Dynamic Analysis for High-Speed Locomotive in Distinct Depths

The study uses coupled finite or boundary element models expressed in terms of the axial wavenumber. It is found to be important to include the track in the model as this determines how the load is distributed at the soil’s surface, which significantly affects the insertion loss of the barrier. Calculations are presented for a range of typical layered grounds in which the depth of the upper soil layer is varied. Variations in the width and depth of the trench or barrier are also considered. The results show that in all ground conditions considered, the notional rectangular open trench performs best.


Introduction
From measurements and computer modeling of railway vibration, it has been found that the most important frequency components are controlled by vibration propagation in upper layers of soil that are often only a few meters deep [1,2].This suggests that a trench that cuts through such a surface layer may potentially give significant reductions in the most important parts of the vibration spectrum.Jones et al. used a two-dimensional boundary element model to study rectangular trenches in the layered ground, considering the effect of their depth and position.The ground consisted of a 2 m layer of alluvial soil over a substratum of stiffer material (say, gravel beds).This study was extended in [3][4][5][6] to include trenches with a retaining structure or a slope, again using twodimensional modeling [7,8].

Model
The geometry is essentially two-dimensional and invariant in the third dimension.Under such conditions, it is possible to use a wavenumber transform in the axial direction in combination with a two-dimensional finite or boundary element model [9][10][11][12].The full three-dimensional solution can be recovered by an inverse Fourier transform over wavenumber [13][14][15][16].This so-called 2.5D approach has been used widely to study railway vibration, it is more efficient than a fully dimensional approach.Similarly, 2.5D finite element / infinite element models have been used [17][18][19].

Open Trench
The barrier applies compressional stress to the soil on either side of This can be equated to the internal stress in the soil on either side of the barrier where k = /cp is the wavenumber of compressional waves in the soil.Solving these equations yields a power transmission coefficient

Conclusions
Filling the trench with a soft barrier material reduces performance significantly because vibration is transmitted through the barrier material and diffracted beneath it.It has been demonstrated that the important parameter is the stiffness per unit area of the barrier material, rather than its impedance, as in the case of transmission at the interface of two semi-infinite media.Despite the reduction in performance, a 3 m deep, 0.05 m wide barrier filled with a material with Young's modulus of 1 MPa reduces overall train-induced vibration by more than 4 dB for the example case considered.This can be improved by reducing the material's stiffness or increasing its width or depth.

Fig. 1 .
Fig. 1.Layered soil adjacent to a railway track

Figure 5 :
Figure 5: Track for a velocity 250 km/h train.

Fig. 11 .Fig. 12 :
Fig. 11.Trenches with sloping sides Fig. 12: The angle of the sides of a 3m deep trench on the insertion loss at 24 m with h1 = 3 m soft upper layer depth.
octave band centre frequency [Hz] I n s e rt io n lo s s [ d B ] octave band centre frequency [Hz] I n s e rt io n lo s s [ d B ] octave band centre frequency [Hz] I n s e rt io n lo s s [ d B ] octave band centre frequency [Hz] I n s e rt io n lo s s [ d B ]

Fig. 15 :Fig. 16 :Fig. 16 :
Fig. 15: Insertion loss at 24 m for a 50 mm wide layer depth of h1 = 3 m.(a) Soft barrier 3 m deep versus open trench the same width.(b) Soft barrier with h = 1.5, 3, and 6 m depth.Response to a line source; calculated with the track included.

Fig 19 :
Fig 19: Insertion loss of a 3 m deep, 0.5 m wide open trench for Delhi (a), Gurugram (b), and (c) Faridabad.The receiver is 16 meters (solid line), 24 meters (dashed line), and 32 meters (dash-dot line) away from the track.

Table 3 .
Vehicle parameters

Table 4 :
The overall velocity levels at 24 m for the passage of traveling at 250 km/h

Table 6 .
Soil properties for the reference sites.