## 3 Numerical Modelling  
The finite difference program FLAC [30] was used to simulate the performance of an MSE wall with the same dimensions as the full-scale model described in Section 2. The wall's height was 3 m and the length of the reinforcement bars was 2.1 m. The geometric details of the MSE wall in FLAC are shown in Figure 6.  
Foundation soil was considered to be a rigid material with a high cohesion value (c = 55.1 MPa; \(\varphi=51^{\circ}\)) and was 5 m deep below the wall system. A linear-elastic model using the Mohr-Coulomb failure criterion was used to simulate the backfill soil and the foundation soil. The backfill soil properties were modeled based on the experimental results, as shown in Table 1. The concrete facing panels were simulated using beam elements and were modeled as elastic materials with the modulus E = 200 Gpa. The strip elements in  
Figure 6: The MSE wall model in FLAC.  
FLAC were used to model a steel reinforcement grid with a tensile strength of 31,850 N/m and tensile stiffness of 20,000 kN/m. Table 3 illustrates the properties of the concrete facing panel, backfill soil, and foundation materials.  
The interface between the backfill soil and concrete facing panel was modeled using the values suggested by [PERSON] et al. [31] and [PERSON] et al. [32]. In detail, the friction angle between the soil and concrete panel was 26\({}^{\circ}\), the interface normal stiffness was 2.4 Mpa/m, and the shear stiffness was 2.4 Mpa/m.  
The apparent friction coefficients for the steel reinforcement and backfill interfaces were calculated based on the suggestions of the current standards [8,12,13,33]:  
* If z \(>\) z\({}_{0}\) = 6 m;  
\[\mathrm{f^{*}}=\mathrm{tan}\ \varphi \tag{1}\]
* If z \(\leq\) z\({}_{0}\) = 6 m;  
\[\mathrm{f^{*}}=\mathrm{f_{0}}^{*}(1-\mathrm{z}/\mathrm{z_{0}})+(\mathrm{z}/ \mathrm{z_{0}})\mathrm{tan}\ \varphi \tag{2}\]  
\[\mathrm{f_{0}}^{*}=1.2+\mathrm{log_{10}}(\mathrm{C_{u}}); \tag{3}\]  
where f* and f0* are the apparent friction coefficients for the steel reinforcement and backfill interfaces; C\({}_{u}\) is the coefficient of uniformity of the backfill soil; z is the depth of the reinforcement layers from the top of the wall, where z\({}_{0}\) = 6 m; and \(\varphi\) is the friction angle of the backfill soil. Table 4 illustrates the properties of the backfill-reinforcement interactions and facing-panel-backfill interactions.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline _Concrete panel_ & & \\ Width & m & 0.75 \\ Height & m & 0.15 \\ Length & m & 1.5 \\ Young’s modulus & Pa & \(2\times 10^{11}\) \\ Compressive strength of & Pa & 35,000 \\ concrete & & \\ _Foundation soil_ & & \\ Unit weight, \(\gamma_{\mathrm{Found}}\) & kg/m\({}^{3}\) & 2700 \\ Friction angle, \(\varphi_{\mathrm{Found}}\) & Degrees & 51 \\ Cohesion, \(\mathrm{c_{Found}}\) & Pa & \(5.51\times 10^{7}\) \\ Bulk modulus & Pa & \(4.39\times 10^{10}\) \\ Shear modulus & Pa & \(3.02\times 10^{10}\) \\ _Backfill soil_ & & \\ Unit weight, \(\gamma_{\mathrm{soil}}\) & kg/m\({}^{3}\) & 2070 \\ Friction angle, \(\varphi_{\mathrm{soil}}\) & Degrees & 34.3 \\ Cohesion, \(\mathrm{c_{soil}}\) & Pa & 5100 \\ Bulk modulus & Pa & \(1.5\times 10^{7}\) \\ Shear modulus & Pa & \(6\times 10^{6}\) \\ _Steel reinforcement_ & & \\ Length & m & 2.1 \\ Steel bar thickness & m & 0.010 \\ Calculation width & m & 1.5 \\ Number of longitudinal bars & Strip & 4 \\ per calculation width & & \\ Young’s modulus & Pa & \(2\times 10^{11}\) \\ Tensile strength & N/m & 31,850 \\ Tensile failure strain & \% & 0.19 \\ Shear stiffness & N/m\({}^{2}\) & \(2\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The MSE model parameters in FLAC.