## 5 Conclusions  
Based on the performed research, the following conclusions can be drawn:  
1. The advanced model of spatiotemporal mining-induced kinematic excitation (SMIKE) for multiple-support structures exposed to mining-induced seismicity is proposed. The uniqueness of this model results from the possibility of its application for any region of mining activity, as it is based on empirical regression functions characterizing different such regions.
2. The proposed SMIKE model takes into account the loss of coherency resulting from the scattering of waves in the heterogeneous ground, the wave-passage effect originated in the different arrival times of waves to consecutive supports, and the site-response effect resulting from the local soil conditions. Hence, it covers the key phenomena of spatial variability of mining-induced ground motion.
3. The two parameters of the SMIKE model can be estimated relatively easily in practice. The space scale parameter \(\alpha\) can be determined from the regression functions for different mining areas delivered by seismologists. The apparent wave velocity in the ground \(v\) can either be detected experimentally or assumed based on the literature for foundation geological conditions.
4. The proposed model was applied to assess the dynamic performance of the five-span bridge under the mining-induced shock recorded in the Upper Silesian Coal Basin (USCB), Poland. The space scale parameter \(\alpha=7\) was determined on the basis of regression curves valid for the USCB region. This value lies within the range of the space scale parameters adopted in the literature. The apparent wave passage velocity \(v=240\) m/s, obtained from discrete experimental data acquired via the vibroseis excitation in situ experiment, is typical for the geological conditions in the field.
5. The dynamic response levels, in terms of maximal principal stresses, were evaluated and compared assuming both the classic uniform excitation model and the proposed spatiotemporal mining-induced kinematic excitation (SMIKE) model. The impact of the wave velocity appears to be crucial: the introduction of the experimentally evaluated velocity modifies (either amplifies or reduces, depending on the span slenderness) the dynamic response level even twice. The introduction of the space scale parameter, based on the regional seismicity characteristics, changed the stress levels up to 20% in comparison with results obtained for the \"traveling\" wave only.
6. The presented analyses show how the SMIKE model application affects the level of the dynamic performance of particular spans of the bridge in the context of the spans' slenderness. For various wave velocities, the response level is up to 3.5 times higher with the SMIKE model than with the uniform one for stocky spans due to the quasi-static effects. The opposite situation is spotted for slender spans. The decrease in the average excitation amplitudes, introduced by the SMIKE model causes a reduction in the global dynamic response level.  
The final conclusion is that the proposed spatiotemporal mining-induced kinematic excitation model, covering the key phenomena of spatial variability of mining-induced ground motion, can be considered equivalent to advanced complex models of kinematic excitation proposed for natural earthquakes. However, the very simple stochastic spatial wave variability generator, together with the deterministic temporal approach, enables the model to be applicable in engineering practice. It is also worth noting that by having empirical regression functions characterizing seismic regions, one can apply the proposed model for seismic scenarios.  
Conceptualization, J.M.D. and D.J.; data curation, P.B.; formal analysis, J.M.D., D.J. and P.B.; investigation, J.M.D. and P.B.; methodology, J.M.D.; supervision, J.M.D. and D.J.; visualization, P.B.; writing--original draft, J.M.D., D.J. and P.B.; writing--review and editing, D.J. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.