## 4 Influence of Subsoil and Building Material Properties on the Natural Frequencies of Building

Table 4: Fundamental natural frequencies of building vibrations depending on the material of bearing walls in the case of a nonflexible subsoil (SM1 subsoil model) and the subsoil with the parameter Cz = 50 MPa (SM2 and SM3 subsoil models). Figure 12: Fundamental natural frequencies of masonry (with brick walls) building vibrations depending on the dynamic parameter Cz describing the material of subsoil (for SM2 subsoil model). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Cz [MPa]**} & \multicolumn{2}{c}{**Fundamental Natural Frequencies of Building Vibrations [Hz]**} \\ \cline{2-4}  & **fx** & **fy** & **ft** \\ \hline \multirow{3}{*}{35} & 3.96 & 4.39 & 4.58 \\  & 40 & 4.12 & 4.54 & 4.75 \\  & 45 & 4.27 & 4.68 & 4.89 \\  & 50 & 4.40 & 4.80 & 5.02 \\  & 55 & 4.52 & 4.91 & 5.14 \\  & 60 & 4.63 & 5.01 & 5.25 \\  & 65 & 4.73 & 5.10 & 5.35 \\  & \(\infty\) & 9.45 & 9.36 & 10.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 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). As could be expected, the stiffest structure of the building is made of reinforced concrete load-bearing walls, the appropriate computed frequencies of which are the highest. Nevertheless, the differences in frequencies regarding the other two typical building construction materials (brick and cellular concrete) are also significant and could be important in the analysis of the SSI effect. The values of the considered frequencies computed for the building with a given wall material were practically the same using the SM2 and SM3 subsoil models. The differences were smaller than 0.5%. Transmission of Mining Vibrations from the Ground to the Foundation of the Building Depending on the Material Properties of the Subsoil and Building  
Numerical analyses concerned the evaluation of vibration transmission from the free-field to the foundations of a building with typical load-bearing wall construction. Two main problems were considered. In the first one, differences in building foundation vibrations depending on the material properties of the subsoil were investigated in the case of an example model masonry building in which the load-bearing walls were built of bricks. The impact on the vibration transmission of two types of subsoil models, SM2 and SM3, was analyzed for different values of the dynamic, elastic, uniform vertical deflection Cz. The values of the Cz parameter varied from 35 MPa to 65 MPa. The Cz parameter corresponding to the foundation on the rock (Cz = \(\infty\) MPa, nonflexible subsoil, SM1 subsoil model) was also taken into account. The second main issue concerned the influence of the material of the building's load-bearing walls on the transmission of mining vibrations from the ground to the foundation of the building. Three typical building materials were considered: brick, reinforced concrete, and cellular concrete. Using the SM2 and SM3 subsoil models, the calculations were performed using the determined subsoil properties (Cz = 50 MPa), corresponding to the actual subsoil from the USC region. All the analyses were conducted for the two representative mining tremors No. 1 and No. 2 in the horizontal x and y directions. The influence of the Cz coefficient value on the transmission of transverse x vibrations from the ground to the foundations (time history and corresponding Fourier spectrum) using the SM2 subsoil model and forcing with mining tremors No. 1 and No. 2 is shown in Figure 13. At the same time, an analogous relationship regarding the longitudinal y direction is shown in Figure 14.  
Figure 13: Cont. Figure 14: Masonry building (brick load-bearing walls) horizontal longitudinal (y) foundation vibration and the corresponding Fourier spectra depending on the material properties of subsoil (Cz [MPa]), computed using the SM2 subsoil model: (**a**) induced by the mining tremor No. 1; (**b**) induced by the mining tremor No. 2.