# Seismic Performance of Modal Transfer Stations on Soft Clays
## 5 Seismic Tunnel-Bridge-Building Interaction  
The deconvolved ground motions calculated in the free-field response analyses were employed as input in the dynamic analyses of the tunnel-soil-bridge-building model, using the same compliant-base approach. For both CU17 and CU85 input motions, the shear stress histories were applied in the two orthogonal directions \"x\" (i.e., transversal) and \"y\" (i.e., longitudinal) at the model's base, considering 100% in each direction. To study the seismic interaction effect on the tunnel-bridge-building system, the results were presented in terms of the \"Interaction factor for the urban bridge\" (Tuf; Figures 10 and 11), which is the transfer function computed between the upper deck of the bridge and its foundation without the presence of the adjacent structures, TF U-F, divided by the transfer function between the upper deck of the bridge and its foundation with the presence of the adjacent structures in the different scenarios, TF U-F\({}_{\text{T}}\). Similarly, the \"Interaction factor for the building\" (Tbf; Figures 12 and 13) was also defined. These results are presented for all the scenarios considered in Figure 3 and Table 1, for the transversal and longitudinal components. Tuf and Tbf allow us to clearly show the effect of the amplification potential and energy distribution within the frequency content of interest. Values of Tuf and Tbf above one correspond to beneficial interactions (i.e., the building and bridge amplification potential decreases due to the adjacent structures), whereas a value below one means a detrimental interaction (i.e., the building and bridge amplification potential increases due to the adjacent structures). These relationships based on the transfer functions allow us to assess the amplification potential and energy distribution for each frequency. In all cases, the relevant frequency is indicated, depending on the fundamental period of the structure and direction analyzed, equal to Tb = 0.45 and 0.6 s (2.2 and 1.6 Hz) for the bridge in the transverse and longitudinal directions, respectively, and Te = 1.01 s (0.99 Hz) for the building in both directions. The characteristic elastic site period of the soil Tpe \(\approx\) 2.0 s (0.5 Hz) is also within this range. Figure 10: Interaction factor for the bridge in the transversal (X) direction under different scenarios for (**a**) the CU17 and (**b**) the CU85 synthetic ground motion. Figure 11: Interaction factor for the bridge in the longitudinal (\(\gamma\)) direction under different scenarios for (**a**) the CU17 and (**b**) the CU85 synthetic ground motion. Figure 12: Interaction factor for the building in the transversal (X) direction under different scenarios for (**a**) the CU17 and (**b**) the CU85 synthetic ground motion. First, it can be clearly appreciated in all cases (Figures 10-13) that the interaction among structures is greater for high frequencies (>1 Hz) and that is almost negligible for low frequencies (<1 Hz). Also, the interaction is larger for the CU17 synthetic ground motion, which concentrates its energy on higher frequencies, than for the CU85 ground motion. This can be associated partially with the dispersion and wave-scattering effect of the short waves, which corresponds to the high-frequency seismic motion component. Wave scattering can occur if there is an important heterogeneity within a uniform soil profile. Although this does not affect the total amount of energy carried by seismic motion, at the limits of heterogeneities, scattering tends to disorganize a wave field through reflection and refraction in such a way that the amplitudes of waves, especially at higher frequencies, are dispersed over different wavelengths [46]. Therefore, in systems formed by several vibration structures (bridges and buildings) located above a soil medium with heterogeneities (such as tunnels), it is most probable that their seismic response would be affected at high frequencies [47].