## 3 Numerical Modeling  
### Model Description  
In this study, the integrated bridge with GRS abutment and FHR facing in staged-construction (GRS-IB) is modeled and analyzed using Plaxis 2D AE.02 Version 2013 program. The design details of the GRS-IB model are taken from the Won and Langcuyan [17]. The GRS-IB model includes a GRS abutment, reinforced soil foundation (RSF), FHR facing, and RC footing. The FHR facing is the substructure that is continuously connected to the superstructure of the RC bridge girder, eliminating the joints and bearings, thus forming an integral bridge structure. The FHR facing has a width of 0.9 m, a footing width of 1.35 m, and a thickness of 0.9 m. The RSF extends by 1.0 m from the toe of the FHR footing. The abutment has a cut slope of 1:1. The bridge loads are supported directly by the FHR facing. The FHR facing is connected to the GRS RW abutment. The abutment uses gravel bags placed at the facing, compacted to a thickness of 0.1 m and a width of 0.4 m. Similar to the reference studies, only the right-hand side of the bridge and abutment is considered. This method of modeling the free-standing geometry of the GRS bridge abutment was also used by [PERSON] et al. [18; 19], [PERSON] et al. [20; 21], [PERSON] [17], and [PERSON] [22]. The integrated approach backfill and the RC bridge girder are removed and converted into their equivalent vertical loads. Thus, the height (H) of the abutment was left at 6.3 m from the base of the wall. As a result, the right-hand side of the GRS-IB model (referred to as Case 1 throughout this paper) is shown in Figure 1a, and its corresponding numerical model using Plaxis 2D is shown in Figure 1b. In addition, the conventional integral bridge (IB) model is included in the study to show the effects of having an IB system without the geosynthetics reinforcement in the abutment. The configuration of the IB model is based on the GRS-IB model, which includes RSF, FHR facing, and RC footing. The design details of the IB model are also taken from the [PERSON] and Langcuyan [17]. Similar to the GRS-IB model, the IB model has a precise span length of 15.0 m and a clear height of 5.3 m. Here, the FHR facing has a width of 0.9 m, a footing width of 4.85 m, and a thickness of 0.9 m. In this design, the RSF extends 1.0 m from the toe of the FHR footing and 1.0 m from the heel of the FHR footing. The FHR footing is wider than the GRS-IB model because the IB model has no GRS abutment. Similarly, the right-hand side of the IB (referred to as Case 2) model is shown in Figure 2a, and its corresponding numerical model using Plaxis 2D is shown in Figure 2b. Figure 1: Design and Plaxis 2D Numerical Model for GRS-IB (Case 1). (**a**) Model Design for GRS-IB. (**b**) Plaxis 2D Numerical Model for GRS-IB. The numerical models are designed with sufficient horizontal and vertical distance from the right end and bottom boundaries, respectively. The horizontal distance from the right end to the wall facing is more than three times the height of the wall. The vertical distance from the base of the wall to the bottom boundary is almost twice the height of the wall. The front boundary is 7.5 m from the wall facing, which is equivalent to half of the bridge, whose clear width is 15 m. Consequently, the boundary conditions are modeled where the vertical sides of the models at \(X=0\) and \(X=30\) are fixed on X-direction. The bottom boundary at \(Y=-12\) is fixed on both X- and Y-direction. In other words, a fixed boundary condition is applied at the bottom of the model, while a roller boundary condition is applied on both vertical sides of the model. The FEM models of the bridge abt  
Figure 2: Design and Plaxis 2D Numerical Model for IB (Case 2). (**a**) Model Design for IB. (**b**) Plaxis 2D Numerical Model for IB.