# Protection of Buried Pipelines from High-Speed Train Vibrations with Expanded Polystyrene Geofoam
## 2 Materials and Methods  
Validation of Numerical Methodology with Experimental Data for Polyethylene Pipelines and Road Moving Loads  
As aforementioned, there are not any relevant bibliographic references with experimental data or in situ measurements investigating the distress of buried pipelines due to HST-induced vibrations. Nevertheless, there exist few experimental tests simulating the response of buried pipes due to traffic loads [19; 24]. [PERSON] et al. [19] used a full-scale model to simulate the repeated loading of heavy traffic. More specifically, 14 tests were carried out using a high-density polyethylene pipe (HDPE 100) within unreinforced and reinforced soil with EPS geofoam blocks and geocells. The model was constructed on a test pit with a floor plan of 2.2 m \(\times\) 2.2 m and a depth of 1 m. Furthermore, the test trench had dimensions of 0.75 m \(\times\) 0.75 m and a 1.75 m depth. A circular plate repeatedly loaded/unloaded the test trench, aiming to simulate the traffic loads. The loading plate had a diameter of 250 mm; hence, a pressure equal to 800 kPa was applied in order to simulate the half axle of a heavy vehicle, while 150 loading cycles were imposed. [PERSON] et al. [24] presented a similar full-scale model. The floor plan of the test pit was slightly smaller in this case, although the same pipe and a similar soil were used. Compared to the first test, a gradually increasing load had been placed on the plate in this case (instead of repeated traffic loads). More specifically, the load was increased linearly from 0 kPa to 800 kPa in 5 s.  
In the present study, these two experimental investigations were used to validate a preliminary numerical model capable of accurately representing traffic loads. The material properties and dimensions of the tests have been simulated utilizing the commercial finite element (FE) software ABAQUS 6.14 [25] to provide a numerical model capable of predicting the response of a buried pipe when exposed to traffic-induced vibrations. Hexahedral linear elements with a reduced integration formulation (C3D8R), with size 50 mm, have been used to simulate the backfill trench and native soil. The pipeline has been modeled with linear four-node shell elements (S4R). Furthermore, the interaction between the loading plate and the soil surface has been assumed to be frictionless and \"hard contact\" conditions along the normal and tangential directions. Figure 1 illustrates the geometry of the employed FE model. Initially, in the first analysis step, geostatic stress was imposed in the model. In the next step, pressure was applied on the rigid circular plate at the soil surface. In the sequence, pressure on the loading plate was applied in the second step to replicate the load pattern of the two pressure plate tests. More specifically, in order to simulate the repeated loading cycles of the model of [PERSON] et al. [19], a pressure equal to 800 kPa was applied 150 times on the pressure plate with a frequency of 0.33 Hz. In the second loading scenario, the pressure gradually increased from 0 kPa to 800 kPa, aiming to replicate the load of [PERSON] et al. 's [24] experimental setup. Analysis was conducted based on the explicit dynamic module of ABAQUS, as it can achieve more accurate results in such dynamic problems with moving loads compared to the implicit dynamic module. The mechanical properties of the HDPE100 pipe in both models were adopted from the study of [PERSON] et al. [24]. The pipeline material has a density, [PERSON]'s modulus, and Poisson's ratio equal to 560 kg/m\({}^{3}\), 1000 MPa, and 0.45, respectively. The soil plastic behavior was simulated using the Mohr-Coulomb model. The internal friction angle and the cohesion of the soil were set equal to 59.86\({}^{\circ}\) and 0.1 kPa, respectively, while the density of the soil Young's modulus and Poisson's ratio are equal to 2062 kg/m\({}^{3}\), 45 MPa, and 0.3,  
Figure 1: Three-dimensional FE model used for validation. respectively. For validation with [PERSON] et al.