## 1 Introduction
[21] established a numerical model for a subgrade by using the discrete element method (DEM) and studied the dynamic characteristics of the subgrade under cyclic loading. The results indicated that the subgrade plays a crucial role in the stability of railway tracks and affects the settlement of tracks. [PERSON] et al. [22] developed a coupled model that incorporates both the DEM and the finite difference method (FDM) to study the dynamic behaviors of the railway ballast assembly. The results showed the superiority of the DEM-FDM coupled model in simulating the interaction between continuum and discrete domains. [PERSON] et al. [23] conducted numerical triaxial tests, in which the rubber membrane and soil  
Figure 1: China Railway Track System (CRTS) II slab track. body were simulated by using the FDM and DEM, respectively. The modeling method of the DEM-FDM model in [22] was adopted in this paper. In summary, the differential subgrade settlement has an important effect on the stress and deformation of the track structure. The analysis methods adopted by previous studies mainly include the analytical method and the finite element method. The nonlinear contact characteristics between layers of a track-subgrade system are often ignored in analytical methods and the mechanical properties of track structures cannot be accurately reflected. A finite element model can accurately simulate the stress and deformation of a track structure. However, the subgrade was simplified as an elastic body and the stress state of the subgrade was rarely paid attention to. The track structure undergoes the following deformation in a subgrade settlement section, which changes the load of the track structure on the subgrade and affects the continued settlement of the subgrade [24]. Therefore, there are coupling effects between subgrade and track structure that must be considered. The subgrade of a high-speed railway is largely composed of graded gravel. The subgrade may be cracked or otherwise deteriorated when the settlement is large. In this case, it is not appropriate to simulate the subgrade as a linear elastic body. In DEM, the granular material is considered as assembled particles interacting by force-displacement law and Newton-second law [25]. It is suitable for simulating discontinuous and large deformation problems, which is consistent with the situation when the subgrade produces a large settlement. The non-uniform contact between the track structure and subgrade in a settlement section cannot be accurately simulated by using the DEM-FDM coupled approach. Based on the above analysis, the slab track was considered as a continuous domain using the FDM. The subgrade was considered as a discrete domain using the DEM. DEM-FDM coupled simulation was realized by adopting interface elements for data interaction. This paper is organized as follows. First, the description of the DEM-FDM coupled mechanism was presented. Second, the coupled model was developed and verified. Finally, the effects of differential subgrade settlement on track deformation and contact forces of gravel grains were studied. The effects of settlement wavelength, settlement amplitude, and other types of settlement were also discussed. It is expected that the obtained results could provide helpful guidance for the maintenance and optimization of high-speed railways.