## 2 Numerical Modelling Using Plaxis 2D
### Description of the Bridge Models
#### 2.1.1. GRS-IBS Model Design  
The GRS-IBS model is designed according to FHWA-HRT-11-026 [8] and is checked to satisfy the internal and external stability based on [PERSON] [17], FHWA-HRT-11-026 [8], FHWA-HRT-11-027 [1], FHWA-NHI-10-024 [4], and [PERSON] [18] (see Figure 3b). The GRS-IBS includes a GRS abttment, reinforced soil foundation (RSF), bearing bed reinforcement, bridge seat, and an integrated approach. In this study, the bridge is assumed to have a clear span length of 15.0 m in order to accommodate four-lane traffic under the bridge and a clear height of 5.3 m, just enough to pass the FHWA minimum vertical clearance for roadways which is specified as 4.3-4.9 m. The bearing width (\(b\)) used is 1.5 m (\(>\)0.762 m minimum), similar to the design of [PERSON]'s GRS IBS [15]. The setback distance (\(a_{b}\)) between the back of the wall facing and the beam seat used is 250 mm. The minimum clear space (\(de\)) or gap between the top of the uppermost facing block and the bottom of the girder (superstructure) is considered to be 100 mm (\(>\)76 mm min). The minimum base width including the block face (_Btotal_) for the bridge span length (_Lspan_) greater than 7.62 m (25 ft) is 1.83 m (6 ft). The author chose _Btotal_ = 3.6 m (\(\approx\)0.6 \(H\)), which also satisfies the minimum base-to-height (_Btotal/H_) ratio of 0.3. The RSF is composed of granular fill  
Figure 3: Design details of each model case: (**a**) GRS-IB; (**b**) GRS-IBS; and (**c**) IB Model. material that is compacted and encapsulated with geotextile. The depth of the excavation for the RSF (\(D_{RSF}\)) is equal to 0.25 \(Btotal=0.9\) m. The total width of the RSF (\(B_{RSF}\)) is equal to 4.5 m, which extends in front of the wall face by one-fourth of the width of the base. In this study, there are two intermediate reinforcements added inside the RSF, similar to the design of [PERSON]'s GRS-IBS [15]. The length of the lowest reinforcement layer at the base of the abutum is equal to 3.6 m (0.43 \(H\)), which is more than the width of the base (\(B\) = 3.1 m, excluding the block face) but more than the minimum base-to-height (\(B\)/\(H\)) ratio (excluding the block face) of 0.3. The CMU blocks used in this study have a width of 0.5 m and thickness of 0.2 m. [PERSON] et al. [15] specifies that after the base length of the reinforcement has been chosen (in this case it is equal to 3.6 m), the reinforcement length should follow the cut slope (in this study it is assumed to be 1:1) up to a \(B\)/\(H\) ratio of 0.7. In this study, the length of the uppermost reinforcement layer in the abutum is assumed to be equal to 6.5 m (0.9 \(H\)), which is higher than the recommended. From the base, the reinforcement length can become progressively longer in the reinforcement zones. The vertical spacing between reinforcements is assumed to be 0.2 m for the first four layers from the base and then 0.4 m for the succeeding layers until the bottom layer of the bearing reinforcement zone. Then, the vertical spacing for the main reinforcement layers at the final zone is 0.2 m. A bearing reinforcement zone is added underneath the bridge seat to support the bridge loads. The vertical spacing for the bearing bed reinforcement is half the primary vertical spacing, which is 0.1 m. The bearing bed reinforcement length is equal to 2.0 m, which is two times the setback (\(a_{b}\)) plus the width of the bridge seat (\(b\)). In this study, there are six bearing bed reinforcement layers, which is sufficient and more than the stipulated minimum. At the integrated approach, the gravelly backfill layers at the beams are wrapped with geotextiles without joints to form a smooth transition from the bridge superstructure. One intermediate reinforcement is added between the main integrated approach reinforcement layers. Here, there are three wrapped layers with a height of 0.30 m and the total reinforcement length is 10 m from the face of the superstructure (girder).