# DEM Simulation of the Load Transfer Mechanism of a GRPS Embankment with a Fixed Geogrid Technique
## 3 Results and Discussions
### Contact Force Chains and Orientations  
The contact force chain in the particle system is the visual expression of the load transfer path. Figure 9 represents the contact force chain for the models under the surcharge load of 100 kPa. The dense area of the force chain represents a larger contact force, while the sparse area represents a smaller contact force. As shown in Figure 9, the strong force chain was mainly distributed above the soil arching, while the force chain below the soil arching was relatively weak, which is consistent with the stress distribution. In addition, in the fixed geogrid model, the tensile force distribution of the reinforcement was more uniform and the amplitude was larger than that of the unfixed geogrid model. The redistribution of stress in the particle system can be reflected by the evolution of the contact force. [PERSON] and [PERSON] (2012) proposed that the Fourier series approximation (FSA) method is suitable for the anisotropy analysis of granular materials. The normal contact force information in the area of interest is counted. Furthermore, in FSA fitting, the density distribution function \(f_{n}(\theta)\) of the normal contact force can be calculated as follows:  
\[f_{n}(\theta)=f_{0}[1+a_{n}\cos 2(\theta-\theta_{n})] \tag{3}\]  
where \(f_{0}\) represents the average value of the normal contact force in the analyzed area, \(a_{n}\) is the FSA anisotropy coefficient of the normal contact force, and \(\theta\) represents the principal anisotropy direction of the normal contact force in the area. Figure 8: Comparison of the stress tensors in the three cases. Taking into account the symmetry of the embankment and the soil arching effect, the analyzed area shown in Figure 9a was used to analyze the evolution of the contact force chain of the soil arching. As shown in Figure 10, the FSA fitting shows that the principal direction of the normal contact force in each model under 100 kPa was about 15\({}^{\circ}\), and the strong force chain played a leading role in the deflection of the principal direction. Figure 11 shows the evolution of the fabric parameters in the soil arching area of the three models under different surcharge loads. The fabric anisotropy coefficient \(a_{n}\), which characterizes the degree of difference in the normal contact force for each contact direction, is more sensitive to changes caused by the rearrangement of particle positions and can more accurately reflect the subtle changes in the fabric of granular materials. The particle system changes the contact principal direction through the rotation and movement of the particles to form a stable microscopic load-transfer structure. As the surcharge load increases to the limit value of the microscopic load-bearing structure, a new microscopic load-bearing structure is rebuilt through the particles' movements (rotation and displacement). The evolution of the anisotropy coefficient and the main direction of the contact force represents the process of microscopic load-bearing structure remodeling. Figure 10: FSA fitting results of the normal contact force in the arching area. Figure 9: Normal contact force chain in the models under a 100 kPa surcharge load. In Figure 11, the principal direction of the normal contact force and the anisotropy coefficient in the arching area both showed an increasing trend when the surcharge load was smaller than 100 kPa. This means that the movements of particles in the arching area of the reinforced and unreinforced models mainly occurred in the surcharge load range of 0-100 kPa (stage 1). The drastic changes of the anisotropy coefficient \(a_{n}\) and the principal direction \(\theta\) of the normal contact force of the particles in the arched area indicated that the large-scale particle position rearrangement occurred in stage 1.