## 3 Numerical Models
### Foundations  
For comparative purposes, a finite element (FE) model of the pile embedded in sand was built. Midas GTS NX 2023 software was used. A general view of the numerical model of the soil and tubular pile is shown in Figure 8. Due to symmetry of the geometry, only 1% of the structure was modelled. The plane of symmetry was defined relative to the XZ axis. The soil was represented by 3D solid elements; the pile tube was discretised by 2D shell elements; and to simulate the pole, 1D beam elements were used. A view of the adopted FE mesh is shown in Figure 9. The FEM model took into account the contact zone at the junction of the soil and the pile by separating the nodes in this area. The analysis was carried out in stages. The first stage involved determining the stresses in the soil medium in situ. In this phase, the separated nodes were connected with rigid elements (Figure 9d) to form a continuum. In the following phases, the possibility of separation in the contact zone was considered and special contact elements were implemented between the shell elements representing the pile (Figure 9e). The model consists of 27,443 second-order (parabolic) elements and 76,052 nodes. The adopted boundary conditions (constraints as well as load) are shown in Figure 10.  
Figure 8: Shape of the foundation FE model.  
Figure 9: View of the FE mesh: (**a**) general view, (**b**) rigid link between the shell and beam elements, (**c**) soil–structure interaction, (**d**) rigid elements between the soil elements in the in situ stage, (**e**) interface elements between the soil and shell elements in the final stage.  
Soil made of moderately compacted sands was selected for the field tests. The piles were planned mainly for installation in non-cohesive soils. In the case of subsoils other than non-cohesive soils, in practice, the peripheral replacement of backfill soils, also designed from sands, is used. The material parameters of the soil were checked according to the EN 1997-2 [21] standard. Field tests of the soil were made using CPTU sonde. Laboratory samples of the soils included sand density, moisture, and mechanical parameter tests in a direct shear apparatus. In numerical calculations, for soil (MSa), the Coulomb-Mohr material model was used, and the following geotechnical parameters were adopted: elastic modulus \(E=25\) MPa, Poisson's ratio \(\mu=0.3\), unit weight \(\gamma=17\)\(\mathrm{kN}/\mathrm{m}^{3}\), friction angle \(\varphi=32^{\circ}\), cohesion \(c=1\) kPa, and dilatancy angle \(\theta=2^{\circ}\). The values of parameters were obtained from field and laboratory tests of the soil.  
For the GFRP tubes, an elastic material model was used with effective parameters: elastic modulus \(E=7\) GPa, Poisson's ratio \(\mu=0.45\), and unit weight \(\gamma=20\)\(\mathrm{kN}/\mathrm{m}^{3}\). The effective parameters were estimated from laboratory tests as the equivalent property of the orthotropic GFRP material. For the steel pole and the steel adapter, which connects the pole and the pile, an elastic material model was used, with nominal values defined in the EN 1993-1-1 standard [22]: elastic modulus \(E=210\) MPa, Poisson's ratio \(\mu=0.3\), and unit weight \(\gamma=78.5\)\(\mathrm{kN}/\mathrm{m}^{3}\). A nonlinear elastic-plastic analysis (MNA) with the contact properties (both side of the GFRP tube interface) was performed.