# DEM Simulation of the Load Transfer Mechanism of a GRPS Embankment with a Fixed Geogrid Technique
## 3 Results and Discussions
### Stresses in the Embankment and Subsoil  
The development mechanism of stress in the embankment can reflect the load transfer process. The redistribution of stress within the embankment caused by the relative movement of soil particles under a surcharge load can reflect the formation process of soil arching. Based on the magnitude of the stress in the embankment and the rotation of the principal stress direction, the formation and development of the soil arching effect can be analyzed. In PFC, the stress of the part of interest in the model can be monitored by arranging the measure circle. The principal direction \(\theta\) of the stress can be calculated as follows:  
\[\theta=\frac{1}{2}\text{arctan}\left(\frac{-2\sigma_{xy}}{\sigma_{xx}-\sigma_ {yy}}\right) \tag{2}\]  
where \(\sigma_{xx}\), \(\sigma_{xy}\), and \(\sigma_{yy}\) represent the horizontal, tangential, and vertical stresses respectively.  
Figure 6: Comparison of the particle displacements of the embankments (surcharge load = 100 kPa).  
Figure 7: Comparison of the particle displacements of subsoil between the piles.  
Figure 8a-c shows the measured stress tensor under the self-weight load of the embankment. The magnitudes of stress were relatively uniform at the same elevation. This indicated that the soil arching had not formed yet at this stage because the relative displacement between the pile and subsoil under the self-weight was very small. In all three models, the internal stress of the embankment gradually increased with the increase in depth. In the unreinforced model, the load on the pile top and the subsoil were basically at the same level. In the reinforced embankment, even if no surcharge load was applied, the role of the reinforcement was initially manifested. The geogrid underwent a small deformation under the self-weight of the embankment and became in tension, which generated the membrane effect. The stresses of the subsoil in the reinforced models were smaller than that in the unreinforced model. In contrast, the reinforcement transferred part of the stress to the pile through the tensile membrane effect, and the soil stress around the reinforcement and the pile top was significantly increased. In addition, the stress distribution around the reinforcement in the fixed geogrid case was more even. The principal direction of the stress above the pile top and the geogrid material was mainly vertical.  
Figure 8d-j shows the stress distribution in the embankment under the loads of 100 and 300 kPa. As the larger load was transferred to the embankment, the soil arching effect caused by the differential settlement between the pile and the subsoil gradually became more pronounced. The larger normal stress and tangential stress were concentrated above the soil arching area. The principal direction of normal stress was essentially consistent with the direction of arching, while the principal direction of tangential stress was perpendicular to the direction of soil arching. In all three models, the stress above the soil arching area was the same, and the main direction of the normal stress was vertical. The stress of the subsoil in the unreinforced case was greater than that in the reinforced cases. In the case of a fixed geogrid, the stress on the pile top included the load transferred from the reinforcement to the pile top.