First, the local behaviour of the ballast is linked to a series of Helmholtz resonators, yielding analytical relationships whose characteristics are explored. Then the resonators are incorporated into a simple model of wave propagation in ducts. By initially neglecting skin friction, the existence of stable, asymptotic conditions is identified. The asymptotes are shown to depend upon the pressure amplitude but to be independent of the upstream rates of change of pressure. The consequences of these results in real tunnels are illustrated.