## 4 Results and Discussion  
### Interaction Behavior between Particles and the Geogrid  
Figure 6 shows the comparison of the pullout force of biaxial and triaxial geogrid samples under 0.5 kN surcharge and compares the DEM results [26] and DEM-FDM results with the experimental results [17]. It clearly shows that the triaxial geogrid with an aperture of 75 mm has better pullout resistance than the biaxial geogrid with an aperture of 65 mm, which is consistent with previous studies. However, it appears that the DEM simulations underestimated the pullout force of the biaxial geogrid after a displacement of approximately 20 mm, and the pullout force of the triaxial geogrid was not predicted well after a displacement of approximately 25 mm. Compared with the DEM results, the DEM-FDM results exhibit higher consistency with the experimental curves, which proves that the DEM-FDM coupled method is better than the DEM method in simulating the pullout behavior of geogrids, especially for the triaxial geogrid. Figure 6: Comparison of geogrid pullout resistance between experimental and simulation results. Comparing the DEM-FDM results and the experimental results, it can be found that the pullout force of the biaxial geogrid reaches the peak after a certain displacement (about 25 mm), and then remains at a stable value. In contrast, the pullout force of the triaxial geogrid increases continuously with the increase of pullout displacement, which indicates that the triaxial geogrid has the potential to increase the pullout force after a 50-mm pullout displacement. The evolution of the contact forces between the particles and geogrid stress during pulling is shown in Figure 7. Each contact force between particles is represented at the contact point by a gray cylinder in the direction of the force, of which the diameter depends on the value of the force and of which the length is proportional to the distance between their centres. All graphs use the same scale factor. Figure 7 displays the strong contact forces in the vicinity of the biaxial geogrid area, which clearly shows the interlocking effect, which is consistent with previous DEM simulations [26]. It can also be seen that in the pullout process, a stress arch is gradually formed around the geogrid, indicating an interlocking effect between the geogrid and the ballast. Comparing the size and distribution of the force chain, it can be concluded that the force chain formed around the triaxial geogrid seems to be larger at the same pullout displacement, indicating that the triaxial geogrid has a better reinforcement effect than the biaxial geogrid. Arching around the geogrid at the front of the box is clearly observable in both models, indicating resistance to pulling. Therefore, the corresponding geogrid area suffered stronger stress, especially in the later stage during pullout. By contrast, at the same stage, the simulation with the triaxial geogrid (Figure 7b) shows larger stress than that with the  
Figure 7: Contact force network and geogrid stress at different pullout displacement: (**a**) biaxial geogrid and (**b**) triaxial geogrid. biaxial geogrid (Figure 7a), which can be attributed to the triangular aperture facilitating stronger interlocking than the square aperture. In order to quantitatively analyse the contact force distribution between particles during pullout, the contact information for the geogrid-reinforced ballast was extracted and analysed, as shown in Figure 8. The sum of all contact forces in each direction interval was measured, and the number and the average value of all contacts were recorded. At the initial stage of the pullout, the contact force vector between ballasts was mainly observed in the vertical direction owing to the self-weight of the ballast and the vertical surcharge. With the progress of the pullout, the horizontal contact force gradually increased and gradually diffused from 0\({}^{\circ}\) to 45\({}^{\circ}\).