## 2 Measurement Campaign for the Bridge, Tunnel and Surface Lines
an almost constant level for the tunnel environment at the surface (a clear reduction is only found for horizontal distances greater than 20 m) whereas the ground vibrations from the surface line continuously decrease with the distance. The amplitudes of the tunnel of around 0.1 mm/s are smaller than the amplitudes of the surface line, approximately one fourth at the far field and even less at the near field. The bridge amplitudes show an increase with train speed with certain maxima for 100 and 160 km/h. An increasing trend with the train speed can also be found in the ground amplitudes from the tunnel track and is more regular from the surface track. The frequency content of the different vehicle, track, ground and bridge measurement points on the different line types are analysed by one-third octave band spectra in the following section. Figure 5: Maximum amplitudes (**a**) of the bridge as a function of the train speeds, (**b**) above the tunnel as a function of the horizontal distance, as a function of the distance and train speeds: \(\square\) 63, \(\circ\) 80, \(\triangle\) 100, + 125, \(\times\) 140, \(\Diamond\) 160 km/h, and (**c**) on the surface line as a function of the distance and train speeds: \(\square\) 40, \(\Diamond\) 63, \(\triangle\) 80, + 100, \(\times\) 125, \(\Diamond\) 140, \(\Diamond\) 160 km/h. One-Third Octave Band Spectra of the Vehicle, Track, Bridge and Soil Vibrations and the Interpretation of Different Frequency Bands  
The vibrations of the different systems (vehicle, track, bridge, soil) and the different measurement points are presented as one-third octave band spectra for the different train speeds. At first, the accelerations of the wheelset are analysed in Figure 6. The wheelset spectra at the tunnel track (Figure 6a) start with amplitudes below 1 m/s\({}^{2}\) at low frequencies, followed by a strong increase and a strong maximum at 63 Hz, and at high frequencies, the accelerations decrease strongly. This is the strongest frequency-dependent behaviour for all the track types. The maximum on the bridge and the surface line (Figure 6c) is not so sharp and a wider high-amplitude range between 63 and 100 Hz is observed. The maximum is due to the vehicle-track resonance where the wheelset is vibrating on the compliant track. The measured track compliances in Appendix A show the different behaviour of the tunnel track with soft rail pads which has little damping and yields the highest resonance amplitudes. The surface track has its high damping from the radiation damping of the soil. Additional relative maxima can be found at the speed-dependent sleeper-passing frequency at 30, 40, 50, 60 and 80 Hz (Figure 6b). The bridge track has the highest amplitude level at high frequencies. The low-frequency wheelset accelerations clearly increase with the train speed, whereas the differences are smaller at high frequencies. The wheelset accelerations give some information about the excitation of ground vibrations. If the acceleration spectra are divided by the squared circular frequency \(\omega^{2}\), displacement spectra are obtained which are identical to the irregularity spectra up to the vehicle-track resonance. Around the vehicle-track resonance, the displacements over  
Figure 6: One-third octave band spectra of the axe-box accelerations on the (**a**) tunnel, (**b**) bridge and (**c**) surface lines, for different train speeds \(\square\) 160, \(\circ\) 125, \(\triangle\) 100, + 80, \(\times\) 63 km/h. estimate the irregularities. On the other hand, the forces that are acting on the track can be estimated by multiplying the accelerations by the wheelset mass (approximately 1500 kg). This is a good estimation above 10 Hz (above the car-body and bogie resonances) and below 100 Hz (where a flexible behaviour of the wheelset is possible). Whereas the forces are nearly constant, the irregularities strongly decrease with frequency (increasing with wavelength).