## 3 Results and Discussion
Exhaustion of the bearing capacity of the soil occurs in two sections: in the upper layer of the soil (\(\Delta T_{31}\)), with a length of 3.05 m, and in the middle layer of soil (\(\Delta T_{21}\)), with a length of 1.97 m. The total excess load \(N_{add}\) is distributed between the pile tip and the sections of the lateral surface of the pile where there is a reserve of bearing capacity. According to the results of the analytical solution, the share of load on the tip of the pile is 0.13 and, on the lateral surface, 0.87, which agrees with the data from experimental studies of piles. At the same time, in the top layer of the soil (EGE-3), the load share is 0.29; in the middle weak layer (EGE-2), 0.23; and in the bottom layer (EGE-1), 0.35, i.e., the lower the soil stiffness, the less load falls on this section. According to the results of the calculations, the graph-analytical and numerical methods were used to construct the graphs of the dependence of settlement on load with the non-linear properties of soils, and the graph of the dependence of settlement on load, obtained via the analytical method and using Formula (7) in the linear formulation. The obtained results are presented in Figure 13 and show good convergence. The maximum difference in settlement values was 12.9%, which does not exceed the engineering ac  
Figure 11: Nature of occurrence and growth of plastic points at soil–pile contact. Figure 12: Calculation scheme of the problem solution using the graph-analytical method at load 2200 kN (red colour shows the contours of the ultimate shear stress diagram, yellow colour shows the contours of the mobilised shear stress diagrams). curacy limit of 15%. In addition, there is a similar characteristic of deformation in the load-deposition graphs, and pile failure occurs at the same value for pile load--2600 kN. However, any proposed problem-solving method should be verified with field pile tests to evaluate the accuracy of the proposed method. Verification of the graph-analytical method was performed based on the results of static pile tests at a construction site. A 20 m long pile with a diameter of 1.2 m was buried in a multilayer foundation represented by dusty sands and loans of different consistencies. The maximum load on the pile was 9600 kN, and the settlement of the pile was 290 mm, i.e., the test was carried out until loss of bearing capacity of the pile. Figure 14 shows the graphs of the dependence of settlement on load for a single pile constructed using the graph-analytical and numerical methods, as well as based on the results of the static test of the pile. Figure 14a shows the results of calculations without the use of friction coefficients at the pile-soil contact point. The deformation characteristic of the curve obtained via the graph-analytical method is similar to the real curve, but the values are smaller than those obtained from the results of the static test of the pile. The numerical calculation showed that at the initial section of deformation, the curve is close to the graph-analytical curve, but after reaching the ultimate load, it quickly goes to failure. To approximate the results of the calculations to the real deformation curve, friction coefficients were taken into account in the graph-analytical and numerical calculations: for sands, the coefficient was taken equal to 1.0; for loans, 0.9. The results presented in Figure 14b show that when friction coefficients are taken into account, the graph-analytical curve approaches the real deformation curve. Thus, based on laboratory tests of soils or field tests of piles, it is possible to obtain values of friction coefficients close to the real ones and relevant to the given conditions of the construction site, which will allow for a more accurate description of the pile deformations under load. In numerical modelling, the use of special interface elements and a reduction in soil strength at the contact point does not always lead to positive results.