# Protection of Buried Pipelines from High-Speed Train Vibrations with Expanded Polystyrene Geofoam
## 3 Results
### Impact of Pipeline Material and Geometry  
Previous results have clearly presented the beneficial role of the implementation of EPS gefoam in the reduction in vibration levels on the pipe surface. This reduction can significantly reduce damage probability during the life-cycle of such important infrastructure, which is even more crucial in the case of gas pipelines. Apart from the induced vibrations, it is important to investigate the effect of the HST dynamic loads on the distress of the pipeline in terms of its potential ovalization, i.e., diameter change. As mentioned, the level of the diameter change is crucial for the integrity and safe operation of the pipelines. The pipeline examined in the previous section is quite thick and stiff (e.g., 12.7 mm); hence, its diameter change is marginal, as illustrated in Figure 15. It is evident that the vertical  
Figure 13: Relationship between \(PPV\) levels at the pipeline top and the increasing passing velocity for various EPS layer heights. diameter change in the unprotected pipeline is equal to 0.3 mm at the passage of each HST bogie (see Figure 15a). This value is reduced below 0.2 mm after the implementation of an EPS19 layer with a thickness of 50 mm. As presented in Figure 15b, the same observation can be made regarding the horizontal diameter change. Furthermore, the vertical and horizontal residual deformations after HST passage are almost zero. For this reason, it can be assumed that the shape of the pipe is not altered regardless of the EPS application. Nevertheless, pipelines with a lower thickness, other material, and and/or smaller burial depths are more prone to significant deformations. For this reason, a HDPE100 (i.e., from the same material that has been used for the initial validation in Section 2.1) pipe with a diameter of 250 mm and thickness of 3 mm has been placed at a 0.5 m depth under the HSR line to investigate its deformations due to the passage of HST Thabs, as has been previously presented for the steel pipe. Analogously, the HDPE100 pipeline has also been protected with a 25 cm EPS layer. In order to investigate the effect of pipe thickness on the response of the HDPE100 pipeline, a similar pipe with an increased thickness (9 mm) has also been examined. Figure 16 displays the impact of HST passage on the diameter change in the polyethylene pipelines with the same diameter and thickness equal to 3 mm or 9 mm. As expected, the diameter change in the pipeline is significantly higher compared to the previously examined larger and stiffer steel pipe. At the first HST axle passage, the vertical diameter change in the unprotected pipe with 3 mm thickness is equal to 1.6 mm. The deformation gradually increased, reaching the maximum value of 7 mm at the passage of the last boogie. Figure 14: Relationship between \(PPV\) levels at the pipeline top and the increasing distance from the rail axis. Figure 15: Impact of EPS on large steel pipe (with diameter \(D\) = 914 mm) diameter change: (**a**) vertical and (**b**) horizontal directions. Furthermore, the peak deformation oscillation width is close to 6 mm, while a vertical residual deflection equal to 0.8 mm is observed after HST passage. Evidently, the EPS layer has a beneficial impact on the reduction in the pipe diameter change, as it has reduced the peak vertical deformation from 7 mm to 3 mm, while the oscillation width is drastically minimized to 1 mm. As shown in Figure 16b, similar observations for the effectiveness of the EPS mitigation measure can be made for the horizontal diameter change. The horizontal residual deformation is significantly higher than the vertical, exceeding 2 mm for the unprotected pipe, whereas the application of the EPS layer reduces it to approximately 1 mm. Figure 16c,d compare the response of a thicker polyethylene pipe before and after adding the EPS layer. As expected, the increase in the pipeline thickness reduces the pipe vertical and horizontal deformations to below 3 mm, whereas the residual deformation at both directions is equal to 1.3 mm.