## 3 Numerical Analyses  
### Numerical Model and Verification  
A large-scale SGC mass specimen (the other two sides were restrained by two steel tubing frames with transparent plexiglass panels), reinforced by nine sheet of single-sheet Geotex 4 \(\times\) 4 with a vertical spacing \(S_{\
u}\) of 0.2 m has been experimentally studied by Reference [6] (Figure 2a). The data monitored from this full-scale SGC mass have been utilized repeatedly for calibrating numerical models (see, for examples, References [6; 12; 13; 22; 23; 25; 33; 34]). Figure 2: (**a**) Schematic diagram and configuration of Soil-Geosynthetic Composite (SGC) mass. (**b**) Simulated compaction procedures adopted for SGC mass in FE analysis. The SGC mass specimen was 2 m high and 1.4 m wide, giving an \(L/H\) ratio of 0.7. The fill was made of a crushed Diabase from a source near Washington D.C. It has a maximum particle size of 33 mm, and classified as well-graded gravel (GW) according to the Unified Soil Classification System (USCS). The results of large-size triaxial tests, with specimen diameter of 150 mm and specimen height of 300 mm, indicated that the backfill has a peak internal angle of friction \(\phi\) of 50\({}^{\circ}\) and an apparent cohesion \(c^{\prime}\) of 70 kPa, for tests conducted under four different confining pressures ranged between 35 kPa and 210 kPa. Polypropylene (PP) woven geotextile was used as the reinforcement; the geotextile has an ultimate tensile strength \(T_{\text{ult}}\) of 70 kN/m, a breakage strain of about 12%, and an axial stiffness \(EA\) of 1000 kN/m at 1% strain, which were obtained from a \"wide width tensile test\" of a geotextile specimen ([35]). The backfill was placed and compacted to 98% maximum dry density into a 0.2 m thick layer. Hollow concrete blocks (397 mm \(\times\) 194 mm \(\times\) 194 mm) were used as formwork during model setup in the specimen preparation stage; they were, however, removed before the surcharge application stage. The entire surface area of the test specimen was vacuum-sealed with a 0.5 mm thick latex membrane, and a prescribed confining pressure of 34 kPa was applied to the GRS walls specimen by mean of vacuuming. A hydraulic-jack, fastened on a 30 cm thick concrete pad, was mounted on the top surface of the specimen. Several linear variable differential transformers (LVDTs) and digital dial indicators were installed on top of the concrete pad to monitor the vertical movement of the SGC mass during shearing. LVDTs and digital dial indicators were also installed along the open face of the SGC mass to measure the lateral movement of the mass. The SGC mass was then sheared gradually until failure; the vertical failure stress and vertical failure strain observed was approximately 2700 kPa and 6.75%, respectively. Two-dimensional FE program, Plaxis2D [36], was used in the numerical analysis. Figure 2b illustrates the numerical geometry, loading conditions and the interface elements employed in the SGC walls mass simulation. The numerical and the experimental models have the same geometrical configuration. In the FE model, the soil and the facing block were represented by 15-noded triangular elements, which provides a fourth-order interpolation for displacements, and the numerical integration involves twelve Gaussian stress points ([36]). The geotextile was represented by a 5-noded geogrid (line) elements with two translational degrees of freedom in each node (\(u_{x},u_{y}\)), while the axial forces are evaluated at the Newton-Cotes stress points, which coincide with the nodes. The stress/strain behavior of the granular backfill material was modeled using the second-order hyperbolic elasto-plastic hardening soil model ([37]); the model computes deformation as the sum of elastic strain and plastic strain, which are generated during deviatoric loading, while the plastic volumetric strain in isotropic compression is simulated by introducing cap hardening in the model.