# Seismic Response Analysis of Concrete Box-Type Subgrade in High-Speed Railways
## 4 Seismic Response of Box-Type Subgrade
### System Dynamic Response Characteristics Under Multi-Dimensional Seismic Coupling
#### 4.1.2 Force and Deformation Characteristics of Box-Type Subgrade  
To investigate the force characteristics of the box-type subgrade structure, the force cloud diagram of the box-type subgrade at the time of maximum amplification effect is presented. To study the force and deformation conditions of the box-type subgrade structure in actual applications and to avoid the influence of boundary effects, the mid-span box-type subgrade structure is analyzed, as shown in Figure 12. It can be observed from the figure that under seismic action, the maximum principal stress in the box-type subgrade is compressive on the top slab surface and tensile on the bottom surface, with the maximum tensile stress being 0.542 MPa, which is within the structural limit range. The side walls are eccentrically compressed, with tensile stress presented on the outer side at the connection with the top slab, but it does not exceed the limit; the bottom slab is under overall compression. Under the maximum design basic acceleration of an earthquake, the stress in each component of the box-type subgrade is far below the design strength and is maintained in a linear elastic state, achieving the design performance objectives and complying with China's seismic fortification standard of \"no damage in minor earthquakes, repairable after moderate earthquakes, and no collapse in major earthquakes\".  
To explore the deformation characteristics of the box-type subgrade structure, the deformation cloud diagram of the box-type subgrade at the time of maximum amplification effect is presented. As shown in Figure 13a, the deformation at the structural joints of the box-type subgrade is more pronounced. The deformation cloud diagrams of the most unfavorable cross-sections in various directions of the box-type subgrade are extracted, as shown in Figure 13b-d. Under the coupled action of multi-dimensional seismic forces, the box-type subgrade is primarily dominated by vertical deformation, which is concentrated in the middle of the top slab. Numerically, the maximum range of deformation of the box-type subgrade is only 0.57 mm, indicating that the structure itself undergoes little relative deformation under seismic action, i.e., no significant bending deformation occurs, suggesting that the box-type subgrade has good adaptability.  
Figure 12: Cloud map of box-type subgrade force cloud map.  
To further investigate the deformation characteristics of each component of the box-type subgrade, the deformation time-history curves of the bottom slab, side walls, and top slab of the box-type subgrade in each direction were extracted, as shown in Figure 14. It can be observed that the displacement time-history curves of each component of the box-type subgrade in all directions essentially coincide, indicating that under seismic action, the box-type subgrade primarily undergoes rigid body motions.  
Figure 14: Displacement time–history curve of each component for box-type subgrade.  
Figure 13: Cloud map of box subgrade deformation.