# Protection of Buried Pipelines from High-Speed Train Vibrations with Expanded Polystyrene Geofoam
## 3 Results
### Impact of EPS Layer Thickness on Pipeline Protection
Case 3: EPS layer with 50 cm height  
The height of the EPS layer has been increased to 50 cm, aiming to further reduce the vibration levels. Figure 11 depicts the Fourier spectra for this mitigation measure. Evidently, the thicker EPS layer effectively reduces HST-induced vibrations for all the examined velocities. For low HST-passing velocity, the vibration peaks have been limited under 0.8 mm/s (see Figure 11a). Similarly, as shown in Figure 11b, in the case of the typical operation velocity of Thalys (300 km/h), the reduction reaches over 60% for certain frequencies (e.g., \(f_{b,1}\), \(f_{b,2}\)). Lastly, the effectiveness of the examined mitigation measure is  
Figure 10: Fourier spectra at the pipeline top when protected with 25 cm thickness EPS layer for HST passage with **(a)** 240 km/h, **(b)** 300 km/h, and **(c)** 360 km/h. also significant for the highest examined passing velocity, as illustrated in Figure 11c. For instance, the vibration peaks at the most dominant frequencies (\(f_{b,2},f_{b,2}\)) have been reduced from 2.2 mm/s and 2 mm/s to 0.8 mm/s and 0.9 mm/s, respectively. Comparison of Performance Indices  
In the sequence, the efficiency of the examined mitigation measure for each HST passing velocity is presented in terms of insertion loss (_IL_) curves [35; 36]. The _IL_ levels  
Figure 11: Fourier spectra at the pipeline top when protected with 50 cm thickness EPS layer for HST passage with (a) 240 km/h, (b) 300 km/h, and (c) 360 km/h. have been calculated for the center frequencies of the 1/3 octave bands between 1.25 Hz and 40 Hz according to the following expression [37]:  
\[IL=20\;log_{10}\frac{V_{rms,soil}}{V_{rms,mil}} \tag{4}\]  
where \(V_{rms,soil}\): soil cutting root mean square of the spectral velocity at each center frequency; \(V_{rms,mi}\): mitigated cutting root mean square of the spectral velocity at each center frequency. Figure 12 demonstrates the insertion loss (\(IL\)) of the examined mitigation measure in the three cases of HST velocities. \(IL\) has been computed at the center frequency of each one-third octave band, from 1.25 to 125 Hz, and the results were averaged to one-third octave bands. In the case of the implementation of an EPS-filled trench with 12.5 cm height, the \(IL\) remains at the same level for all the examined velocities in all octave bands with central frequencies lower than 31.5 Hz. More specifically, the insertion loss is close to 4.8 dB for these middle octave bands. At the higher octave bands, the insertion loss varies between extremely low or high values. In general, the use of an EPS layer with a 12.5 cm thickness slightly reduces the vibrations level at the top of the pipeline, yet this reduction is not satisfactory. Figure 12b illustrates the \(IL\) curves for the 25 cm EPS layer, where the insertion loss is increased compared to the previous case. Herein, the amplitude of insertion loss at the octave bands with a center frequency below 31.5 Hz is close to 6.7 dB for all the examined HST passing velocities. The insertion loss reaches its peak value of 12 dB at the 1/3 octave band with a center frequency of 40 Hz after implementing EPS19 when Thalys passes with  
Figure 12: Insertion loss curves at the pipeline top for EPS layer with thickness equal to (a) 12.5 cm (b) 25 cm, and (c) 50 cm. 360 km/h. Figure 12c shows the insertion loss curve for the thicker EPS layer of the present investigation. The insertion loss is increased in comparison with the cases of thinner EPS layers, i.e., \(IL\) ranges close to 7.3 dB for the octave bands with center frequencies lower than 31.5 Hz. Those values remain at the same level for all the examined frequencies. It should be mentioned that the insertion loss also varies for the higher \(1/3\) octave bands. In addition, a commonly used vibration index, i.e., the peak particle velocity (\(PPV\)), has been used to assess the efficiency of each EPS configuration.