## 3 DEM-FDM Coupled Modeling of Pullout Test
### DEM-FDM Coupled Model of Pullout Test  
Figure 5 shows the DEM-FDM coupled model of the large box pullout test, which was performed using the combination of PFC6.0 and FLAC6.0. The dimensions of the pullout box and the geogrid size and position are the same as those used in the laboratory. The pullout model mainly contains two parts, an idealized-shape clump in PFC3D to represent the ballast particle and the solid element in FLAC3D to represent the geogrid, of which the mechanical behavior and calibration were described above. In order to compare the pullout performance of the biaxial and triaxial geogrids, the effective reinforcement area of the biaxial geogrid sample (with 12 apertures of 65 mm) and the triaxial geogrid sample (with 20 apertures of 75 mm) were almost the same in laboratory tests and simulations, at 50.7 and 48.7 cm\({}^{2}\), respectively, as shown in Figure 5c. This idealized-shape model is expected to offer an irregular shape using the least number of spheres necessary to provide particle interlocking. It has been proven that the simplified two-ball clump approach can provide similar interlocking effects between particles [17]. A more complex shape of  
Figure 3: Calibration test simulation and calibration results: (**a**) a single rib test of triaxial geogrid; (**b**) single rib test of biaxial geogrid and (**c**) force-strain curve.  
particles would increase the computational time but not influence the comparison of the general interlocking behavior of geogrids.  
The simulation procedures followed the sample preparation performed in the experiment. First, ballast particles were generated in the lower half of the box and then recycled to equilibrium. Then, two frictionless walls were placed in the middle of the box, and then the geogrid mesh was imported and placed between the above two walls. Because there  
Figure 4: The buckling of the FLAC triaxial geogrid model under compression: (**a**) top view and (**b**) front view.  
Figure 5: DEM-FDM of large box pullout test: (**a**) embedded geogrid specimen and simulated surcharge; (**b**) 2-ball clump used in the simulation and (**c**) FDM geogrid model used in the simulation.  
will be large contact forces at the initial stage of ballast particle generation, two protective walls on both sides of the geogrid were used to protect the geogrid. Next, another portion of the ballast particles were generated in the upper space of the geogrid and cycled until they were balanced. After that, a wall was formed on the upper surface of the ballast to prepare for further surcharge loading. Finally, the protective wall was deleted and the whole sample was cycled to equilibrium. The top surcharge of 0.5 kN was achieved using a static load.  
In PFC3D, the size of the non-spherical clump is defined as the equivalent diameter of a sphere with the same volume. The 2-ball clump, as shown in Figure 5b, has the equivalent volume of a sphere of 40-mm dimensions. The specimen contained approximately 1600 two-ball clumps with a mean size \(D_{50}\) of 40 mm and a coefficient of uniformity \(C_{u}\) of 1.0, as shown in Figure 5a. This can be considered satisfactory as ballast is usually reasonable uniformly graded to provide large enough voids to facilitate good drainage. The normal and shear stiffness of the particles were 1.0 \(\times\) 10\({}^{8}\) N/m and the stiffnesses of the walls were set at the same values as those of the particles. The clump, wall and geogrid friction coefficients were all set to be 0.6. The density of the ballast particles was 2600 kg/m\({}^{3}\). A constant horizontal pullout rate was given to the right-hand node at the end of the geogrid. To avoid any dynamic effects, the pullout rate was gradually increased linearly with time from zero to the final rate at the initial 1-mm displacement. The simulation was terminated when the total pullout displacement reached 50 mm. In the simulation process, the pullout force and pullout displacement were recorded.