## 3 Results
### Response Spectrum at Superstructure Level  
Figures 16-18 contain the response spectrum for each of the 3 main directions and for each analysis/model:  
* The 30 probabilistic simulations and the computed mean/80% NEP curves;
* The deterministic model analysis curve;
* The EC design model curve.  
Figure 16: Acceleration response spectrum at superstructure level-X direction.  
Figure 15: Probabilistic linear-equivalent soil behavior curves: (a) G-\(\gamma\); (b) D-\(\gamma\).  
Table 4 contains the spectral acceleration and frequency for the peaks of the acceleration response spectrum for each of the three models presented below:  
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Probabilistic**} & \multicolumn{2}{c}{**Deterministic**} & \multicolumn{2}{c}{**Design**} \\ \cline{2-7}
**Direction** & \multicolumn{2}{c}{**SA [g]**} & \multicolumn{1}{c}{**f [Hz]**} & \multicolumn{1}{c}{**SA [g]**} & \multicolumn{1}{c}{**f [Hz]**} & \multicolumn{1}{c}{**SA [g]**} & \multicolumn{1}{c}{**f [Hz]**} \\ \hline X & 0.96 & 1.00 & 0.94 & 1.00 & 3.55 & 1.40 \\ Y & 4.97 & 1.71 & 2.90 & 1.72 & 6.64 & 2.10 \\ Z & 0.61 & 1.83 & 0.56 & 5.43 & 2.77 & 11.68 \\ \hline \hline \end{tabular}  
The response spectrum graphs show large differences in behavior between the usual design model used in the current engineering practice and the SSI models. Typically, the design model overestimates the seismic response of the superstructure, even by as much as 3.5 times for the X direction (along the bridge superstructure axis). Due to this very large acceleration value, the behavior of the structure for the design model will be governed by a large rocking motion of the pier, generated by the superstructure motion in the horizontal direction, while the foundations remain relatively static. This is actually in perfect agreement with the general seismic behavior as it is generally understood by the engineering community. Still, the sophisticated SSI analyses show exactly the opposite, as follows: the ground motion is applied from the ground up and the behavior of the structure is quite chaotic; it is not governed solely by the superstructure displacement. For the vertical direction Z, the design model overestimates the superstructure response across the whole frequency range.  
Overall, the design model generates a stronger structural response than the SSI analyses, for both the deterministic and probabilistic approach.  
Figure 17: Acceleration response spectrum at superstructure level-Y direction.  
\begin{table} \end{table}
Table 4: Peak values of acceleration response spectrum.  
Figure 18: Acceleration response spectrum at superstructure level-Z direction.  
Regarding the probabilistic SSI model, for the X direction, a good agreement with the deterministic analysis is obtained, with only minor differences between them. For the Y direction, the shape of the graphs is similar; the main peaks show a small frequency shift, but a big difference in amplitude, as follows: the probabilistic model generates a 1.7 times stronger structural response. This means that the probabilistic model manages to point out a \"weak point\" in the structure, where the deterministic model actually underestimates the structural response.  
For the vertical direction, the deterministic model misses a peak which can be found in multiple probabilistic simulations and is statistically relevant.