Analysis of resonance effect for a railway track on a layered ground

When a train runs on soft ground it can approach or even exceed the speed of surface waves in the ground. Under such conditions the amplitudes of the track response increase considerably. Moreover, a resonance-like phenomenon can occur in which a clear oscillation trail can be observed behind the moving axle loads. An investigation is presented of this resonance frequency and the critical speed effect for a track on a layered half-space subject to a moving load. Three different methods are used to investigate this resonance frequency: (i) the spectrum of the response to a moving load, (ii) analysis of the dispersion curves of the ground, and (iii) frequency analysis of the response to a stationary load. A parameter study is presented of a layered half-space ground with different P-wave speeds, S-wave speeds, and depth of the upper layer. The critical speeds are found in each case; in such a layered ground, the critical speed is greater than the Rayleigh wave speed of the soft upper layer due to the influence of the underlying half-space. The oscillating frequencies are shown to vary with the speed of the moving load, tending to reduce when the load speed increases. The P-wave speeds of both the upper layer and the underlying half-space are found to have negligible influence on the critical velocity and on the oscillating frequency; the S-wave speed of the half-space has only a small influence. Larger differences are found when the depth of the layer is varied. Finally, a formula for calculating this resonance frequency is proposed.