## 5 Results and Discussions  
The calibrated numerical models with \(Dr\) = 30%, 50%, and 80% were subjected to selected sets of motions (both vertical and horizontal) to simulate the seismic response of the underground structure. To study the effects of vertical motion, simulation cases without vertical motion were performed for comparison. Figure 7 compares the uplifts of \(Dr\) = 30%, 50%, and 80% cases with and without vertical motion. The results show that most cases are located inside the 1.1:1.0 and 0.9:1.0 lines (uplift with vertical motion:uplift without vertical motion = \(\mathit{UP}_{\mathit{VM}}\):\(\mathit{UP}\)) with few exceptions (\(\mathit{UP}_{\mathit{VM}}\) is much lower than \(\mathit{UP}\)). In order to explore the relationship between the uplift and the vertical input motion, three characteristics (peak acceleration; Arias intensity, \(\mathit{Ia}\); and cumulative absolute velocity, \(\mathit{CAV}\)) of both horizontal and vertical motions were used. The peak input acceleration is the most commonly used characteristic. In addition, results from [PERSON] and [PERSON] [8] showed that the magnitude of the uplift is positively correlated with the energy of the input motion. Therefore, \(\mathit{Ia}\) and \(\mathit{CAV}\) related to the energy of input motions were also used to explore the relationship between the uplift and the vertical input motion. Figures 8-10 show the relationships between the uplift ratio (\(\mathit{UP}_{\mathit{VM}}\)/\(\mathit{UP}\)) and three characteristics and ratios of three characteristics (peak input acceleration ratio = vertical peak input acceleration/horizontal pear input acceleration, \(\mathit{Ia}\) ratio = vertical \(\mathit{Ia}\)/horizontal \(\mathit{Ia}\) and \(\mathit{CAV}\) ratio = vertical \(\mathit{CAV}\)/horizontal \(\mathit{CAV}\)). The data points in these figures show that \(\mathit{UP}_{\mathit{VM}}\) is much lower than \(\mathit{UP}\) when the vertical input motion has a higher peak acceleration,  
Figure 6: Comparisons of earthquake motion indices: (**a**) peak acceleration; (**b**) Arias intensity; and (**c**) cumulative absolute velocity. Figure 7: Comparisons of uplifts with and without vertical motions. In order to understand the real mechanisms of the vertical motion affecting the uplift magnitude, results and input motions of TCU071\(-\)N (the N\(-\)S direction of TCU071 motion), TCU063\(-\)N, and HWA027\(-\)N of Dr = 30% cases are plotted in Figures 11-13. The intensity indices and uplift magnitudes for the TCU071\(-\)N, TCU063\(-\)N, and HWA027\(-\)N cases are listed in Table 5. TCU071\(-\)N represents the case where the vertical motion significantly lowers the uplift magnitude (\(>\)20%), TCU063\(-\)N represents the case where the vertical motion has a minor effect on the uplift magnitude (\(<\)5%), and HWA027\(-\)N represents the case where the vertical motion increases the uplift magnitude (\(>\)10%). Figures 11a-13a show the time histories of the uplift with and without the vertical input motion. Excess pore pressure time histories of _PM2_ (located underneath the bottom of the structure) (Figures 11b-13b) show that the inclusion of the vertical motion caused a transient response of the excess pore pressure for all cases. However, the amplitude and frequency of the transient response of the excess pore pressure in TCU071\(-\)N were significantly higher than those in TCU063\(-\)N and HWA027\(-\)N. As the transient response of the excess pore pressure  
Figure 8: Uplift ratio vs. vertical peak input acceleration and peak input acceleration ratio. Figure 10: Uplift ratio vs. _CAV_ of vertical motion and _CAV_ ratio. Figure 9: Uplift ratio vs. _Ia_ of vertical motion and _Ia_ ratio. is highly related to the input motion, the time histories of vertical motions and amplitudes of FFT of horizontal and vertical motions were also examined (Figures 11c,d-13c,d).