## 4 Influence of Subsoil and Building Material Properties on the Natural Frequencies of Building
Figure 14.  
Similar results analysis regarding the influence of the Cz subsoil parameter on the transmission of vibrations from the free field to the foundations, as in the case of the SM2 subsoil model, were also performed for the SM3 subsoil model. It can be stated, for example, that the difference between the maximum vibration acceleration values calculated for the Cz coefficient values of 35 MPa and Cz = 65 MPa in the x direction induced by mining tremor No. 1 and No. 2 was equal, respectively, to 25% and 22.2%--comp. Figure 15 and Figure 13.0 The difference between the maximum vibration acceleration values calculated for the Cz coefficient values of 35 MPa and Cz = 65 MPa in the y direction induced by mining tremor No. 1 and No. 2 was equal, respectively, to 24.1% and 21.7%--comp. Figure 16 and Figure 13.1 By analyzing the SM3 ground substrate model and comparing the FFT courses calculated on the building foundations based on the recorded free-field vibration courses induced by mining tremors No. 1 and No. 2, it could be stated that in the horizontal direction x for mining tremor No. 1, two clear bands of dominant frequencies could be distinguished, amounting to 5.3 Hz and 10.25 Hz--comp. Figure 13.2  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Maximum Value of \(a\) [m/s\({}^{2}\)]} \\ \cline{2-7}
**Cz [MPa]** & \multicolumn{6}{c}{**SM2 Model**} & \multicolumn{6}{c}{**SM3 Model**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Direction x**} & \multicolumn{2}{c}{**Direction y**} & \multicolumn{2}{c}{**Direction x**} & \multicolumn{2}{c}{**Direction y**} \\ \cline{2-7}  & **No. 1** & **No. 2** & **No. 1** & **No. 2** & **No. 1** & **No. 2** & **No. 1** & **No. 2** \\ \hline
35 & 0.19 & 0.81 & 0.23 & 0.63 & 0.18 & 0.70 & 0.22 & 0.65 \\
40 & 0.21 & 0.87 & 0.25 & 0.68 & 0.19 & 0.74 & 0.24 & 0.69 \\
45 & 0.23 & 0.93 & 0.26 & 0.73 & 0.20 & 0.78 & 0.25 & 0.72 \\
50 & 0.26 &In the case of forcing No. 2, the bands of dominant frequencies were smaller than the dominant frequency bands induced by mining tremor No. 1 and were 3.7 Hz, 4.7 Hz and 5.7 Hz. In the case of the horizontal direction \(y\), the bands of dominant frequencies were almost the same for the assumed values of the coefficient Cz. The character of the vibrations transmitted from the free field to the fixed model (Cz = \(\infty\) MPa) was different compared with the courses for the case with the included Cz = 35-65 MPa (comp. Figure 16). As mentioned above, further numerical analyses were focused on assessing the impact of the building's construction material on the transmission of vibrations from the free field to the foundations. The influence of three types of construction material, i.e., brick wall, reinforced concrete, and cellular concrete, on the ground-foundation vibration transfer in the case of two subsoil models (assuming the real soil properties under the building corresponding to Cz equal 50 MPa) is shown in Figures 17-20 and Figure 13.3  
For forcing No. 1, in the case of the SM2 subsoil model, the highest acceleration values in the transverse direction x were obtained for the building model made of reinforced concrete material, whereas for the two remaining materials, the level of foundation accelerations was similar--comp. Figure 17 and Figure 13.4 From the mining tremor No. 1 and the three analyzed materials, in the vibration courses of the foundation, two frequency bands dominated, the lower one around 5.5 Hz and the higher one in the range from 9.3 Hz to 10.3 Hz--comp. Figure 13.5 From forcing No. 2, in the level of the building foundation, a low dominant frequency band of 4.7 Hz could be distinguished for the three adopted materials of building models, and additionally, for the model with reinforced concrete material, a band of 5.7 Hz. Additionally, for models with three different materials, a common higher band of dominant frequencies 8.7-10.2 Hz could be distinguished--comp.