## 1 Introduction
The conducted studies and the accumulated practical experience have shown that the change in mechanical properties of soils at the contact point occurs under the influence of the technology of pile construction, which is called the \"installation effect\" [21; 22]; under the influence of pile installation technology [21; 22]; and under the influence of friction reduction at the contact point. Numerous results of laboratory shear tests of soils on solid materials such as concrete, metal, and polymer  
Figure 1: Pile distribution diagrams: (**a**) axial forces; (**b**) shear stresses when the load is applied to the pile: 1—100 kN, 2—200 kN, 3—400 kN, 4—600 kN, 5—800 kN, 6—900 kN, 7—1000 kN, 8—100 kN [13]. confirm the fact of that the strength of soils reduces when interacting with foundations of buildings and other elements of structures erected in soil mass [23; 24; 25; 26]. The reduction in strength of the contact zone soil is influenced by the type of soil, the roughness of the material, moisture, and density; however, the greatest influence is exerted by the relative roughness \(R_{n}\), as evidenced by its large number of laboratory studies [27; 28]. However, the proposed analytical calculation methods do not allow for taking into account the change in the mechanical characteristics of soils at the contact point. Recently, interface models designed to describe the behaviour of the soil layer involved with a structure have become very popular and can be implemented in various design software packages. As a rule, these models are based on laboratory shear tests of soil on the material and, depending on the number of input parameters, can predict the behaviour of the soil at the contact point with varying degrees of accuracy. For example, [PERSON] and [PERSON] [29] proposed a simple interface model to describe the behaviour of sandy soils based on the Mohr-Coulomb strength criterion. [PERSON] and [PERSON] [30; 31] proposed a contact interface model with 10 input parameters based on the performed shear tests of sandy soils over different materials. The plots of shear stresses versus shear strains obtained numerically using the proposed model agreed well with the results of laboratory tests. A similar model was proposed by [PERSON] et al. [32], which was extended to unify the interface behaviour with different roughness, and also, [PERSON], [PERSON], and [PERSON] [33; 34] proposed a model with 10 input parameters that takes into account density, roughness, and de-strengthening at the contact point but was not designed to describe the behaviour of water-saturated and clayey soils. Due to the fact that in reality, soil properties are random, some authors have presented a different approach to pile design, taking into account reliability calculations, in order to design the most economical structure. By analysing a number of parameters such as the pile diameter, spacing and location, and their degree of influence on slope reinforcement with piles, the authors in [35] proposed an approach using the multi-objective optimisation (MOO) design system, which allows for choosing the most optimal solution for these parameters to reduce the involved construction cost while retaining the same reliability level. Similar studies on calculating the stability of slopes taking into account the soil spatial variability were also carried out by other authors [36; 37]. Thus, the interaction between the pile and the soil mass is complex and multifactorial. At the same time, the existing calculation methods do not fully reflect the actual operation of the pile and the processes occurring in the soil when loads are transferred to them. In addition, piles are designed in the elastic stage of the soil, which leads to underutilisation of the bearing capacity of the pile. The combination of these factors leads to increased construction costs and increased complexity of construction and installation work due to the increase in the length and diameter of the pile, and the need for more powerful pile driving equipment.