## 3 DEM-FDM Coupled Modeling of Pullout Test
### Calibration of FDM Geogrid Model  
In order to obtain quantitatively reliable mechanical behavior, these geogrid models need to be calibrated. In previous DEM studies [14; 15; 16; 17; 18], the determination of the values of these parameters was a complex task, considering the stiffness and the friction coefficient \(f\) of the spheres constituting the geogrid. Moreover, the parameters of the bonds control the flexibility and strength of the geogrid, and their adjustment requires different experiments, in which each parameter or group of parameters acts independently. However, the mechanical parameters of the FDM geogrid model using FLAC3D are directly related to the polymer material, which can be regarded as a homogeneous elastic-plastic model. To reflect the stress-strain characteristics of the geogrid, the elastic-plastic model is used in the geogrid model, the calibration of which does not present any challenge.  
Following previous studies [17; 18; 26], the single rib tensile test was conducted to calibrate the stiffness and strength of biaxial and triaxial geogrids. For the biaxial geogrid model, the force at failure for a single rib test is 1.37 kN at a failure strain of 10.5% [17]. For the triaxial geogrid model, the force at failure for a single rib extension test is 1.18 kN at a failure strain of 8.9% [28]. Because biaxial and triaxial geogrid models are made of the same polymer materials, the same material parameters are used. However, when using the same numerical parameters, it is difficult to find agreement between the calibration test results and the single rib test results of both biaxial and triaxial geogrids. Figure 3a,b show the differences in rib length and nodes between the two types of geogrids. Even though the data shown in Figure 3c do not seem to match very well with the reported failure force and strain (less than 10%), a better calibration of the grid would not change the general behavior in terms of aggregate-geogrid interlocking. Figure 3 shows the geometries of the  
Figure 2: Comparison of geogrid models: (**a**) DEM biaxial geogrid; (**b**) DEM triaxial geogrid; (**c**) FDM biaxial geogrid; (**d**) FDM triaxial geogrid and (**e**) FDM geogrid rib from a side view.  
calibration test and the calibration results of the geogrid models. The parameters are as follows: [PERSON]'s modulus \(E\) is 800 MPa, [PERSON]'s ratio \(v\) is 0.3 and yield strength \(\sigma^{t}\) is 134 MPa.  
Apart from the stiffness of the geogrid, geogrid out-of-plane stiffness, or flexural rigidity, is another geogrid property, which can be used to evaluate the out-of-plane deformation of geogrids under their own mass, when these are extended over the edge of a planar surface. [PERSON] et al. [28] performed a compression test of a geogrid in the laboratory and a DEM compression test of a single-layer geogrid. Although this test is only performed on geogrids for manufacturing quality control purposes, it is a useful qualitative indicator used to assess the geogrid models. When the geogrid specimen was horizontally compressed from both sides, the middle part of the geogrid was arched. However, the DEM geogrid model only deformed in the geogrid plane and no arching occurred out of the plane as shown in Figure 4. On the contrary, the FDM triaxial geogrid model with 54 apertures in this study shows asymmetric buckling under compression, which is similar to the buckling observed experimentally. These comparisons indicate that the mechanical behavior of geogrids can be reproduced using the FDM geogrid model that can transmit forces and moments; therefore, the calibrated set of parameters is acceptable.