Wavefront evolution of compression waves propagating in high speed railway tunnels

The amplitude of micro-pressure wave emitted from the exit portal of a high-speed railway tunnel is approximately proportional to the pressure gradient of the internal wavefronts approaching the portal. For long tunnels, the evolution during propagation is an important factor for estimating the pressure gradient in the exit wavefront. Moreover, the relationship between the entrance and exit states depends upon the conflicting influences of inertia and damping along the propagation. In this paper, the investigation is done to study the evolution of wavefronts with different initial waveforms and to assess the influence of friction and train speed in the process. This work is based on numerical simulations of wavefront propagation using a third-order monotonic upwind scheme for conservation laws and backed up by field measurements. Numerical analyses show that the wavefront evolution not only depends on the pressure amplitude and the maximum pressure gradient of the initial wavefront but also depends strongly on the shape and timing of the peak steepness of ∂P/∂t. The predictions also demonstrate the existence of a critical tunnel length. For any particular train and tunnel entrance, the magnitudes of the micro-pressure waves increase with the tunnel length when this length is below the critical one and decrease with the tunnel length otherwise. The critical length decreases with the increase of the tunnel wall friction and the train speed.