## 4 Discussion
### The Impact of SMIKE Model Parameters on the Dynamic Performance of the Bridge  
#### 4.3.1 The Impact of the Wave Propagation Velocity  
In Section 4.2, the impact of the SMIKE model application on the dynamic response level of the bridge located in the USCB with known geological conditions was assessed. The first model's parameter, space scale parameter \(\alpha=7\), was determined on the basis of regression curves valid for the entire USCB region. The second parameter, the wave velocity \(v=240\) m/s, was evaluated on the basis of the in situ experiment. However, when experimental research is not possible, wave velocity may also be assumed, for known local geological conditions, based on the literature. Hence, it seems reasonable to analyze the relations between the wave velocity and the dynamic performance of a structure to find out whether, or for what wave velocities, the use of the SMIKE model leads to more conservative results for a multi-support structure than the use of the classic uniform excitation model. Four potentially occurring in the region wave propagation velocities of 240 (measured), 600, 1000, and 2000 m/s were adopted for ground accelerations simulations at consecutive bridge supports. The dynamic responses of the bridge for the assumed velocities are compared to results obtained under the assumption of uniform kinematic excitations. The resultant stress-time histories for points: S2 and L3 are presented in Figure 18, followed by the envelopes of maximal principal stresses along the bridge length shown in Figure 19a. The ratios of maximal principal stress envelopes (SMIKE model to uniform model) are depicted in Figure 19b. In the case of point S2, located on the stocky span, the greatest maximum stress level is obtained with the SMIKE model for the wave velocity of 1000 m/s (see Figure 18a). Different relation occurs for point L3, placed on the longest, slender span, where the greatest stress level occurs under the uniform excitation (see Figure 18b). Figures 17b and 19b illustrate how the SMIKE model application affects the dynamic response levels of particular parts of the bridge for different assumed wave velocities. Figure 17: The SMIKE Model (red line) vs. the Uniform Model of Excitation (black line): **(a)** the comparison of the maximal principal stress envelopes, **(b)** the stress envelope ratio: SMIKE to uniform model. The response level along short, stocky spans is much higher under the SMIKE model for all assumed wave velocities. The stress ratios reach:  
Figure 19: The SMIKE Model vs. the Uniform Model of Excitation: (**a**) comparison of the maximal principal stress envelopes, (**b**) the stress envelope ratio: SMIKE model to uniform model. Figure 18: Time-stress histories obtained for the SMIKE model with the wave velocities: 240 m\(/\)s (red line), 600 m\(/\)s (violet line), 1000 m\(/\)s (blue line), 2000 m\(/\)s (green line), and for the uniform excitation (black line) at representative points: (**a**) S2 (in the middle of the second span), (**b**) L3 (in the middle of the third span). about 2--for \(v=240\) m/s,
* about 3--for \(v=600\) m/s,
* about 3.5--for \(v=1000\) m/s,
* about 2.5--for \(v=2000\) m/s. This means that the quasi-static effects appearing in the stocky spans take on values high enough to outweigh the reduction in the average excitation amplitudes, which leads to the growth in the global dynamic response. The opposite trend can be noticed for the third slender span. The decrease in the average excitation amplitudes introduced by the SMIKE model causes a reduction in the global dynamic response level. The slower the wave velocity, the greater the reduction of the global response level at this span. The dependences of maximal principal stresses on the wave propagation velocity for the points located in the different structural parts are presented in Figure 20. Each line in the presented charts is created by selecting and linking the maximum value of the time-maximal principal stress history for the following wave velocities: 240, 600, 1000, and 2000 m/s.