## 3 Results
### Determination of Parameters of the SMIKE Model Used for the Dynamic Analyses  
#### 3.3.1 Experimental Evaluation of Wave Propagation Velocity  
The estimation of the wave passage velocity was based on the discrete experimental data acquired via the vibroseis excitation in situ test (see Section 2.2.2). The cross-correlation function and phase angle characteristics of the registered signals were used to determine the wave velocity. Five series of excitations in the form of linear sweeps with a variable frequency range were conducted. The characteristics of each excitation series are summarized in Table 3. The duration of each series was 60 s. Due to the short distance between the vibroseis and the abutment, the exciting force was limited to 60 kN (30% of the maximum generator power). In the fifth series, the excitation force was increased to 100 kN. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Natural Frequency [Hz]**} & \multirow{2}{*}{**Differences [\%]**} \\ \cline{2-3} \cline{5-5}  & **FE Analysis Model No. 1** & & **OMA** \\ \hline
1 & 1.57 & 1.50 & 4.6 \\
2 & 1.87 & 2.48 & 24.6 \\
3 & 3.48 & 3.36 & 3.6 \\
4 & 14.30 & 14.26 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of experimental and numerical values of natural frequencies. Figure 8: Comparison of the basic modes of vibration of the bridge obtained in the experimental and the numerical way. Firstly, the cross-correlation functions of the registered signals were used to determine the apparent wave velocity. The signals registered on piers P1, P2, and P3 (see Figure 3) were pairwise compared. Due to the large distance from the source of vibrations to pier P4, the signals recorded at this measurement point turned out to be disturbed by high background noise. For this reason, the signals from P4 were no longer considered. To obtain the wave velocities for different excitation frequencies, the signals recorded in measurement points were modified by narrow-pass filters with frequencies 10, 12, 14, and 16 Hz. Then, the cross-correlation functions of the signals were calculated for the following point pairs: P1-P2, P1-P3, and P2-P3. Examples of signals of frequency 14 Hz and their cross-correlation functions are presented in Figures 9 and 10, respectively. On the basis of the location of each cross-correlation function maximum, the time delay was defined for the extracted frequency range. As can be seen in Figure 10, the cross-correlation functions for the signal component frequency of 14 Hz reach the maximum values at 0.16, 0.42, and 0.26 sec for the pair P1-P2, P1-P3, and P2-P3, respectively. Since the registered accelerations are shifted in time by the value needed for the wave front to cover the distance between the piers, the time shifts can be used to determine the apparent wave velocities between particular piers. For the known distances between piers, i.e., 23 m between P1 and P2, 103 m between P1 and P3, and 80 m between P2 and P3, the calculated wave velocities are 135, 254, and 344 m/s for the above-mentioned pairs, respectively. The mean wave velocities between particular piers (averaged over five series) are summarized in Table 4 for different frequencies. Additionally, in the last row of Table 4, the mean apparent wave velocities between support pairs (averaged over different frequencies) are presented. Figure 10: The cross-correlation functions for signal pair: (**a**) P1–P2, (**b**) P1–P3, (**c**) P2–P3. Figure 9: Acceleration component of the frequency 14 Hz registered at point: (**a**) P1, (**b**) P2, (**c**) P3. Analyzing Table 4, one can notice that the wave velocities between the particular piers are different. This phenomenon, portrayed in Figure 11, is caused by inhomogeneous soil conditions. The lowest wave velocity was obtained for the layers of natural soil (sand and clay) lying between the piers P1 and P2. Much higher wave velocity was determined between the piers P2 and P3, where the road with the stiff foundation layers runs.