## 4 Discussion
Based on Figure 8, it can be observed that the spring constant \(K_{x}\) increases with the increasing values of the soil's shear modulus \(G\) and the foundation area \(A\) while keeping Poisson's ratio and the coefficient \(\alpha\) constant. Based on Figure 9, it can be observed that the spring constant \(K_{x}\) increases with increasing values of the coefficient \(\alpha\) and the foundation area \(A\) while keeping the soil's shear modulus \(G\) and Poisson's ratio constant \(\
u\). Furthermore, the influence of the foundation area \(A\) is significantly greaterthan the influence of the coefficient \(\alpha\). Whereas based on Figure 10, it can be observed that the spring constant \(K_{x}\) increases with increasing values of the soil's shear modulus \(G\) and Poisson's ratio \(\
u\) while keeping the coefficient \(\alpha\) and the foundation area \(A\) constant. Furthermore, the influence of the soil's shear modulus \(G\) is significantly greater than the influence of Poisson's ratio \(\
u\). The study also furnishes valuable nomograms (presented in Figures 11-13) that facilitate the direct reading of the spring constant \(K_{x}\). These nomograms utilize common soil parameters, namely the shear modulus \(G\) and Poisson's ratio \(\
u\), along with foundation characteristics such as area \(A\) and the aspect ratio \(\alpha=\frac{\alpha}{b}\) for rectangular foundations. As such, they can serve as a useful resource for engineers seeking rapid preliminary estimations of \(K_{x}\) in their analyses. The values of the spring constant \(K_{x}\) can be calculated directly from the derived Formulas (8) and (9), or can be easily read from the nomograms (Figure 11) determined in the previous chapter. For example, for the surface area of a rectangular foundation \(A=5\) m\({}^{2}\), the side ratio \(\alpha=\frac{\alpha}{b}=5\), and soil parameters \(\
u=0.1\) and \(G=80\) MN/m\({}^{2}\), the value of the spring constant calculated from Formulas (8) and (9) is \(K_{x}=453.018\) MN/m. In turn, the value of the spring constant calculated for the coefficient \(\beta_{x}\), given in paper [10; 11; 13; 14; 16] (i.e., at a constant value of \(\
u=0.3\)), is \(K_{x}=411.085\) MN/m. Therefore, the error resulting from the application of the solution given in [10; 11; 13; 14; 16] in relation to the formulas given in this paper is (\(453.018-411.085\))/\(411.085=10.20\%\). In turn, with similar parameters as given above, but for the side ratio \(\alpha=\frac{\alpha}{b}=10\), the value of the spring constant \(K_{x}\) was, in the first case--\(K_{x}=517.834\) MN/m, and in the second case--\(K_{x}=464.348\) MN/m. Therefore, the error was already \(11.52\%\). In another example, for the surface area of a rectangular foundation \(A=5\) m\({}^{2}\), the side ratio \(\alpha=\frac{\alpha}{b}=5\), and soil parameters \(\
u=0.5\) and \(G=20\) MN/m\({}^{2}\), the value of the spring constant calculated from Formulas (8) and (9) is \(K_{x}=130.940\) MN/m. In turn, the value of the spring constant calculated for the spring coefficient \(\beta_{x}\) given in papers [10; 11; 13; 14; 16] (i.e., for a constant value of \(\
u=0.3\)) is equal to \(K_{x}=140.142\) MN/m. Therefore, the error resulting from the application of the solution given in papers [10; 11; 13; 14; 16] is equal to (\(130.940-140.142\))/\(140.142=-6.57\%\). However, with similar parameters as given above, but for the side ratio \(\alpha=10\), the value of the spring constant \(K_{x}\) will be in the first case \(K_{x}=145.91\) MN/m and in the second case \(K_{x}=158.30\) MN/m. Therefore, the error amounts to \(-7.83\%\). The stiffness of the subsoil in the horizontal direction has a significant impact on the horizontal displacements of the entire structure or its elements, especially in the case of structures founded on flexible soils such as soft clays or beats. With the increase in the stiffness of the subsoil, the structure encounters greater resistance from the ground during horizontal displacements, which results in smaller lateral displacements.