###### Abstract  
The key to modeling the interlocking of geogrid-reinforced ballast is considering both the continuous deformation characteristics of the geogrid and the discontinuity of the ballast particles. For this purpose, pullout tests using biaxial and triaxial geogrids were simulated using the coupled discrete element method (DEM) and finite difference method (FDM). In this coupled model, two real-shaped geogrid models with square and triangular apertures were established using the solid element in FLAC3D. Meanwhile, simplified shaped clumps were used to represent the ballast using PFC3D. The calibration test simulation showed that the accurately formed geogrid model can reproduce the deformation and strength characteristics of a geogrid. The pullout simulation results show that the DEM-FDM method can well predict the relationship between pullout force and displacement, which is more accurate than the DEM method. For ballast particles of 40 mm in size, both the experiment and simulation results showed that the triaxial geogrid of 75 mm is better than the 65-mm biaxial geogrid. In addition, the DEM-FDM method can study the interaction mechanism between the particles and the geogrid from a microscopic view, and also reveal the similar deformation behavior of the geogrid in the pullout process. Therefore, the DEM-FDM coupled method can not only investigate the interlocking mechanism between the ballast and particles but can also provide a great method for evaluating the performance of different types of geogrids.  
D 2021 11 9001 10.1001.  
In contrast with the above continuous element methods, the discrete element method has been frequently used to study the interaction between geogrids and soil [13; 14; 15; 16]. The geogrid has been modeled using a set of bonded particles to form the geogrid's true shape and the surrounding soil particles have been modeled using clumps or balls. Through analyzing the contact between the particles and the bonded particles in the geogrid, the discrete element method can well simulate the interaction between the geogrid and the surrounding soil. Although the microscopic parameters of geogrids composed of bonded particles can be obtained through a series of index calibration tests [17; 18], it is difficult to intuitively show stress-strain characteristics similar to those of a real geogrid, which makes it difficult to capture the real deformation characteristics of the geogrid in pullout simulations. To combine the advantages of these continuous and discontinuous methods, the discrete/continuous coupled numerical method can be used to simulate the interaction between the geogrid and the surrounding soil. [PERSON] et al. [19; 20] developed a 3D finite-discrete element framework to model the interaction between a geogrid and soil under pullout conditions. In addition to simulating the pullout testing of a geogrid, this framework was also used to simulate the reinforcement of the foundation by the geogrid [21].  
In this paper, the DEM-FDM coupled method was used to model the pullout test, taking into account both continuous and discontinuous elements. Using the coupled method, the ballast particles can be modeled using irregularly shaped clumps in PFC3D, and the biaxial and triaxial geogrids can be modeled using the continuous element in FLAC3D. The above method can not only effectively simulate the interaction between the geogrid and the surrounding soil, it can also conveniently study the deformation behavior of the geogrid. Compared with the experimental data, the numerical simulation results show that the coupled method can not only better predict the development of pullout force but can also be used to study the detailed response of the geogrid and surrounding ballast. This numerical method provides new insights into geogrid interlocking behavior and the optimization of the geogrid reinforcement effect.