## 1 Introduction  
In the case of building structures (buildings, bridges, retaining walls, masts, etc.) that transfer their loads to the ground via foundations, deformations of the subsoil must be taken into account. When designing foundations of any type, including isolated footings, strip wall footings, slabs, or piles, it is very important to prevent excessive settlements that could damage the structure or reduce its utility value. Nowadays, in the era of using technologically advanced software and computers, taking into account a number of factors that significantly affect the deformation of a structure in the calculation models is not a problem for a structural engineer [1, 2]. Nevertheless, the time needed to perform such calculations is often significantly extended (up to several or even a dozen or so hours). Therefore, a simplified structure scheme and a typical method of support are still often used for the structural and dynamic calculations of building structures. In engineering calculations, the support of a structure is often assumed in the form of fixed, hinged, or pinned supports, which allow for free movement along a specific direction or a specific surface. With such assumptions, the structure itself is treated as a deformable body, and the supports as being rigidly connected to a non-deformable medium. The adoption of such a simplified method of modeling any support of a structure can cause significant differences between the results obtained from structural calculations and the work of the actual structure. This, in turn, can have an impact on the uneconomical design of structures. A very often adopted model of elastic subsoil in engineering calculations is the Winkler model [3], in which it is assumed that the settlement w at any point in the ground is directly proportional to the pressure p applied at this point, i.e., \(p=K\cdot w\). The settlement of a given point only depends on the pressure applied at this point and is completely independent of the pressures acting in the vicinity. It is, therefore, a set of springs that are not connected to each other. The \(K\) coefficient is called the modulus of subgrade reaction. This is a so-called one-parameter model. In the literature, there are the so-called two-parameter models, which better describe the actual behavior of the soil under a foundation, i.e., they take into account soil deformations that often occur at a considerable distance from the acting loads. In these models, structural elements are introduced that connect single elastic bonds and ensure their mutual cooperation. Two-parameter models were proposed by, among others: [PERSON] [4], [PERSON] [5], [PERSON] [6], [PERSON] [7], and [PERSON] [8]. In the first three models, the additional structural elements include an incompressible layer subjected to shear, a shearing layer placed between two spring layers with different elasticity characteristics, a tensile tendon (for a one-dimensional problem), or a tensile membrane (for a two-dimensional problem). In the last two models, the cooperation of individual springs, which are connected to each other by additional springs that have different stiffness characteristics, was assumed. For many years, elastic half-space has been considered and adopted in the literature for calculations. In such a space, soil is treated as a continuous, homogeneous, and elastic body of infinitely large dimensions, which is limited on one side by a half-plane. In such a model, there is an assumption that the soil can be treated as an environment to which, under certain conditions, the formulas of the elasticity theory can be applied. According to this theory, the elastic properties of the soil are characterized by [PERSON]'s modulus of soil \(E\) and [PERSON]'s ratio \(\
u\). As studies have shown, this theory allows for a sufficiently accurate reflection of the actual state and can be applied to both cohesive and non-cohesive soils [9; 10; 11]. However, it is important to properly interpret and estimate soil parameters.