## 3 Numerical Analysis Results and Discussion under Static Loading
### Lateral Stresses behind the Wall Facing  
The lateral stresses or earth pressures behind the wall facing at the end of the bridge construction (Case 1A, 2A, 3A) after the applied general traffic loading (Case 1B, 2B, 3B) and applied railway loading (Case 1C, 2C, 3C) are presented in Figure 11a-c. In the figure, the lateral earth pressures behind the wall facing from 0.90 m above the base up to the top of the abutment have been considered to eliminate the part of the integral bridge footing (Case 1 and Case 3). The lateral earth pressures are the closest polynomial fit of the lateral Cartesian total stresses obtained from the Plaxis 2D output and are plotted alongside with the theoretical values of the at-rest earth pressures (\(K_{0}\) condition), Rankine's active earth pressures (\(K_{a}\) condition), and lateral earth pressures for Case 2 with strip (bridge) loading. The at-rest and active lateral earth pressures were computed using the formulas \(\rho_{at-rest}=\left(q+\gamma H\right)K_{0}\) and \(\rho_{active}=\left(q+\gamma H\right)K_{a}-2c^{\prime}\sqrt{K_{a}}\)[17], where \(q\) is the roadway and approach backfill surcharge loads (Case 1A, 2A, 3A = 18 kPa; Case 1B, 2B, 3B = 30 kPa; and Case 1C, 2C, 3C = 68 kPa); the backfill soil unit weight is \(\gamma\) = 19 kN/m\({}^{3}\); the coefficient of earth pressure at-rest (\(K_{0}\)) was assumed as 0.50 in the initial condition of the Plaxis 2D simulation; and the coefficient of the active earth pressure (\(K_{a}\)) was computed using [PERSON]'s formula, \(K_{a}=\tan(45-\varphi/2)^{2}\), where \(\varphi\) = 51\({}^{\circ}\), and the cohesion in this case was not considered, thus \(\left(2c^{\prime}\sqrt{K_{a}}=0\right)\) and \(K_{a}=0.1254\). In this study, Case 2A-C (GRS-IBS) models have different loading conditions because the bridge surcharge loads are directly supported by the reinforced bridge seat located at 0.75 m to 2.25 m from the wall facing. The bridge loads are taken as strip loads on top of the rigid wall. The theoretical values of the lateral earth pressures on the GRS retaining wall, due to strip load, are computed based on the Boussinesq theory, \(\Delta\rho_{h}=\frac{2q}{\pi}\left(\beta-\sin\beta\cos 2\alpha\right)\)[18], where \(\beta=\tan^{-1}\left(\frac{x_{2}}{2}\right)-\tan^{-1}\left(\frac{x_{1}}{2}\right)\) and \(\alpha=\tan^{-1}\left(\frac{x_{2}+x_{1}}{2}\right)\) in radians. The \(q\) is the bridge surcharge loads (Case 2A = 100 kPa; Case 2B = 130 kPa; and Case 2C = 150 kPa); \(x_{1}\) is the distance from the wall facing to the first point of the bridge surcharge load; \(x_{2}\) is the distance from the wall facing to the end point of the bridge surcharge load; and \(z\) is the vertical distance from the top of the wall. Hence, in comparing the theoretical and numerical results of the lateral earth pressures, the values are not in good agreement, yet the trends are slightly similar. Generally, the maximum lateral earth  
Figure 10: Vertical displacement increments at the top of the wall abutment, \(\Delta q\) (mm), after the applied static loadings: (**a**) Case 1B, 2B 3B (general traffic loading) and (**b**) Case 1C, 2C, 3C (railway loading). pressures for Case 2A-C based on the Plaxis 2D results are found below the bearing zone with a height from 4.0 m (0.63 \(H\)) to 4.8 m (0.76 \(H\)) above the base of the wall, whereas the maximum lateral earth pressures for Case 2A-C based on the form of the theoretical values are found at 5.80 m (0.92 \(H\)) above the base of the wall. The deviations may be attributed to the presence of the geosynthetic reinforcements at the bearing zone (under the bridge seat) between heights 4.8 m (0.76 \(H\)) to 6.3 m (\(H\)). Moreover, the lateral earth pressure trends of Case 2A-C are reasonably different from those of Case 1A-C and Case 3A-C due to the strip load. The results in Figure 11a-c show that the Case 2A-C models exhibited the largest lateral earth pressures, which are in agreement with its corresponding lateral displacement (\(dx\)) behavior at the wall facing (refer also to Figure 7).