## 3 Toe Load Analysis
### Mechanical Model of the GRS Segmental Wall
The difference between \(\Sigma T_{\mathrm{con}}+F_{\mathrm{t}}\) and \(E_{a}\) may be attributed to a small portion of the earth pressure that was counterbalanced by the friction resistances between the facing blocks and between the facing column and backfill soil. The resistance between the facing blocks was not considered in the mechanical model, as shown in Equation (3), for the convenience of application, which may lead to some conservativeness for the predictions of connection loads. It is also noted that the value of \(\Sigma T_{\mathrm{con}}+F_{\mathrm{t}}\) is relatively small under toe interface friction angles of no more than 10\({}^{\circ}\). This may be attributed to local soil failure \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline _Baseline model_ & \\ Toe interface friction angle (\({}^{\circ}\)) & 5, 10, 15, 25, 45 \\ Toe interface shear stiffness (MPa/m) & 3.6, 10.1, 14.0, 19.1, 26.1 \\
**H = 4 m** & \\ Toe interface friction angle (\({}^{\circ}\)) & 5, 10, 15, 25, 45 \\ Toe interface shear stiffness (MPa/m) & 2.3, 7.4, 10.5, 14.5, 20.1 \\
**H = 8 m** & \\ Toe interface friction angle (\({}^{\circ}\)) & 5, 10, 15, 25, 45 \\ Toe interface shear stiffness (MPa/m) & 4.4, 12.6, 17.5, 24, 33 \\
**H = 10 m** & \\ Toe interface friction angle (\({}^{\circ}\)) & 5, 10, 15, 25, 45 \\ Toe interface shear stiffness (MPa/m) & 4.8, 14.9, 20.9, 28.9, 39.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter values for baseline model and parametric analysis. occurring within the reinforced soil mass, resulting in the earth load acting on the wall facing less than the active earth pressure, in the two weaker toe restraint cases. Local soil shear failure developing in GRS walls with poor toe restraint was also observed in the numerical modeling reported by [PERSON] et al. [19]. Figure 10 shows the ratios of the toe load (\(F_{\rm t}\)) and reinforcement load (\(\Sigma T_{\rm con}\)) to the total load (\(\Sigma T_{\rm con}+F_{\rm t}\)) under different toe restraint conditions. The toe load ratio increased with the toe interface friction angle, whereas the reinforcement load ratio decreased. The toe load ratio was 14.0% for a toe interface friction angle of 5\({}^{\circ}\) and increased to 29.7% when the toe interface friction angle was 15\({}^{\circ}\). When the toe interface friction angle overpassed 15\({}^{\circ}\), the toe load ratio increased slowly, reaching only 33.5% for a toe interface friction angle of 45\({}^{\circ}\). This may have been caused by the influence of toe restraint on the horizontal facing displacements, as shown in Figure 11. When the toe restraint was weaker, a larger shear displacement between the lowest facing block and the leveling pad led to larger horizontal displacements in the bottom part of the wall. The larger, horizontal facing displacements resulted in high reinforcement connection loads and, thus, smaller toe loads. As the toe interface friction angle increased from 5\({}^{\circ}\) to 15\({}^{\circ}\), the significant decrease in the facing displacements induced a quick increase in the toe load ratio. When the toe interface friction angle was in the 15-45\({}^{\circ}\) range, the negligible change in the facing displacements led to a slow increase in the toe load ratio. Figure 10: Ratios of toe load and reinforcement load under different toe restraint conditions. Figure 9: Loads carried by toe and reinforcement layers under different toe restraint conditions.