## 3 Results of the Numerical Simulations  
Figure 4 shows the calculated excess pore pressure ratio time histories for two different depths in Cases 2 and 3. In both cases, the excess pore pressure ratio reached 1.0 at a depth of \(-\)1.5 m and gradually decreased with increasing depth to \(-\)4.5 m. The excess pore pressure increased sharply at approximately 5-6 s in each case, which is a similar trend to that of the input earthquake motion. The fluctuation in the pore pressure response was more significant in Case 3, demonstrating that the volumetric strain and variation in the stress state were more prominent in stronger earthquakes. The excess pore pressure ratio at \(-\)4.5 m for Case 2 was lower than that for Case 3 because of the difference in the amplitude of the input earthquake. This indicates that liquefaction occurred at a deeper depth when a stronger earthquake was induced for identical ground conditions. Figure 5 shows the excess pore pressure ratio time histories calculated for two different depths in Cases 11 and 12. At a depth of \(-\)9.5 m, 100% liquefaction occurred in Case 12, whereas almost 50% liquefaction occurred in Case 11. At a depth of \(-\)5.5 m, 100% liquefaction occurred in both cases. This is a similar trend to that of Cases 2 and 3 in Figure 4. However, the liquefied  
Figure 3: Time histories of the input earthquake motions. area was much deeper in Cases 11 and 12 than in Cases 2 and 3. It can be predicted that much more kinematic interaction would be induced in Cases 11 and 12 than in Cases 2 and 3. Table 5 presents the ranges of the maximum depth at which the excess pore pressure ratio reached 1.0 for each analysis case. It shows that as the thickness of the liquefiable layer increased and the input seismicity increased, the depth at which the excess pore water pressure ratio reached 1.0 also increased. It also demonstrated that the magnitude of the input earthquake and the seismic site have a significant effect on the level of liquefaction, and it is expected that this phenomenon will affect the dynamic behavior of the shaft structure. Figure 6 shows peak bending moment profiles for the shaft along the depth in each analysis case. As shown in this figure, the bending moments for the cases with longer earthquake return periods were generally larger than those for the cases with shorter earthquake return periods. The peak bending moment measured for the earthquake with a 2400 y return period was almost 2.5 times larger than that for the earthquake with a 500 y return period. In addition, the calculated dynamic bending moment increased as the bedrock depth increased. The peak bending moments for cases with a bedrock depth of 21 m were almost 25 times larger than those for cases with a bedrock depth of 5 m. This indicates that the kinematic force induced by liquefaction at deeper soil depths has a significant influence on the dynamic shaft behavior. The location at which the peak bending moment occurred was deeper than the center of the total depth. In addition, the location at which the peak bending moment occurred became deeper with an increase in the earthquake return period. This indicates that stronger earthquakes produced larger liquefied areas, and that greater kinematic force induced by liquefaction was exerted on the shaft structure. Figure 7 shows a representative graph of the lateral displacement time histories for the shaft and far-field soil. The shaft and soil behaved in-phase for the entire earthquake duration. This means that the shaft behavior was governed by the soil behavior, which was induced by kinematic interaction. In addition, the residual displacement of the soil at the surface was larger than that of the shaft. This phenomenon could indicate the occurrence of relative displacement after liquefaction. Figure 8 shows the maximum lateral shaft and soil displacement profiles along the depth for Cases 5 and 11. The lateral displacement was slightly greater in Case 11 than Case 5; however, the discrepancy was smaller than that of the bending moment.