## 3 Toe Load Analysis
### Influence Factors of the Toe Load Ratio  
The capacity of the wall toe and reinforcement layers for carrying a load is expected to be associated with various factors. For example, a variation in wall height will induce a change not only to the earth load on the facing column but also to the shear stiffness of the toe interface, which may influence the distribution of the total load between the toe and reinforcement layers. To study the influence of different factors on the toe and reinforcement load ratio, we changed the factors of wall height, facing batter, reinforcement spacing and stiffness, and backfill friction angle based on the baseline numerical wall model presented in Figure 7. Tables 5 and 6 provide the factor values and other parameter values affected by these factors. The reinforcement tensile strength in Table 6 was determined using the linear relationship between the creep stiffness values and the ultimate tensile strength for HDPE geogrids, proposed by [PERSON] [PERSON] [45]. When one factor was investigated, only the values of this factor and the involved parameters were changed, while the rest of the parameters were set to their baseline values. Figure 12 shows the toe and reinforcement load ratio versus the toe interface friction angle in walls with different heights. Since the variation characteristics of the reinforcement load ratio are opposite to those of the toe, hereafter, only the toe load ratio is discussed. Figure 12 shows that the toe load ratio decreased with wall height under the same toe restraint condition. For example, the toe load accounted for approximately 51% and 22% of the total load in the 4 m and 10 m high walls, respectively, when \(\varphi_{\text{t}}=45^{\circ}\). This is attributed to the larger reinforcement connection loads motivated by the larger facing displacements \begin{table}
\begin{tabular}{c c} \hline \hline
**Factors** & **Value** \\ \hline Wall height \(H\) (m) & 4, 6, 8, 10 \\ Facing batter \(\omega\) (\({}^{\circ}\)) & 0, 5, 10, 15 \\ Reinforcement stiffness \(J\) (kN/m) & 330, **725**, 1120 \\ Reinforcement tensile strength \(T\) (kN/m) & \(J/6.3\) \\ Reinforcement spacing (m) & 0.4, **0.6**, 0.8 \\ Plane strain backfill friction angle \(\varphi\) (\({}^{\circ}\)) & 35, **40, 45** \\ Backfill dilation angle \(\psi\) (\({}^{\circ}\)) & \(\varphi\)-30 \\ Block–backfill interface friction angle \(\varphi_{\text{ps}}\) (\({}^{\circ}\)) & \(\varphi\) \\ Leveling pad–foundation soil interface friction angle \(\varphi_{\text{pf}}\) (\({}^{\circ}\)) & \(\varphi\) \\ Soil–reinforcement interface friction angle \(\varphi_{\text{sr}}\) (\({}^{\circ}\)) & \(\tan^{-1}\) (\(2/3\times\tan\varphi\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of influence factors. Figure 11: Horizontal facing displacements under different toe restraint conditions. and, thus, the smaller earth load transmitted to the toe interface in the taller walls. As the wall height increased, there was a diminishing influence of wall height on the toe load ratio. Figure 13 shows the effects of the facing batter on the ratio of the earth load carried by the toe and reinforcement layers. The figure shows that the toe load ratio increased with the facing batter under the same toe conditions. As the facing batter increased, the earth load acting on the facing column decreased, resulting in a decrease in the horizontal facing displacements. Lower facing displacements reduced reinforcement connection loads and, thus, the contribution of the reinforcement layers to carrying the earth load, which led to an increase in the toe load ratio. However, the facing batter had little effect on the toe load ratio if it was less than \(5^{\circ}\). Figure 14 shows the influence of reinforcement stiffness on the relative contribution of wall toe and reinforcement layers to load capacity. The toe load ratio decreased as the reinforcement stiffness increased at the same toe interface friction angles, but at a diminishing rate.