## 3 Numerical Analyses
### Numerical Model and Verification
The interactions between the backfill/geosynthetic, backfill/facing block, and block/block were simulated using the zero-thickness interfaces elements, which follow Mohr-Coulomb constitutive behaviour. The parameters for the interface Mohr-Coulomb constitutive model are: friction angle (\(\phi_{i}\)), cohesion (\(c_{i}\)), dilation angle (\(\psi_{i}\)), shear modulus (\(G_{i}\)), Poisson's ratio \(\
u_{i}\) (default value = 0.45), and oedometer modulus (\(E_{\text{oed,i}}\)) [36]. The degree of bonding of the interface can be set directly using a strength/stiffness reduction factor \(R_{i}\):  
\[c_{i} =R_{i}c_{\text{soil}} \tag{5}\] \[\phi_{i} =\tan^{-1}(R_{i}\tan\phi_{\text{soil}})\] \[\psi_{i} =\left\{ \begin{array}{ll}0&\text{for}\ \ R_{i}<1.0\\ \psi_{\text{soil}}&\text{for}\ \ R_{i}=1.0\end{array} \right.\] \[G_{i} =R_{i}^{2}G_{\text{soil}}\] \[E_{\text{oed,i}} =2G_{i}\frac{1-\
u_{i}}{1-2\
u_{i}},\]where: \(c_{\rm soil}\) is the soil apparent cohesion; \(\phi_{\rm soil}\) is the soil friction angle; \(\psi_{\rm soil}\) is the soil dilatancy angle, and \(G_{\rm soil}\) is the soil shear modulus. All the input parameters involved in this study are tabulated in Table 3. The default value of \(R_{i}\) is 1.0, which represents a fully bonded interface. The value of the interface property between soil-reinforcement \(R_{i}\) was taken to be 0.8 in this research. The FE analysis was conducted in two stages, that is, filling and compaction stage, and surcharge application at the top surface of the SGC mass stage. The wall was constructed in stages, that is, 0.2 m thick soil lifts were placed and compacted until the final wall height of 2 m was achieved. Compaction of each soil lift was simulated by applying an equivalent compaction load. To examine the effect of simulated compaction procedures on the reinforcement, three types compaction procedures have been simulated:  
1. Type-I: A uniformly distributed load is applied to the top surface of each soil lift as the mass is gradually constructed from the bottom up, see (i) of Figure 2b ([15]). 2. Type-II: A uniformly distributed load is applied at the top and bottom surfaces of each soil lift as the mass is gradually constructed from the bottom up, see (ii) of Figure 2b ([18]). 3. Type-III: A moving strip load of width \(w\) is applied to the top surface of each soil lift as the mass is gradually built from the bottom up, see (iii) of Figure 2b. Three different strip widths have been considered: 0.175 m, 0.35 m, and 0.70 m. In the simulation, the strip load moves either away or towards the modular block under consideration. Each of these compaction loads is removed from the existing soil layer prior to the placement of the next soil lift. A variety of compaction pressures: 10, 30, 44, 60, and 70 kPa have been considered in the parametric study. In particular, the compaction pressure of 44 kPa represents the compaction pressure induced by the plate compactor (MBW-GP1200), as used in the SGC Test No. 2 of Reference [6], whereas the compaction pressure of 70 kPa has been corresponded to the pressure induced by the Caterpillar CW-34 roller compactor. In the numerical model, both the horizontal and vertical displacements of the bottom boundary were fixed.