## 5 Effects of Reinforcement Length
### Lateral Displacements at Wall Facing  
At the end of construction, the horizontal displacement ratios (dx/H) taken from the wall facing of the GRS-IB models with a different length-to-height ratio of reinforcements are shown in Figure 5. The figure shows three points at the wall facing: (1) at the base, (2) at the mid-height, and (3) at the top of the wall. The results show that maximum lateral displacements occurred at the top of the wall and the least at the base of the wall. It can be observed that the least reinforcement length, with the length-to-height ratio of 0.3H, was obtained the highest dx/H. The dx/H value gradually decreases as the reinforcement lengths increase from 0.3H to 1.1H. Thus, the reinforcement length-to-height ratio of 1.1H obtained the least dx/H at the end of construction. According to [PERSON] [7], one of the factors that affect the magnitude of lateral displacement at wall facing is the reinforcement length. Generally, the increase in the length-to-height ratio of reinforcements from 0.5H to 0.7H decreases the lateral displacements of the MSE wall by 50% (rough estimate) during the construction. In this study, the wall is modeled with 0.90 m thick FHR facing and GRS wall abutment; hence the increase in the length-to-height ratio of reinforcements from 0.5H to 0.7H decreases the lateral displacements at the wall by only 10%. In addition, the increase on the length-to-height ratio of reinforcements from 0.3H to 1.1H decreases the maximum lateral displacements at the wall facing by 29%. Note that the lateral displacements at the wall facing presented in the figure have been carried from the beginning of the construction and were not set to zero at the end of construction.  
The same behavior can be observed at the mid-height of the wall facing but with lesser values than those at the top of the wall. It can be observed that the least reinforcement length, with the length-to-height ratio of 0.3H, obtained the highest dx/H. The dx/H value gradually decreases as the reinforcement lengths increase from 0.3H to 1.1H. Thus, the reinforcement length-to-height ratio of 1.1H obtained the least dx/H at the end of construction. At mid-height, the increase in the length-to-height ratio of reinforcements from 0.5H to 0.7H decreases the lateral displacements at the wall by 5%, which is equivalent to half of that at the top of the wall. In addition, the increase on the length-to-height ratio of  
Figure 5: Lateral Displacement Ratio at Wall Facing.  
reinforcements from 0.3H to 1.1H decreases the lateral displacements at mid-height of the wall facing by 17%.  
Moreover, it can be observed that the length-to-height ratio of reinforcements has no visible effects at the base of the wall. In this case, the increase on the length-to-height ratio of reinforcements from 0.3H to 1.1H decreases the lateral displacements at the base of the wall by less than 1%. The total reinforcement length (L) required for internal stability is determined by adding the nonacting Rankine length (Lr) and the embedment length (Le) beyond the potential failure surface [7,34]. The calculation suggests that the minimum required reinforcement length can be used at the base of the wall because the theoretically-calculated values of Lr and Le are minimal. Based on the internal stability calculation for extensible reinforcement like geosynthetics, the minimum requirement for the reinforcement length at the wall base is less than 0.3H. Thus, in this case, the reinforcement length longer than 1.80 m may not have any remarkable effect on the lateral displacements at the wall facing. This explains why the length-to-height ratio of reinforcement from 0.3H to 1.1H has no visible effects at the base of the wall, as shown in Figure 5.