## 4 Detailed Analysis of Tunnel and Bridge Characteristics
### Narrow-Band Spectra of the Tunnel Vibrations  
Firstly, the axle-box accelerations are analysed in a spectrogram plot in Figure 10. The time-dependent Fourier spectra are shown for the slab track in the tunnel up to \(t=45\) s and for the ballast track at the surface track for \(t>45\) s. The Fourier spectra of all four wheels of a bogie show regular maxima at about 15, 30, 45, 60, 75 and 90 Hz which are due to the wheel out-of-roundness. The additional maximum at \(f_{\rm S}=72\) Hz close to the fifth out-of-roundness frequency is due to the sleeper distance and the train speed of 160 km/h. Besides these common characteristics, clear differences between the tunnel and the surface line can be observed. On the slab track in the tunnel, the frequencies between 60 and 75 Hz are amplified whereas higher frequencies between 75 and 90 Hz are dominant on the surface line, which indicates the higher vehicle-track resonance for the ballasted track. The increased amplitudes below 10 Hz are generated by the higher irregularities of the ballast track. The four different wheels have different out-of-roundness components. In Figure 10a the first order out-of-roundness is stronger, in Figure 10c the second and in Figure 10b the third and the sixth component. The out-of-roundness in the frequency range  
Figure 9: Vibrations of the soil at horizontal distances from the surface track (a) 5 m, (b) 17.5 m, (c) 30 m and (d) 100 m, one-third octave band spectra for different train speeds: 160, \(\Circle\) 125, \(\Circle\) 100, \(+\) 80, \(\times\) 63 km/h. between 60 and 80 Hz are usually increased by the vehicle-track interaction of the slab track in the tunnel. The axle-box accelerations of different train speeds are presented in Figure 11 as Fourier spectra. The discrete peaks from the out-of-roundness of the wheel are clearest for the low train speeds of 63 and 80 km/h (Figure 11a,d). For higher train speeds, only a few out-of-roundness peaks dominate. For 125 km/h, the sleeper passage is most clearly visible at 60 Hz where it is amplified by the wheelset-track resonance. The wheelset-track resonance can also be found for 160 km/h in Figure 11p. Figure 10: Spectrograms of the wheel/axle-box accelerations during the passage through the tunnel and the surface line, (**a**) wheelset 1 right, (**b**) wheelset 1 left, (**c**) wheelset 2 right and (**d**) wheelset 2 left. Figure 11: Fourier spectra of the wheel accelerations (**a**,**d**,**g**,**j**,**m**,**p**), the sleeper velocities (**b**,**e**,**h**,**k**,**n**,**q**) and the soil at 20 m (**c**,**f**,**i**,**l**,**o**,**r**) in the tunnel section for train speeds: (**a**–**c**) 63, (**d**–**f**) 80, (**g**–**i**) 100, (**j**–**l**) 125, (**m**–**o**) 140 and (**p**-**r**) 160 km/h. The Fourier spectra of the slab track and the soil above the tunnel are analysed for the different train speeds on the mid and right-hand side of Figure 11. The characteristic high-frequency range can be clearly found for these measurement points, but they are modified by the different transfer functions of the track and the soil. The sleeper point shows generally a wider frequency band from 50 to 80 Hz, and, for the soil point, the band has lower frequencies between 30 and 60 Hz. The high frequencies above 60 Hz are probably reduced because of the stronger damping effect of the soil. In the amplified frequency range between 30 and 40 Hz, no peak or maximum, which is unique for all train speeds and which would indicate a resonance of the soil, could be found. The smooth maximum of the transfer function of the soil seems to be the reason for the raised amplitudes at this frequency range. In the soil, the peaks from the wheel irregularities can be found at speed-dependent out-of-roundness frequencies, for example at 40, 50 and 60 Hz for the 100 km/h train speed (Figure 11i) or at 32, 40, 48 and 56 Hz for 80 km/h (Figure 11f). On the track, the out-of-roundness components are not sharp peaks but wider frequency bands due to the Doppler effect for moving loads.