# DEM Simulation of the Load Transfer Mechanism of a GRPS Embankment with a Fixed Geogrid Technique
## 3 Results and Discussions
### Pile Efficacy  
The efficacy \(E\) of the pile in the embankment proposed by [PERSON] et al. [23] was used to evaluate the load transfer efficacy in the GRPS embankment. The soil arching structure transfers the load to the pile top. The load transfer efficacy \(E\) can be written as:  
\[E=\frac{F_{p}}{W} \tag{4}\]  
where \(F_{p}\) and \(W\) represent the vertical load shared by the pile and the load shared by the subsoil between the piles, respectively. Moreover, in the fixed geogrid model, the geogrid directly transfers the load through the bonding contact with the pile; therefore, the vertical load \(F_{p}\) that is shared by the pile can be divided into two parts: one is the load transferred from the embankment soil to the pile top through the soil arching, while the second is the vertical load transferred to the pile top through the tensile membrane effect. Therefore, the pile efficacy that is induced by the soil arching effect is recorded as \(E^{\prime}\) and can be calculated as follows:  
\[E^{\prime}=\frac{F_{p}-F_{R}}{W} \tag{5}\]  
where \(F_{R}\) represents the vertical load transferred from the reinforcement to the pile top. As Figure 12 represents, the efficacy \(E\) in the fixed geogrid embankment was always higher than those in the other models. The peak efficiency in the fixed geogrid, unfixed geogrid, and unreinforced cases were 66, 62, and 52% respectively. However, in the fixed geogrid model, the pile efficacy \(E^{\prime}\) (induced by soil arching) was between 28 and 40%, which was smaller than that of the unreinforced model. This indicates that the reinforcement that was mechanically connected to the pile top could reduce the bearing ratio of the soil arching. It is worth noting that during the surcharge load of 400-450 kPa, the load transfer efficiency in the unreinforced model dropped rapidly from 54 to 42%. This was attributed to the evolution of the soil arching structure and the reformation of the microscopic load-bearing structure, as discussed earlier. The changing trend of efficacy was the same as the changing trend of the fabric parameter \(a_{n}\), which also showed that the microstructure reformation of the granular system was an important mechanism that affected the soil arching development and load transfer mechanism. The reinforcement could effectively improve the load transfer efficacy, which was consistent with the research of [PERSON] et al. [22] and [PERSON] et al. [7]. In addition, this result also reflected that the fixed geogrid technique was beneficial to the efficacy of the piles in the GRPS embankment. Figure 12: The curves of efficacy \(E\) versus surcharge load. To clarify the load transfer mechanism of the fixed geogrid technology, Figure 13 shows the load-bearing ratio of subsoil between piles, the soil arching effect, and the tensile membrane effect in the fixed geogrid model. Among them, the vertical load ratio that was transmitted by the reinforcement through the tensile membrane effect could be quantified as \(E^{\prime}\) - \(E\), and the load-sharing ratio of the soil between the piles was 1 - \(E\). The load transfer process could also be divided into three stages based on the previous mesofabric evolution: Stage 1 was the rapid development and shaping stage of soil arches. The proportion of the load shared by the soil between the piles gradually decreased from 50 to 37%, and the load transferred from the soil arching to the piles increased by 10%, while the proportion of the vertical load transferred by the reinforcement increased from 22 to 25%. Stage 2 was the gradual stabilization stage of the soil arching. The increase in the load transferred from the soil arching to the piles became smaller, accompanied by a further decrease in the soil load between the piles. The vertical load transferred by the reinforcement was stable at about 25%. Stage 3 was the soil arching reformation stage. The load-bearing ratio of the soil arching gradually decreased after reaching the peak value, and the tensile membrane effect of the reinforcement was more prominent.