## 3 Toe Load Analysis
### Influence Factors of the Toe Load Ratio
This is because the larger reinforcement stiffness led to a higher capacity of reinforcement layers for carrying loads, resulting in a lower toe load ratio. Figure 12: Influence of wall height \(H\) on the ratios of toe and reinforcement loads. Figure 13: Influence of facing batter \(\omega\) on the ratios of toe and reinforcement loads. Figure 15 shows that reinforcement spacing had less influence on the toe load ratio when \(\varphi_{\rm t}\leq 10^{\circ}\). For the range of \(\varphi_{\rm t}=15\)-\(45^{\circ}\), the toe load ratio increased with the reinforcement spacing. An increase in reinforcement spacing reduces global reinforcement stiffness [16], which induced a decrease in the fraction of the earth load carried by the reinforcement layers and an increase in the toe load ratio. The effects of the backfill friction angle is presented in Figure 16. The toe load ratio increased with the friction angle of the backfill under the same toe conditions. This is because of a larger normal stress at the toe interface, induced by an increase in the downward friction between the backfill and the wall facing when the backfill friction angle increased. The larger toe interface normal stress resulted in a further increase in the horizontal toe load. Figure 14: Influence of reinforcement stiffness \(J\) on the ratios of toe and reinforcement loads. Figure 15: Influence of reinforcement spacing \(S\) on the ratios of toe and reinforcement loads. The toe load ratio plotted in Figures 12-16 increased rapidly with toe interface friction angles in the 5-15\({}^{\circ}\) range and then changed only slightly in all cases. This indicates that the involved factors had little influence on the distribution shape of the toe load ratio with the toe interface friction angle. Moreover, at the lower toe interface friction angle of 5\({}^{\circ}\), the toe load ratio was less than 20% in all the cases. In a field wall, the friction angles of the interfaces at the wall toe would change with the surface roughness of the facing block and leveling pad and the foundation soil properties. For GRS walls constructed along rivers or seashores or in mountains, the soil at the wall toe and even the toe itself may be scoured away by wave actions, flooding, or debris flows. [PERSON] et al. [47] reported a practical case where the toe of a geosynthetic railway embankment in the mountains of Kyushu, Japan experienced strong scour and erosion caused by flooding. [PERSON] et al. [48] reported that about 13% of 339 reinforced soil walls supporting bridge abutments inspected in the state of Ohio, USA experienced soil erosion at the wall toe. In these extreme cases, the shear strength of the interfaces at the wall toe must have reduced sharply, resulting in a significant decrease in the toe resistance. Hence, for GRS walls constructed in mountains and by rivers and seashores, it is recommended to ignore the toe resistance to increase margin of safety against reinforcement overstressing. The typical friction angle of the toe interface can be considered as in the range of 25-45\({}^{\circ}\), because the relatively constant ratio of toe load to the integral thrust behind the facing (almost no more than 50% in any condition) is observed in this range, as shown in Figures 12-16. However, in a series of 3.6 m high GRS test walls on a rigid foundation, it was observed that the toe carried nearly 80% of the earth load acting on the facing [9]. This indicates that a rigid foundation may magnify toe load capacity. In addition, the changes in the fractions of toe and reinforcement load with wall height, facing batter, reinforcement stiffness, and spacing in this study are consistent with the observations of other studies [19; 21; 31].