## 4 Results
### Seismic Response  
As stated before, the SFT is a massive tubular structure, and its structural response dramatically increases with external forcing. To check the maximum or dominant structural response of SFT, a comparison of static, hydrodynamic and seismic response needs to be provided [16; 23]. The El-Centro (1940) ground motions are assumed for the SFT numerical example to evaluate the dynamic behavior of the SFT for the three-dimensional ground motion input. Three components of El-Centro ground motions used as input motions are shown in Figure 10. The effective seismic forces using these ground motions are applied simultaneously at the nodal points in the three-dimensional numerical model. For the evaluation of the ground motion's effects on the structural behavior of the SFT, two cases are defined: Case (1): The ground motion component S00E was applied in the longitudinal direction (\(X\)-direction); component S90W was applied in the transverse; and the vertical component was applied in the vertical direction of the SFT, respectively; this case will be referred to as Load  
Figure 10: Ground motion input (El-Centro 1940 site Imperial Valley irrigation district): (**a**) S00E component; (**b**) S90W component; and (**c**) vertical component. Figure 9: Hydrodynamic bending moments along the length of the SFT with time: (**a**) bending moment \(\mathrm{M_{Y}}\) and (**b**) bending moment \(\mathrm{M_{Z}}\). Combination 1 (LC1). Case (2): The ground motion component S90W was applied in the longitudinal direction; component S00E was applied in the transverse direction; the vertical component was applied in the vertical direction of the SFT, respectively; this case will be referred to as Load Combination 2 (LC2). The ground motion component S00W is the maximum ground motion input having a peak ground acceleration (PGA) of 0.35 g. In contrast with the previous sections, the unfactored static and hydrodynamic loads are used here for evaluating the structural behavior of the SFT. A comparison of the static, hydrodynamic and seismic response envelope curves of the SFT is shown in Figure 11. The maximum response of the tunnel is used to produce the envelope curves. The SFT response envelope curves of transverse and vertical displacements are shown in Figure 11a,b respectively; the longitudinal response of the SFT is very small and is not shown. The transverse displacements of SFT in Figure 11a show a large difference between the static and dynamic analysis. The approximate relative differences in maximum transverse displacements of the SFT from analysis cases LC2, LC1 and hydrodynamics to that of the static case are 95%, 94% and 42%, respectively. The vertical displacements of the SFT are nearly the same for static and hydrodynamic analysis. Similarly, for LC1 and LC2, the vertical displacements of the SFT are almost the same, as shown in Figure 11c. The approximate relative differences in maximum vertical displacements of the SFT from analysis cases LC2, LC1 and hydrodynamics to that of the static case are 28%, 28% and 1.7%, respectively. The transverse response is more affected by the ground motions, while the vertical response is more affected by gravity and hydrodynamic (waves and currents) actions. The transverse response is extremely large for the seismic analysis as compared to the vertical response; for instance, the relative difference in transverse and vertical displacements for LC1 and LC2 are 61% and 65%, respectively. Figure 11b,d represents the SFT bending moment M\({}_{Z}\) and bending moment M\({}_{Y}\) envelope curves, respectively. Similar trends prevail for bending moments as described for displacements. The shape of bending moments clearly demonstrates the effectiveness of the adopted mooring configuration. Figure 11: Comparison of static, hydrodynamic and seismic response envelope curves of the SFT: (**a**) \(Y\)-displacement; (**b**) bending moment M\({}_{Z}\); (**c**) \(Z\)-displacement; and (**d**) bending moment M\({}_{Y}\). LC1, Load Combination 1.