## 3 Numerical Modeling
### Material Parameters  
#### 3.2.1 Soil Material Input Parameters  
The properties of the soil materials used in this study are summarized in Table 1. The soil backfill is a gravelly material. The constitutive model used to simulate the behavior of the soil backfill is the hardening soil (HS). The HS model is an advanced model for the simulation of soil behavior. It is an elastoplastic hyperbolic model that accounts for stress-dependency of stiffness moduli, which results in an appropriate behavior of the granular soil during the loading stage. In the HS model, the soil stiffness is defined more accurately by using three different parameters: (1) secant stiffness in standard drained triaxial test \(\mathrm{E}_{50}^{\mathrm{ref}}\), (2) tangent stiffness for primary oedometer loading \(\mathrm{E}_{\mathrm{oed}}^{\mathrm{ref}}\), and (3) unloading and reloading stiffness, \(\mathrm{E}_{\mathrm{ur}}^{\mathrm{ref}}\), which is by default equal to 3 \(\times\)\(\mathrm{E}_{50}^{\mathrm{ref}}\)[23; 24]. Several related studies have also used the HS model to simulate the backfill soil, including [PERSON] et al. [18], [PERSON] et al. [20; 21], and [PERSON] et al. [27; 28]. In this study, the parameters used for the backfill soil were taken from [PERSON] et al. [20] and [PERSON] [17].  
The granular soil inside the gravel bags is assumed to have the same parameters as the adjacent backfill soil to avoid the complexity of the results. Since both materials are compacted and placed in a similar manner, the parameters are reasonably expected to be similar. The soil foundation and the retained original soil are modeled using linear elastic (LE). Both are assumed to have stiff properties to eliminate the influence of foundation deformation on the behavior of the bridge models. In addition, the influence of the pore water pressure was not considered in the analysis. Thus, all soil materials are modeled with drained properties. Literature reveals that the shear strength of the actual soil-structure interface is generally less than the surrounding soil [23; 27; 28; 29; 30]. Studies conducted by [PERSON] and [PERSON] [31] and [PERSON] et al. [32] on geogrids reinforcements were able to replicate the experiment's results using a strength reduction factor of 0.67. In this study, the interface coefficient at the backfill soil and reinforcements, as well as the wall facing elements, is computed as \(\mathrm{R}_{\mathrm{inter}}=\tan\delta/\tan\varphi\)[28; 33], where \(\delta=2/3\cdot\varphi\) and \(\varphi\) are the friction angle of the soil material. The interface coefficient \(\mathrm{R}_{\mathrm{inter}}\) for soil foundation and the retained original soil are assumed rigid and are assigned with a value of 1 (see Table 1).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & **Unit** & **Backfill Soil** & **Gravel Bags** & **Retained Soil** & **Foundation** & **FHR** \\ \hline Material & - & HS & HS & LE & LE & LE \\ \hline Unit weight, \(\gamma\) & kN/m\({}^{3}\) & 19 & 19 & 20 & 20 & 24 \\ \hline \(\mathrm{E}_{\mathrm{o}}\)\({}^{\mathrm{ref}}\) & kN/m\({}^{2}\) & \(34.0\times 10^{3}\) & \(34.0\times 10^{3}\) & - & - & - \\ \hline \(\mathrm{E}_{\mathrm{o}}\)\({}^{\mathrm{ref}}\) & kN/m\({}^{2}\) & \(25.1\times