## 2 Numerical Modelling Using Plaxis 2D
### Material Input Parameters
#### 2.3.4 Loading Conditions  
In this study, the three bridge numerical models are simulated under static and dynamic loadings. The static loading condition is a simple condition wherein the vertical loads (dead load (DL); live load (LL)) are assumed stationary and applied uniformly on top of the bridge and abutment. There are three static loading conditions that are considered in this study, which are summarized in Table 3. In terms of Case A, this condition considers the end of the bridge construction at which in the equivalent bridge girder and approach backfill (or gravel base), total dead loads are activated. In terms of Case B, this condition considers the presence of the general traffic loads after the bridge construction. The general traffic loadings are equal to the live loads of general vehicles and trucks, in addition to the bridge girder and approach backfill (or gravel base) total dead loads. Finally, in terms of Case C, this condition considers the presence of the railway loads after the bridge construction. The railway loadings are equal to the rail track total dead loads and train live loads, in addition to the bridge girder and approach backfill (or gravel base) total dead loads. From Table 3, Case 2A-C have different values of the loading compared to Case 1A-C and Case 3A-C. This is because in Case 2A-C, the bridge loads are supported by the 1.5 m-width bridge seat, while for Case 1A-C and Case 3A-C, the bridge loads are supported by the 0.9 m-width FHR facing. Thus, the values for Case 1A-C and Case 3A-C are converted from the reference model, which is Case 2. The equation used is \(Case_{1,3}=~{}(b_{2}/b_{1,3})(Case_{2})\), where \(Case_{1,3}\) is the equivalent load for Case 1(A-C) and Case 3(A-C); \(Case_{2}\) is the load for \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameters** & **Unit** & **FHR Facing** & **CMU Blocks** \\ \hline Material model & - & LE & LE \\ Unit weight, \(\gamma\) & kN/m\({}^{3}\) & 24 & 21 \\ Elastic modulus, \(E\) & kN/m\({}^{2}\) & 30 \(\times\) 10\({}^{6}\) & 30 \(\times\) 10\({}^{6}\) \\ \(v\) (nu) & - & 0.15 & 0 \\ \(R_{inter}\) & - & 1 (rigid) & 1 (rigid) \\ \(K_{0,x}\) & - & 1 (automatic) & 1 (automatic) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Wall facing material input parameters. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model Cases** & **Case 1** & **Case 2** & **Case 3** \\ \hline
1. Case A (end of construction) & & & \\ \hline Bridge total DL (kPa) & 167 & 100 & 167 \\ Approach backfill total DL (kPa) & 18 & 18 & 18 \\ \hline
2. Case B (general traffic loads) & & & \\ \hline Bridge total DL + general traffic LL (kPa) & 217 & 130 & 217 \\ Approach backfill total DL + general traffic LL (kPa) & 30 & 30 & 30 \\ \hline
3. Case C (railway loads) & & & \\ \hline Bridge total DL + rail track total DL + train LL (kPa) & 250 & 150 & 250 \\ Approach backfill total DL + rail track total DL + train LL (kPa) & 68 & 68 & 68 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Static loading condition for each model case. Case 2 at a specific condition (Case A-C); \(b_{2}\) is the width bridge seat in Case 2 that carries the applied bridge loads and is equal to 1.50 m; and \(b_{1,3}\) is the width of the FHR facing in Case 1 and Case 3 that carries the applied bridge loads and is equal to 0.90 m. For the calculation of static loadings, the plastic calculation type and elastoplastic drained analysis are used, for which the consolidation of soil is not considered. Hence, time of construction does not have substantial effects on the behavior of the numerical models. During phase construction, the pressures from the previous phase are carried over until the completion of the structure. For the dynamic loading condition, the earthquake is simulated by imposing a uniform prescribed line displacement at the bottom boundary (\(Y=-12.0\) m) of the model [24; 31].