## 3 Numerical Analysis Results and Discussion under Static Loading
### Vertical Displacements at the Top of the Wall Adutment  
2.1 Effects of the Wall Facing Type and Construction on Vertical Displacements at the Top of the Wall Adutment  
The vertical displacements (\(dy\)) at the top of the wall abutment at the end of the bridge construction (Case 1A, 2A, 3A) after the applied general traffic loading (Case 1B, 2B, 3B) and railway loading (Case 1C, 2C, 3C) are shown in Figure 9. In the figure, the horizontal distanceS (\(x\)) from the wall facing from 0.90 m (for Case 1A-C and Case 3A-C) and 0.50 m (for Case 2A-C) until 7.8 m and 11.2 m are the reinforced zone and backfill soil zone, respectively. The horizontal distance (\(x\)) beyond 11.2 m from the wall facing is the retained soil zone where \(dy\) is the same from that point towards the end boundary at 22.5 m from the wall facing. The vertical displacements (\(dy\)) shown in the figures are carried over from the start of the construction until the end of the bridge construction, without any corrections;  
Figure 8: Lateral displacement ratio, \(dxR\), at the wall facing, showing the increase of \(dx\) after the applied surcharge loads. in other words, there is no reset of vertical displacements done in the Plaxis 2D staged construction mode. The results show that the GRS-IB (Case 1A-C) models obtained the maximum _dy_ of 65.72 mm, 70.95 mm, and 85.18 mm, located at 1.80 m, 1.95 m, and 2.40 m from the wall facing after the integral bridge construction (Case 1A), applied general traffic loading (Case 1B), and applied railway loading (Case 1C), respectively. Moreover, the GRS-IBS (Case 2A-C) models obtained the maximum _dy_ of 84.26 mm, 95.32 mm, and 106.01 mm after the integral bridge construction (Case 2A), applied general traffic loading (Case 2B), and applied railway loading (Case 2C), respectively, located at 1.80 m from the wall facing. Lastly, the IB (Case 3A-C) models obtained the maximum _dy_ of 31.09 mm, 34.57 mm, and 44.30 mm after the integral bridge construction (Case 3A), applied general traffic loading (Case 3B), and applied railway loading (Case 3C), respectively, located at 3.91 m and 4.31 m from the wall facing. Nevertheless, the _dy_ at the top of the authentic in the GRS-IB (Case 1A-C), GRS-IBS (Case 2A-C), and IB (Case 3A-C) models are less than the allowable vertical displacement of 0.5% (_dy/x_). The GRS-IBS models exhibited the greatest vertical displacements compared to those of the GRS-IB and IB models, which are located at the bridge seat, specifically at 1.80 m from the wall facing. In addition, the results show that the GRS retaining wall abutment of the GRS-IB and GRS-IBS models exhibited greater vertical displacements than those of the unreinforced IB models. This may be attributed to the effects of the wall facing type and construction. Similar to the lateral displacement behavior at the wall facing, the type of wall facing and its construction also greatly affect the vertical displacement behavior of the models and the magnitude of the vertical displacements increases as the applied loading increases. At this point, each bridge design shall be compared to better understand its corresponding vertical displacement behavior. First, we will discuss the GRS-IB versus IB models. The results show that the GRS-IB (Case 1A-C) models exhibited twice as much vertical displacements than those of the IB (Case 3A-C) models despite having the geosynthetic reinforcements. This is because during the construction of the GRS-IB models, the GRS wall abutment was constructed without the FHR facing. The gravel bags and  
Figure 9: Vertical displacements at the top of the wall abutment, _dy_ (mm): (**a**) Case 1A, 2A 3A (end of bridge construction); (**b**) Case 1B, 2B, 3B (general traffic loading); and (**c**) Case 1C, 2C, 3C (railway loading). geosynthetic-wrapped facing of Case 1A-C are flexible and as a results of the increasing lateral earth pressures during construction, the wall facing greatly moved outwards and exhibited more deformation than the FHR facing, thus inducing more _dy_ in the backfill soil zone.