# Protection of Buried Pipelines from High-Speed Train Vibrations with Expanded Polystyrene Geofoam
## 3 Results
### Impact of EPS Layer Thickness on Pipeline Protection  
Case 1: EPS layer with 12.5 cm height  
In the first scenario, an EPS layer with a 12.5 cm thickness is implemented above the buried pipeline to reduce HST-induced vibrations. Figure 9 compares the Fourier spectra on the pipeline top before and after the implementation of the EPS blocks in the scenario of HST passage with 240 km/h. The beneficial role of the EPS layer is clearly illustrated, as all the dominant vibration peaks from 0 Hz to 100 Hz have been significantly reduced. For instance, the most dominant peak at 46.4 Hz has been reduced from 1.9 mm/s to 1.2 mm/s. Furthermore, the peaks at other dominant frequencies (e.g., 3.5 Hz, 7.2 Hz, 49.9 Hz) have a reduction equal to 40%. In the sequence, the effectiveness of the examined EPS layers has been investigated at the passage of Thalys with its typical operational velocity, 300 km/h. As presented in Figure 9, the high level of vibration peaks reduction is more evident in the lower frequency range (0-30 Hz). The proposed mitigation measure also plays a beneficial role at higher frequencies (>75 Hz). On the other hand, the examined mitigation measure is not effective at medium frequencies between 30 Hz and 75 Hz. Within this range, the most dominant frequency is located at 58 Hz, for which the EPS implementation slightly reduces the peak from 2.1 mm/s to 2 mm/s. Lastly, as shown in Figure 9, the same trend is evident for the high passing velocity modeling scenario (360 km/h). A high reduction in all the vibration peaks at the low- and high-frequency range can also be observed. In this case, the most dominant frequencies are located at low frequencies (e.g., 5.4 Hz, 10.7 Hz, 26.5 Hz, 31.9 Hz), and the peaks of those frequencies have a reduction of over 40% compared to the unprotected pipe. Case 2: EPS layer with 25 cm height  
According to the previous results, the implementation of EPS blocks between the track and the buried pipeline successfully reduces HST-induced vibrations. Nevertheless, since the reduction in the vibrations level is relatively low, the implementation of a thicker layer of EPS is investigated in this section. More specifically, the thickness has been doubled; thus, the impact of an EPS layer with a thickness of 25 cm has been examined. As was expected, the vibration peaks remain at the same frequencies as previously, while the amplitude of the vibrations is substantially lower. For instance, in the case of an HST running with 240 km/h, the dominant peak at 46 Hz is reduced to 0.8 mm/s, 50% lower than 1.2 mm/s the layer with a height of 12.5 cm (see Figure 10). The same observation can be made for \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Velocity** & \(f_{b,1}\) & \(f_{b,2}\) & \(f_{b,3}\) & \(f_{b,4}\) & \(f_{b,5}\) & \(f_{a}\) & \(f_{s}\) \\ (km/h) & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** \\ \hline
240 & 4 & 7 & 11 & 14 & 18 & 20 & 111 \\ \hline
300 & 4 & 9 & 13 & 18 & 22 & 25 & 139 \\ \hline
360 & 5 & 11 & 16 & 21 & 27 & 30 & 167 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dominant frequencies for the examined HST velocities. all dominant frequencies, with amplitude reduction of up to 50%. Figure 10b illustrates the Fourier spectra for HST passage with 300 km/h. The peak vibrations level is reduced to 1.5 mm/s at 58 Hz. Furthermore, it should be mentioned that all the other vibration peaks are kept under 1 mm/s. The reduction in the vibrations level is also remarkable when the HST runs at high velocity (360 km/h) as all vibration peaks have been successfully reduced under 1 mm/s (see Figure 10c). It should be mentioned that vibration peaks at the high-frequency range are almost zero after implementing EPS blocks with 25 cm height. Figure 9: Fourier spectra at the pipeline top when protected with 12.5 cm thickness EPS layer for HST passage with (**a**) 240 km/h, (**b**) 300 km/h, and (**c**) 360 km/h.