## 4 Results and Discussions
### Ultimate Bearing Capacity (UBC) Variability in Hybrid Composite Pile Foundation Systems
Displacement magnitude progressively decreases as soil relative density increases, with displacement distribution evolving from concentrated deformation at pile heads in looser soils to a more distributed displacement along pile shafts in denser conditions. The timber-concrete system exhibits larger maximum displacements than its steel-concrete counterpart under identical conditions, attributable to timber's lower elastic modulus (1.22 \(\times\) 10\({}^{7}\) kN/m\({}^{2}\) versus 2.01 \(\times\) 10\({}^{8}\) kN/m\({}^{2}\) for steel). Increasing soil relative density from loose to dense conditions reduces maximum pile displacement by 40-50% in both systems, though this effect is more pronounced in the timber-concrete configuration. The steel-concrete composite consistently outperforms its timber counterpart, exhibiting 15-25% lower total displacements across all density scenarios despite the different foundation systems. These simulations effectively capture soil-structural interaction mechanisms, demonstrating the design's optimization potential when composite pile systems are appropriately matched to site-specific conditions. Figures 11a-e and 12a-e reveal intricate performance characteristics across different computational methodologies and soil density conditions for hybrid steel-concrete and timber-concrete composite piles. The results demonstrate substantial variability in load-bearing capacities, with significant divergences observed between analytical methods. For the hybrid steel-concrete composite pile, the ultimate bearing capacity exhibits a pronounced scaling effect with the increasing relative density. At very loose soil conditions (10% Dr), the ultimate bearing capacity ranges from 353.1 kN (Vesic method) to 2287.8 kN ([PERSON] method), representing a remarkable threefold to sixfold variation. As soil density increases to very dense (95% Dr), this methodological disparity becomes even more pronounced, with capacities ranging from 7474 kN (Brom method) to 14,379 kN (Vesic method). The finite element method (FEM) using PLAXIS 3D software provides additional insights, demonstrating remarkable alignment with the Vesic method at very dense conditions. At 95% Dr, the PLAXIS simulation yields 14,202 kN, which is remarkably close to the  
Figure 9: Total displacement contours of hybrid steel–concrete composite pile under varying soil relative densities—(**a**) very loose, (**b**) loose, (**c**) medium-density, (**d**) dense, and (**e**) very dense sand conditions—illustrating progressive reduction in maximum displacement with increasing soil compaction. Vesic method's result of 14,379 kN, suggesting the computational validation of theoretical predictions. The hybrid timber-concrete composite pile exhibits similar methodological variations, but with less extreme magnitudes. In very loose soil conditions, ultimate bearing capacities range from 244.1 kN (Vesic method) to 1593.5 kN ([PERSON] method). The progression to very dense conditions reveals capacities spanning from 6149.8 kN (Berezantsev method) to 9537.5 kN ([PERSON] method). Figure 10: Total displacement contours of hybrid timber–concrete composite pile under varying soil relative densities—(**a**) very loose, (**b**) loose, (**c**) medium-density, (**d**) dense, and (**e**) very dense sand conditions—demonstrating influence of soil density on displacement magnitude and distribution. Different analytical methods (Coyle and Castello, [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], Meyerhof, and FEM) yield varying results, highlighting the complexity of geotechnical bearing capacity predictions while consistently demonstrating the steel-concrete composite's enhanced load-bearing characteristics, particularly in dense and very dense soil conditions. Material composition, interface characteristics, and soil density critically influence the ultimate bearing capacity of hybrid composite piles, with the steel-concrete variant consistently outperforming its timber-concrete counterpart due to superior material properties and structural integrity.