## 4 Influence of Subsoil and Building Material Properties on the Natural Frequencies of Building  
The nature of the SSI phenomenon depends mainly on the properties of the subsoil and the properties of the building structure. Natural frequencies of buildings, especially fundamental natural frequencies, are the parameters that allow you to simply identify one of the most important characteristics of the structure--building stiffness. The above proposed 3D FEM models were used for the numerical evaluation of the influence of both subsoil and building material properties on the natural frequencies of typical low-rise buildings with load-bearing walls. The fundamental natural frequencies of masonry (with brick walls) building vibrations depending on the dynamic parameter Cz describing the material of subsoil (for SM3 subsoil model) are listed in Table 3. The results obtained in the case of nonflexible subsoil (SM1 subsoil model, Cz = \(\infty\) MPa) are also presented in Table 3. Additionally, this relationship for the SM2 subsoil model is shown graphically in Figure 12. The frequency of horizontal transverse vibration is denoted by fx, the frequency of horizontal longitudinal vibration is marked by f, and the frequency of torsional vibration is denoted by ft.  
A notable influence of ground material properties on the fundamental natural horizontal (fx and fy) and torsional (ft) vibration frequencies can be observed. The values of appropriate frequencies of the same building could significantly vary depending on the parameter Cz. The differences in frequency values are particularly visible in the case of the comparison of the impact of weak or moderate (Cz = 35-65 MPa) and nonflexible (Cz = \(\infty\) MPa) subsoil--they can reach more than twice. However, even in the case of substrates with a much smaller difference in properties, this influence is also very clear. The frequency values (fx, fy, ft) are reduced as the substrate stiffness decreases. These observations apply to both the SM2 and SM3 subsoil models. The influence of material properties of load-bearing walls on the natural frequencies of the low-rise building is presented in the case of example three typical construction materials: brick, reinforced concrete, and cellular concrete. For numerical analysis using  
Figure 11: Foundation vibration of the masonry building (brick load-bearing walls) and the corresponding Fourier spectra computed using SM1, SM2, and SM3 subsoil models vs. measured building foundation vibration in the case of horizontal longitudinal direction (y): (**a**) induced by the mining tremor No. 1; (**b**) induced by the mining tremor No. 2. SM2 and SM3 subsoil models, the moderate stiffness of the subsoil was assumed, and Cz = 50 MPa was taken into account. The results of the computations for the SM2 and SM3 subsoil models, as well as the case of the SM1 subsoil model (nonflexible subsoil, fixed base model), are presented in Table 4.  
The results obtained lead to the conclusion that the fundamental natural frequencies of a building with a fixed type of structure, founded on the same subsoil, clearly depend on the material of the load-bearing walls used. This effect is especially visible in the case of nonflexible subsoil (SM1 subsoil model). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material of Bearing Walls**} & \multirow{2}{*}{**Subsoil Model**} & \multicolumn{2}{c}{**Fundamental Natural Frequencies of Building Vibrations [Hz]**} \\ \cline{3-5}  & & **fx** & **fy** & **ft** \\ \hline \multirow{3}{*}{brick} & SM1 & 9.45 & 9.36 & 10.45 \\  & SM2 & 4.39 & 4.78 & 5.00 \\  & SM3 & 4.40 & 4.80 & 5.02 \\ \hline \multirow{3}{*}{reinforced concrete} & SM1 & 18.86 & 21.48 & 23.14 \\  & SM2 & 4.92 & 5.44 & 5.74 \\ \cline{1-1}  & SM3 & 4.93 & 5.45 & 5.75 \\ \hline \multirow{3}{*}{cellular concrete} & SM1 & 8.89 & 8.77 & 9.95 \\ \cline{1-1}  & SM2 & 4.70 & 5.09 & 5.39 \\ \cline{1-1}  & SM3 & 4.72 & 5.11 & 5.41 \\ \hline \hline \end{tabular}
\end{table}