## 3 Toe Load Analysis  
### Mechanical Model of the GRS Segmental Wall  
In GRS retaining walls with segmental block facings, the integral thrust behind the wall facing is theoretically counterbalanced by the reinforcement connection loads and toe resistance if the facing is considered a beam. Thus, the mechanical model of the GRS segmental wall can be assumed as the following:  
\[F_{e}=\sum T_{con}+F_{t} \tag{3}\]  
where \(F_{\text{e}}\) = the integral thrust behind the facing, \(\Sigma T_{\text{con}}\) = the total reinforcement connection load, and \(F_{\text{t}}\) = the horizontal toe load. Experimental and numerical studies have demonstrated that toe restraint condition has a significant impact on the loads carried by the wall toe and reinforcement layers [9; 19; 20; 21; 30; 32; 33]. The accuracy of Equation (3) and the impact of toe restraint on this equation was quantitatively analyzed using a numerical approach. The numerical model of the SR-18 wall was modified to have a more typical geometry (Figure 7) and more typical material parameter values (Table 4) for this analysis. The embedment soil at the toe was not included in the baseline numerical model, as shown in Figure 7, considering that the passive soil resistance in front of the toe is usually ignored in the conventional design method [15]. This is because the passive soil resistance may be lost unexpectedly and unpredictably by scouring and excavation during a long period of service. Nonetheless, a comparison of the connection loads in the SR-18 walls with and without the embedment soil is presented to demonstrate the effects of the embedment soil. Figure 8 shows that the influence of the embedment soil on the connection loads in the SR-18 wall can be ignored. [PERSON] and [PERSON] [45] reported the range of creep stiffnesses at a 2% strain for HDPE geogrids was approximately 330-1120 kN/m. The average value of this range (i.e., 725 kN/m) was selected for this numerical model. The value of the interface friction angle between reinforcement layers and backfill \(\varphi_{\text{sr}}\), as shown in Table 4, was determined via the formula \(\varphi_{\text{sr}}\) = tan\({}^{-1}\) (2/3 \(\times\) tan\(\varphi\)), where \(\varphi\) = the backfill friction angle [41]. It is noted that parameters with the same values as those of the SR-18 wall (as shown in Tables 1-3) were not listed in Table 4.  
Figure 7: Baseline numerical model of GRS wall. The toe restraint condition was quantified using the interface friction angle between the lowest facing block and the leveling pad. The shear strength of the leveling pad-foundation soil interface was not considered in this analysis as a result of its small effect on the capacity of the wall toe to carry load in cases where the leveling pad was embedded in the foundation soil. [PERSON] and [PERSON] [46] found that, for GRS walls with embedded leveling pads, only the shear resistance at the facing block-leveling pad interface acts as the toe resistance to counterbalance a portion of the horizontal earth load because the passive soil resistance in front of the leveling pad inhibits the development of shear stress and displacement at the base of the leveling pad. In cases of an exposed leveling pad, it is the leveling pad-foundation soil interface that works to carry the earth load because the wall is more likely to slide along this weaker interface. However, even if the leveling pad