## 4 Measurement Results
### Measurements Related to Under-Ballast Plates and Troughs  
The idea of a mitigation of ground vibration by a concrete plate under the ballast was first realised near Altheim in Germany. BAM measured the ground vibration along a measuring axis at the reference track (Figure 9a) and at the track with a 0.3 m thick concrete plate (Figure 9b). Some irregularities can be seen at distances between 10 and 25 m on the embankment. The regular measuring points on the original soil at longer distances show a maximum region around 12 Hz which is clearly reduced by the under-ballast plate; see also Figure 9c. Figure 8: Under-ballast mat at the Raron site [23], measured ground vibration at 8 m distance from (**a**) the reference track, (**b**) a track with under-ballast mat, and (**c**) the ground vibration reduction; different train speeds of \(\square\) 175, \(\Circle\) 160, \(\triangle\) 120, and + 80 km/h. Figure 7: Measured ground vibration reduction of ten track sections in Herne with normal (\(\Diamond\), \(\ast\), \(\blacksquare\), \(\triangleright\)), heavy (+, \(\times\), \(\triangledown\)), and wide (\(\square\), \(\bigcirc\), \(\bigtriangle\)) sleepers and soft under-sleeper pads with static stiffnesses \(k_{lL}=\square\) 0.08, \(\Circle\) 0.06, \(\bigtriangle\) 0.03, + 0.06, \(\times\) 0.1, \(\Diamond\), \(\ast\), \(\blacktriangleright\) 0.1 N/mm\({}^{3}\), (**a**) measurements with a shaker [22], (**b**) calculation with dynamic pad stiffnesses. The same mitigation principle has been used for several solutions with concrete troughs which are often combined with under-ballast mats. The measurement results from [24] are further analysed for the reduction effect at different sites, for different trains and different train speeds. Figure 10 shows the ground vibrations at 8 m distance with and without concrete trough. Generally, the high-frequency components between 32 and 64 Hz dominate. At low frequencies, however, a speed-dependent maximum can be observed, most clearly at 10 Hz for the freight train. The slow regional (\"Doppelstock\") train in Baden has also a maximum at 10 Hz. The faster passenger trains at the Ulm site show all the same results, a maximum at 12 to 16 Hz, and the fastest train ICE at Sinzheim has the maximum at 25 Hz. Each of these low-frequency maxima is clearly reduced by the trough (Figure 10b), whereas the high-frequency maximum is more pronounced for the trough solutions due to the under-ballast mat which is used together with the trough. The low-frequency component has a strong reduction of up to 15 dB and a wider frequency range up to 20 Hz for the slowest and up to 32 Hz for the fastest train (Figure 10c). In addition, a reduction of about 10 dB can be found at higher frequencies for the Sinzheim and Baden measurement sites where soft under ballast mats (\(k_{M}{}^{\prime\prime}\approx 0.06\) N/mm\({}^{3}\)) have been used. The average reduction effect for all troughs, trains and sites, which is shown in Figure 11 (square markers [24]), is less strong and less specific for the low-frequency reduction. On the other hand, the first measurements at the Sinzheim trough (Figure 11, circle markers [25]) resulted in a stronger and wider reduction, as well as measurements at an under-ballast plate in Graz (Figure 11, triangle markers [26]). Figure 10: Concrete troughs after [24], measured ground vibration at 8 m distance of (**a**) the reference tracks, (**b**) tracks with concrete troughs, and (**c**) the ground vibration reduction; different trains at different sites: \(\square\) Intercity train, Ulm, \(\Circle\) freight train, Ulm, \(\Circle\) ICE train, Sinzheim, + regional train, Baden. Figure 9: Under-ballast plate at the Altheim site; measured ground vibration at distances of \(\square\) 7, \(\Circle\) 10, \(\triangle\) 20, + 30, \(\times\) 50 m from (**a**) the reference track, (**b**) a track with under-ballast mat, and (**c**) the average ground vibration reduction at the far field.