# Effect of Boundary Conditions on the Mechanical Behavior of the Geogrid-Soil Interface
## 3 Results and Discussion
### Growth Pattern and Fitting of Pullout Resistance under Different Boundary Conditions  
The plot of the pullout displacement vs. pullout resistance and the growth pattern of pullout resistance subjected to four types of boundary conditions were shown in Figures 10-13, respectively. The curve of pullout resistance versus pullout displacement obtained from geogrid-soil interface under top rigid and positive rigid boundary condition (T(R)&P(R)) and top flexible and positive rigid boundary condition (T(F)&P(R)) presented strong strain-hardening behavior, as shown in Figures 10a and 11a. In contrast, the curve characteristic of the reinforced interface under top rigid and positive flexible boundary condition (T(R)&P(F)) and top flexible and positive flexible boundary condition (T(F)&P(F)) presented slight strain-softening behavior, as shown in Figures 12a and 13a. Moreover, it was found that the pullout resistance under four types of boundary conditions was directly proportional to the value of the normal stress and that the pullout resistance increased with the rise in the vertical stress. Figure 9: The plot of boundary reduction coefficient (_BRC_) of top and positive boundary. Figure 11: (**a**) The pullout displacement versus pullout resistance under T(F)&P(R); (**b**) the growth pattern of pullout resistance under T(F)&P(R). Figure 12: (**a**) The pullout displacement versus pullout resistance under T(R)&P(F); (**b**) The growth pattern of pullout resistance under T(R)&P(F). Figure 10: (**a**) The pullout displacement versus pullout resistance under T(R)&P(R); (**b**) the growth pattern of pullout resistance under T(R)&P(R). With increasing of the normal loading, the growth patterns of the pullout resistance were almost similar under four types of boundary conditions, as presented in Figures 10b, 11b, 12b and 13b, respectively. In accordance with the growth patterns, the pullout resistance could also be separated into two regions, such as region I and region II. In the region I, the pullout resistance under four types of boundary conditions was different, but the increment was almost the same, about 0.8 kN. In the region II, the growth rate of pullout resistance decreased obviously, but the pullout resistance was still showing an increasing trend. Hence, it can be concluded that the boundary conditions could affect the magnitude of pullout resistance, but the impact of boundary conditions upon the increment of pullout resistance was little. In addition, the polynomial fitting was also used to analyze the relationship between the normal loading ranging from 80 to 200 kPa and the pullout resistance under four types of boundary conditions. The polynomial fitting curve and equations were shown in Figures 10b, 11b, 12b and 13b and Table 2, respectively. According to the fitting equations, the maximum pullout resistance corresponding to the normal loading could be calculated. Under (T(R)&P(R)), the maximum pullout resistance was 10.90 kN, and the corresponding normal loading is 186.0 kPa. Under (T(F)&P(R)), the maximum pullout resistance was 10.88 kN, and the corresponding normal loading is 173.1 kPa. Under (T(R)&P(F)), the maximum pullout resistance was 5.981 kN, and the corresponding normal loading is 185.0 kPa. Under (T(F)&P(F)), the maximum pullout resistance was 5.986 kN, and the corresponding normal loading is 186.0 kPa. Based on the above fitting results, the safety of the boundary reduction coefficient (\(BRC\)) obtained by Section 3.1 was also evaluated. Under the (T(F)&P(R)), the vertical loading corresponding to the maximum pullout resistance was 173.1 kPa, which was greater than 100 kPa. Hence, the \(BRC\)-T could be taken as 0.9. By reducing the results under (T(R)&P(R)), the maximum pullout resistance used for design was 9.81 kN under (T(F)&P(R)), which was less than the fitting results of 10.88 kN, and the safety factor was 1.1. Therefore, the \(BRC\)-T of the top boundary was reliable. Additionally, under the (T(R)&P(F))