## 4 Conclusions  
1. The interaction of a pile with a soil mass is complex and multifactorial, which is reflected in the graph-analytical method. At the same time, the normative methods of calculation do not fully reflect the actual operation of the pile and the processes occurring in the soil when loads are transferred to them, as well as changes in the properties of the contact zone soils. In addition, piles are designed at the initial stage of non-linear soil behaviour, which leads to underutilisation of the bearing capacity of the pile. The combination of these factors leads to higher construction costs and increased complexity of construction and installation work due to the increased length and diameter of the pile. 2. Laboratory tests on the schemes \"soil-soil\" and \"soil-concrete\" on the direct shear device showed that the strength of soils in contact with the concrete plate is lower than the strength of the same soil in its natural mass. To the greatest extent, the reduction in strength of the soils of the contact zone is influenced by the technology of construction of structures in soil mass, the type of soil, and the roughness of the solid material. According to the results of the performed laboratory tests, the strength reduction factor at the contact point with concrete was equal to 0.53 for clays and 0.44 for loans. 3. In the paper, an improved graph-analytical method of calculating a single pile settlement is proposed to utilise the non-linear behaviour of soil on the lateral surface and under the tip of the pile, the possibility of its detachment and slippage after reaching the ultimate strength of the soil, the change in the properties of the contact zone soils, and the load distribution on the pile between its lateral surface and the tip. 4. A comparison of the graphs of the dependence of settlement on load obtained using the graph-analytical and numerical methods showed good convergence of the results. The maximum discrepancy of the settlement values was 12.9%, which does not exceed  
Figure 14: Graphs of settlement versus load of a single pile: (**a**) without using the strength reduction factors; (**b**) using the strength reduction factors. In this paper the interaction of the pile with three layers of soil has been considered; however, it is possible to increase the number of layers if necessary. Then, with each new layer, a new term in Equation (7) will be added and a new equation containing the unknown will be added to the system of Equation (6). Since the form of the added equation does not change except for the shear stress and the length of the pile section in contact with the new soil layer, increasing the number of layers does not cause difficulty in solving the equations. Since increasing the number of layers increases the number of unknowns and the number of equations, in this paper, the soil mass was limited to three layers to reduce the number of calculations. the engineering accuracy limit of 15%, indicating that this method can be used for calculations. In addition, a similar characteristic of deformation of the graphs is observed, and pile failure occurs at the same load value--2600 kN. 5. Verification of the proposed graph-analytical method with the results of static pile testing showed that without the use of the strength reduction factors that reduce the strength of the contact zone soils, the graphs have a similar deformation character, but the calculated settlement values are less than the actual ones. The use of the strength reduction factors of 0.9 for loans and 1.0 for sands brought the calculated settlement values obtained by the graph-analytical method closer to the actual values. This indicates that these factors should be taken into account in the calculations. 6. For a more accurate prediction of the settlement of a single pile calculated using the graph-analytical method, it is recommended to determine the strength reduction factors experimentally, either with laboratory tests or static tests of pile analogues, in similar engineering-geological conditions.