r - The Hong Kong Polytechnic University

frequencies of interest and the train speed. This range is divided into n intervals with width Δ k y and center
wavenumber k yi , which can be obtained from the following:
kyu
− kyl
1
Δ ky
= , kyi
= ( i− ) Δ k , 1~
2 y
i = n
(27)
n
in which k i represents the wavenumber of the i-th cosine-shaped rail surface. By substituting k yi and Δ k y into
Eq. (28), the amplitudes of irregularity profile α
i
for the i-th cosine-shaped rail surface can be obtained.
α = 2 G% ( k ) Δk
(28)
Case Study and Discussion
i w/
r yi y
Table 1 Irregularities parameter for FRA track classes (Hamid and Yang 1982).
Track class 6 5 4 3 2 1
'
A [10-7 m-cycle] 1.06 1.69 2.96 5.29 9.52 16.72
As shown in Figure 6, an illustrative example is given on the vibration mitigation of the floating slab track for
use in a tunnel embedded in a visco-elastic half-space subjected to a moving train. The 2.5D finite/infinite
method described previously was employed to calculate the ground response caused by a train moving over
uneven rails. Figure 7 shows the element mesh used, which has a width of 52 m and a depth of 22 m, with
different colors representing different material properties. Only half of the system is adopted in analysis due to
the symmetry consideration. To study the screening effect of the floating slab track on the vibrations caused by
the moving train over irregular rails, two cases are studied. In the first case, an elastic foundation is inserted
between the concrete slab and concrete tunnel lining to simulate the effect of the floating slab track. In the
second case, a direct fastened track, i.e., with no consideration made for the elastic foundation, is considered.
All the material properties, including soil properties, tunnel and track parameters, for the analytical model have
been listed in Table 2, where the elastic foundation has a Young’s modulus much smaller than that of the
concrete slab. Using the present data for soil, the shear and compressional wave velocities C s and C p computed
are also shown in Figure 6. Besides, the centroid of the tunnel is located at a depth of h = 13.5 m beneath the
ground, the inner diameter of the tunnel is 5.4 m, and the wall thickness of the tunnel is t = 30 cm.
Figure 6 Soil-tunnel model adopted in analysis
52 m
13.5 m
22 m
Figure 7 Finite/infinite element mesh
The train consists of 6 identical cars, with the following data: length = 19 m, a = 2.3 m, b = 12.6 m, weight of
car body (including passengers) W cb = 411.6 MN, bogie mass m b = 3,600 kg, wheelset mass m w = 1,700 kg,
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