## 4 Results and Discussion
### Full-Scale Model Results
#### 4.1.3 Failure Load  
As presented in Figure 9, the maximum tensile force in the reinforcement bars was 31,823 N at a test load of 300 kN/m\({}^{2}\). When the load level was 302 kN/m\({}^{2}\), the maximum tensile force in the reinforcement layers was 31,881 N, which was higher than the ultimate tensile force of 31,850 N. Thus, at that moment, failure occurred in the MSE wall. The longitudinal steel bars suddenly ruptured at the drilled cross-sectional area where the tensile force reached its maximum value in the reinforcement bars.  
Figure 9: _Cont._  
The failure load was determined to be 302 kN/m\({}^{2}\), which was 15 times greater than the design load. In terms of the load-bearing capacity, the MSE wall structure in the experimental model could resist very high surcharge loads. However, in terms of long-term serviceability, the selected steel bars would be appropriate for the structure durability during a service life of 100 years under a design load of 20 kN/m\({}^{2}\)[3].  
At a failure load level of 302 kN/m\({}^{2}\), the failure surface in the reinforced soil could be determined by connecting the maximum tensile force points in each reinforcement layer. Figure 10 demonstrates that the failure surface in this study was similar to the Rankine theory [2]. In detail, in the first half of the wall, the failure surface started from the top of the wall and further away from the wall face at approximately 0.3 H. In deeper positions, the failure surface stopped at the toe of the wall (wall base). This failure pattern was similar to the reports of [PERSON] et al. [2], [PERSON] et al. [8], [PERSON] and [PERSON] [7], [PERSON] and [PERSON] [36], and [PERSON] [11]. However, the failure surface at the toe of the wall was far from the wall facing (0.2 H). [PERSON] and [PERSON] [7] explained that friction between the rigid foundation of an MSE wall and the soil reinforcement affects the failure surface of the reinforced soil mass.  
Table 5 illustrates the length of the reinforcement bars in the failure zone L\({}_{\text{a}}\) in this study and the values calculated from the standards from AFNOR [12]. The L\({}_{\text{a}}\) values in reinforcement layers 4, 3, and 2 were close to the theoretically estimated values. The failure surface of the lowest layer was slightly different due to the strain gauge locations.  
Figure 9: Tensile force distribution in different studies: (**a**) [PERSON] and [PERSON] [7]; (**b**) [PERSON] and [PERSON] [28]; (**c**) this study.  
In summary, the failure surface in this full-scale MSE model using a cohesive backfill soil and self-fabricated steel reinforcement was in good agreement with other studies as well as most of the current standards [12; 13; 37]. Hence, a self-fabricated steel reinforcement and locally available backfill soil could be used as the reinforcement material for MSE walls applied in the conditions of Vietnam.  
The correlation equation between the maximum tensile force in the reinforcement bars (\(F\)) and the depth (\(z\)) measured from the top of the wall is illustrated in Figure 11 and is shown in Equation (5). The parabolic shape of the failure surface in the reinforced soil in this study was similar to the reports of [PERSON] and [PERSON] [7] and [PERSON] et al. [35].  
Figure 10: Failure surface in the reinforced soil mass.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Depth (m)**} & \multirow{2}{*}{**Reinforcement Layer**} & \multicolumn{2}{c}{**Full-Scale Model Results**} & \multicolumn{2}{c}{**Current Standards**} \\ \cline{3-6}  & & **L\({}_{\mathbf{a}}\) (cm)** & **L\({}_{\mathbf{e}}\) (cm)** & **L\({}_{\mathbf{a}}\) (cm)** & **L\({}_{\mathbf{e}}\) (cm)** \\ \hline
0.375 & 4 & 95 & 115 & 90 & 120 \\
1.125 & 3 & 95 & 115 & 90 & 120 \\
1.875 & 2 & 60 & 150 & 67.5 & 142.5 \\
2.625 & 1 & 60 & 150 & 22.5 & 187.5 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The length of reinforcement bars in the failure zone and backfill zone.