# Effect of Boundary Conditions on the Mechanical Behavior of the Geogrid-Soil Interface
## 4 Conclusions  
This study used HDPE geogrid-reinforced coarse sand to conduct a series of lab pullout tests. The impacts of numerous parameters on the mechanical behavior of the geogrid-soil interface, including boundary conditions and normal loads, were investigated. Additionally, the boundary reduction coefficient (\(BRC\)) was obtained and verified by fitting results. The following conclusions were obtained.  
(1) The mechanical behavior of the geogrid-soil interface was impacted by both the top and positive boundary conditions, with the positive boundary having a substantially bigger effect on pullout resistance than the top boundary condition. The track of particle movement and stress concentration was the responsible.  
(2) With the rise in the normal loads, the effect of the top boundary decreased gradually. The flexible boundary should be taken for the design of structures, especially for positive. When the normal loading was up to 120 kPa, the \(BRC\)-T and \(BRC\)-P can be taken as 0.9 and 0.5, respectively.  
(3) The pullout curve under (T(R)&P(R)) and (T(F)&P(R)) presented strong strain- hardening behavior, while (T(R)&P(F)) and (T(F)&P(F)) presented slight strain-softening behavior.  
(4) The growth patterns of the pullout resistance were almost similar under four boundary conditions, and the pullout resistance could also be divided into two regions. The boundary conditions affect the pullout resistance, while the vertical loading matching the maximum pullout resistance was not related to boundary conditions.  
(5) The apparent cohesion of the geogrid-soil interface was greatly affected by the boundary conditions, while the apparent friction angle was largely unaffected.  
In this paper, the normal static loading was used in the test. In addition to static loading, the reinforced soil structures were generally subjected to dynamic loading. The follow-up work will study the influence of dynamic loading and boundary conditions on the geogrid-soil interface.  
Writing--original draft preparation, Z.Z.; writing--review and editing, G.Y.; validation, Z.W. and H.W.; funding acquisition, J.J. All authors have read and agreed to the published version of the manuscript.  
Figure 15: The variation laws of apparent cohesion and apparent friction angle under different boundary conditions.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Boundary** & **Fitting Equation** & **Apparent** & **Apparent Friction** \\
**Conditions** & & **Cohesion/kPa** & **Angle/Degree** \\ \hline T(R)\&P(R) & \(y=0.103x+15.46\) (\(R^{2}=0.99\)) & 15.46 & 5.88 \\ T(F)\&P(R) & \(y=0.111x+8.56\) (\(R^{2}=0.99\)) & 8.56 & 7.41 \\ T(F)\&P(F) & \(y=0.101x+2.34\) (\(R^{2}=0.99\)) & 2.34 & 5.77 \\ T(R)\&P(F) & \(y=0.110x+0.68\) (\(R^{2}=0.99\)) & 0.68 & 6.28 \\ \hline \hline \end{tabular} where \(y\) is shear stress of the geogrid-soil interface, \(x\) is the normal loading.  
\end{table}
Table 3: Shear strength parameters under four types of boundary conditions.  
**Funding:** This research was supported by the National Natural Science Foundation of China (NSFC) (grants Nos. 52079078 and 51709175), Scientific Research Foundation for the Returned Overseas Scholars of Hebei Province (grant No. CL201722), Natural Science Foundation of Hebei Province (grant No. E2018210097 and E2019208159), Science and Technology Research Projects of Universities in Hebei Province (grant No. QN2018255), and Scientific and Technological Research Projects of Colleges and Universities in Hebei Province (grant No. BJ2020045).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.  
**Conflicts of Interest:** The authors declare no conflict of interest.