An alternative modelling tool to the FDTD method is the

Fig. 14. Left: (a) Trench deployment, Right: (b) Subgrade stiffening.Figure optionsDownload full-size imageDownload as PowerPoint slide
An alternative approach is to use subgrade stiffening at strategic ground locations (Fig. 14b). This serves to increase the Seocalcitol stiffness and thus dampen the propagation of vibration. Possible stiffening techniques include deep vibro-compaction, deep soil mixing, stone columns, grouting or vacuum consolidation. A more comprehensive comparison between techniques can be found in [177]. Despite this, it should be noted that the deployment of such ground vibration mitigation measures is financially intensive and should be avoided if possible.
6.2. Critical velocity effects
When train speeds approach the underlying Rayleigh wave speed of the supporting soil it is possible that large increases in track vibration may occur. This is an area of increasing importance for high speed rail because as operational speeds increase, the probability of train speeds approaching this ‘critical velocity’ at a particular site increases. Another important aspect is the ‘track critical velocity’, which is often described as the minimal phase velocity of bending waves propagating in the in the track supported by the ballast. Despite this, it is typically found that ‘track critical velocity’ is many times higher than the soil Rayleigh wave velocity.