## 2 Materials and Methods
### Numerical Modeling  
The problem was modeled in PLAXIS 2D, (Version 8.2) using the axisymmetric mode, which is suitable for rotationally symmetric structures such as conical foundations subjected to vertical loading (Figure 8). This approach reduced the problem to a 2D slice (a radial cross-section), while still capturing the full 3D behavior, due to symmetry. For axially loaded conical foundations, the main stress and displacement fields are also symmetric about the vertical axis. Thus, a two-dimensional axisymmetric modeling was chosen, which accurately reproduced the soil-structure interaction, settlement, and failure modes. Figure 8: _Cont._  
The geometry was defined based on the dimensions of the reduced-scale foundation, including the cone height, base diameter, and embedment depth in the soil. Numerical modeling was carried out for laboratory tests of a cone-top pile model, as well as an isolated shallow foundation. Loading was also simulated under 3, 6 and 9 mm/m horizontal soil displacement in the expandable box, as well as in the absence of horizontal soil deformations (Figures 9-11). The horizontal displacement of soils simulated a tension zone with the possible formation of cracks in it, and was achieved by displacement of the sections in the extendable stand to the above-mentioned values. Figure 8: Numerical modeling of the conical foundation without horizontal displacement of the soil: (**a**) setting initial loading parameters; (**b**) deformed mesh; (**c**) displacement vectors in mm; (**d**) shear strains in %; (**e**) Total displacement in mm; (**f**) horizontal displacement in mm. Figure 9: _Cont._  
The soil domain was defined as large enough to minimize boundary effects, typically extending by 4-5 times the cone diameter in all directions, from the edge of the foundation. Vertical boundaries were fixed in the horizontal direction (roller boundaries) for zero horizontal displacement simulation, and with the possibility of subsequent movement of the right border to simulate soil deformation, while the bottom boundary was fully fixed in both directions, to simulate realistic soil confinement. Figure 9: Numerical modeling of the conical foundation with 3 mm/m horizontal displacement of the soil: (**a**) deformed mesh; (**b**) displacement vectors in mm; (**c**) horizontal displacement in mm; (**d**) vertical displacement in mm; (**e**) total displacement in mm; (**f**) shear strains in %. The soil was modeled using the Mohr-Coulomb model, appropriate for initial static loading conditions. The conical foundation was modeled as a non-porous, linear elastic volume, or as a rigid body, depending on the stiffness assumption. Material properties were defined using the appropriate Young's modulus and Poisson's ratio. The mesh was generated using 15-node triangular elements, for higher accuracy. Local mesh refinement was applied in the vicinity of the cone-soil interface, especially around the tip and base edges, to capture stress concentration zones. Global mesh was set to medium or fine, depending on the convergence requirements. Static loading was applied vertically at the top of the foundation, and incrementally, using phased construction stages, to simulate realistic loading behavior. The simulation  
Figure 10: Numerical modeling of the conical foundation with 6 mm/m horizontal displacement of the soil: (**a**) horizontal displacement in mm; (**b**) vertical displacement in mm; (**c**) total displacement in mm; (**d**) shear strains in %. results included settlement, vertical stress distribution, and plastic strain development in the surrounding soil. Contour plots and load-settlement curves were extracted to analyze the bearing behavior and validate against experimental results. For isolated shallow (columnar) foundations, two static loading conditions were considered: without horizontal soil displacement and with horizontal displacement of the soil (\(\epsilon\)= 3 mm). Simulation with greater horizontal soil displacement resulted in loss of bearing capacity of the foundation.