## 4 Results and Discussions
### Ultimate Bearing Capacity (UBC) Variability in Hybrid Composite Pile Foundation Systems  
Table 6 presents comprehensive mechanical and physical parameters of sand across varying relative densities, while Table 2 details three pile materials (steel, concrete, and timber) used in the foundation system. These are essential for numerical simulation of hybrid pile behavior. The characterization ranges from very loose to very dense conditions, providing a robust computational modeling framework. The Mohr-Coulomb material model  
Figure 8: Mechanical behavior and load transfer mechanisms of hybrid composite piles across different soil densification states: (**a**) Case Study I Q\({}_{\text{b}}\)/Q\({}_{\text{alt}}\) (%), (**b**) Case Study I Q\({}_{\text{s}}\)/Q\({}_{\text{alt}}\) (%), (**c**) Case Study II Q\({}_{\text{b}}\)/Q\({}_{\text{alt}}\) (%), and (**d**) Case Study II Q\({}_{\text{s}}\)/Q\({}_{\text{alt}}\) (%). is consistently applied across all density states, appropriately capturing the elastoplastic stress-strain behavior of sand under typical pile foundation loading conditions. Drained conditions are specified for all density states, reflecting sandy soils' typical rapid pore water pressure dissipation during loading. A constant Poisson's ratio of 0.3 is maintained throughout, representing typical sandy soil lateral deformation characteristics. The modulus of elasticity increases substantially with relative density, ranging from 12,000 kN/m\({}^{2}\) in very loose sand to 70,100 kN/m\({}^{2}\) in very dense sand, highlighting the importance of accurate soil stiffness characterization in hybrid pile numerical simulations. The unit weight parameters show notable trends: dry unit weight increases with relative density while saturated unit weight remains constant at 22.60 kN/m\({}^{3}\). This relationship is particularly relevant for effective stress and pile capacity calculations under varying groundwater conditions. The study emphasizes key outcomes of PLAXIS 3D simulations (e.g., total displacement patterns, UBC validation); detailed mesh parameters were streamlined to focus on soil-structure interaction trends. The finite element model employed 15-node tetrahedral elements with adaptive mesh refinement, achieving convergence at a global tolerance of 0.1%. Mesh sensitivity studies confirmed stable results (\(\pm\)2.1% variation in UBC) across three refinement levels (coarse: 12,500 elements; medium: 34,000 elements; fine: 68,500 elements). These details can be further expanded, including displacement contours and stress distributions across mesh configurations. The research's prioritization of analytical comparisons aligns with its goal of balancing technical depth with readability for engineering practitioners. The friction angle increases progressively from 28\({}^{\circ}\) to 40\({}^{\circ}\) with increasing relative density, while the dilatancy angle shows a more dramatic range from 0\({}^{\circ}\) to 20\({}^{\circ}\)--significantly influencing the shear strength behavior and volume change characteristics in the numerical model. Cohesion values increase slightly with relative density (0 to 0.706 kN/m\({}^{2}\)), and the constant interaction factor (R\({}_{\text{int}}\)) of 0.8 across all density states indicates consistent pile-soil interface behavior. These parameters enable the comprehensive numerical simulation of hybrid pile behavior, facilitating the detailed analysis of load transfer mechanisms and foundation performance across various soil conditions. The finite element analysis (Plaxis 3D) results shown in Figures 9a-e and 10a-e illustrate the total displacement patterns of hybrid steel-concrete and timber-concrete composite piles under varying relative soil density conditions. Maximum displacements primarily occur at pile heads, reaching approximately 1.35 \(\times\) 10\({}^{-3}\) m (steel-concrete) and 1.55 \(\times\) 10\({}^{-3}\) m (timber-concrete) in the lowest-density conditions.