## 5 Interpretation and Recommendations for the Measurement of Mitigation Effects  
The train-induced ground vibration is usually strong in the frequency range of 10 to 100 Hz, whereas the high frequencies above 100 Hz and the very low frequencies below 10 Hz are small because of the material damping and the layering of the soil. Therefore, the reduction effects in these extreme frequency ranges are uncertain, namely the intended mitigation effects of soft elements are difficult to assess. The vehicle-track resonances usually fall in the range of high amplitudes and help to check the properties of the elastic elements. The low-frequency mitigation is mainly between 10 and 30 Hz at a typical maximum in the high-amplitude region. This low-frequency maximum can be attributed to the static axle loads and their impulses on the railway track. This has been checked by axle-box measurements and narrow-band spectra of the ground vibration [21]. The regular response to the axle impulses is limited to the close near field of the track and to frequencies below 10 Hz. Only the irregular response due to the scattering by a randomly varying ballast and soil can yield far-field amplitudes at higher frequencies of 10 to 30 Hz [27]. Reductions at frequencies below 10 Hz are ratios from small numbers and should be carefully checked. They can probably stem from different layering of the isolated and un-isolated track section, but also reduced irregularities of a newly installed isolated track should be considered.  
Besides the problem of amplitude ratios for small amplitudes, the presentation as a relative reduction makes the mitigation effect strongly dependent on the reference system. This can be avoided by the calculation of absolute force reductions. In measurements, however, only relative mitigation effects can be established which are usually better for a stiff reference system (for example, a tunnel line compared to a surface line).  
The following recommendations for measuring mitigation effects can be given:  
1. The original spectra for the isolated and un-isolated track should be reported for to check if the established reduction is for the main amplitudes or for smaller and more random amplitudes (see Figures 4, 5 and 8-10).  
Figure 11: Measured ground vibration reduction of tracks with concrete troughs. \(\square\) average of 6 different sites, with soil correction [24], \(\square\) at Sinzheim, after installation [25], \(\triangle\) an urban track in Graz [26].  
2. The reduction should not be measured in the near field of the track as the quasi-static response could lead to a too positive mitigation effect. A measurement point at the tunnel wall, for example, is generally too close to the track.
3. It is better to measure a line of measurement points to check the regularity of the soil (see Figure 9).
4. It is always useful to measure the properties of the soil at each track section, that is, the wave velocity (stiffness), the damping (the attenuation with distance), and the transfer function of the soil. Even nearby track sections can have different soil properties as was found for the Regensburg, the Lengnau site, and the Ulm site.
5. If the soil is different at the isolated and un-isolated track section, a correction should be made based on the measured transfer functions of the soil.
6. The reduction depends strongly on the reference system. A stiff reference would give the \"best\"-mitigation effect. (The disappointing results at the Regensburg site (Figure 4) are probably due to the soft rail pads of \(k_{\text{R}}=40\) kN/mm that have been used for the un-isolated reference track and for all isolated track sections).
7. As the low-frequency reduction depends on the train speed, it is recommended to analyse the reduction separately for different train types and train speeds, as has been demonstrated by the measurements for the under-ballast mat (Figure 8) and the trough solutions (Figure 10).