## 6 The Pushover Analysis of Soil-Structure System
### Analysis Results  
Consistent with Section 5.2, it is assumed that the soil pressure of the overburden is increased by 50% considering the vertical earthquake effect [46]. The shear forces at the bottom of each center column of the structural mid-span under gravity are shown in Figure 14. From the figure, it can be seen that with the increase in applied horizontal acceleration, the lateral drift ratio of the center column is also increasing, and shear forces of each sections reach their peak with a lateral drift ratio of about 0.5%.  
When the vertical load only considers the self-weight of soil and the structure, the shear force of traditional center column shows a gradual decrease after reaching the peak value. In contrast, although the peak shear force borne by the split column is only about \(1/3\) of that of the traditional one, its horizontal deformation capacity is excellent, and there is no obvious decreasing section. The split column can still bear the shear deformation even though the inter-story drift ratio has reached \(1/100\).  
When the vertical loads consider both gravity and inertia forces, both the upper and the lower traditional columns show a significant decreasing trend after exceeding the peak shear force during the pushover process, and the decreasing trend in Figure 15 is more obvious than the decreasing trend in Figure 14. This step illustrates that the vertical inertia force of the overlying soil has an important influence on the seismic performance of underground structures. At this time, although the split column still needs to bear a large vertical pressure, its deformation capacity is outstanding and has good ductility performance.  
Figure 16 presents the equivalent plastic strains of center column concrete under four typical cases of inter-story drift ratio, which are \(1/1000\), \(1/550\), \(1/250\), and \(1/100\)[49; 50], corresponding to their respective color areas in Figure 16. Upon implementing the split column configuration, it is observed that the concrete's equivalent plastic strain throughout various phases consistently registers lower values in comparison to the traditional monolithic column. When the inter-story drift ratio reaches \(1/100\), the maximum equivalent plastic strain  
Figure 14: Lateral force–drift ratio curves of columns in the soil–structure system under gravity. (**a**) Upper column. (**b**) Lower column.  
Figure 13: Pushover modes of the soil–structure system.  
of concrete in the split column is about 0.25%. The zones of concrete damage are uniformly distributed around the top and bottom sections of split column, representing a prominent departure from the failure pattern exhibited by the prototype monolithic columns.  
Figure 16: Equivalent plastic strain development of concrete in the center column. (**a**) Upper traditional column. (**b**) Upper split column. (**c**) Lower traditional column. (**d**) Lower split column.  
Figure 15: Lateral force–drift ratio curves of columns in the soil–structure system under gravity and vertical earthquake effect. (**a**) Upper column. (**b**) Lower column.  
In addition, comparing Figures 11, 12 and 16, it can also be found that the equivalent plastic strain distribution mode shown in Figure 12 is closer to that shown in Figure 16, which means that Mode B is preferred for the pushover analysis of underground structures. Specifically, the horizontal drift is applied while the rotation degrees of freedom at the top of the column are also restrained. This particular pushover methodology serves to accurately simulate the stress distribution within columns of underground structures, thereby yielding more authentic seismic performance curves.