# Analysis of Failure Mode of Reinforced Embarments Overlying Voids Based on Discrete Method
## 2 Model Building
### Construction of Discrete Element Model  
The PFC particle flow method decomposes the bulk system into discrete units, which are used as the basic units to visually express the interaction states and motion properties between the units at each moment in time. The software replaces the selection of the constitutive model of the material itself by setting the contact between particles. Since the discrete elements do not need to satisfy the deformation coordination relationship, it has a greater advantage in simulating the large deformation of discontinuous media such as soil. At present, the PFC software has become a recognized numerical simulation software and has penetrated into almost all directions in the field of geotechnical engineering. \begin{table}
\begin{tabular}{c c} \hline
**Property** & **Value** \\ \hline Gravity, \(\gamma\) (\(\mathrm{kN/m^{3}}\)) & 17.03 \\ Specific gravity of particles, Gs & 2.65 \\ Porosity ratio, e & 0.585 \\ Water content, w (\%) & 0.15 \\ Uniformity factor, Cu & 1.39 \\ Coefficient of curvature, Cc & 0.94 \\ \hline \end{tabular}
\end{table} 
Table 1: Physical properties of sandy soils. Figure 3: Grain size distribution curves of sandy soils. Figure 2: Schematic diagram of testing devices and materials: (**a**) model box; (**b**) loading and measuring devices; (**c**) geogrid; (**d**) water pumping equipment. Based on the above laboratory experiment dimensions, PFC2D software was used to establish a computational model of the reinforced embankment overlying a void, by generating spherical particles to simulate the sandy soil and the geogrid, and by creating wall units to simulate the model boxes and loading plates. Figure 4 shows a schematic of the numerical simulation model. In the model, blue particles represent soil particles, red particles represent the geogrid and blue lines represent walls. The surrounding boundary walls is fixed. The wall is a rigid body and does not produce deformation. The bottom surface of the loading plate is set as the horizontal observation surface M. The position of the observation surface M decreases as the loading plate decreases. The load P in the load-settlement curve is obtained by dividing the loading plate contact force F monitored on profile M by the loading plate width B. The settlement ratio S/B is obtained by dividing the wall displacement S directly monitored by the loading plate width B in the Fish language that comes with the PFC. Based on the computational resources of the hardware, the generation of particles in discrete element software according to laboratory-tested soil particle grading curves is difficult to realize; therefore, it is necessary to extend the radius of the soil particles. When the radius multiplier is too small, the number of soil particles will be extensive while improving the accuracy of the simulation, and thus, the calculation cannot be converged; when the radius multiplier is too large, the simulation results of the discrete element will have a large deviation from the actual situation. Based on the requirements of calculation efficiency and simulation accuracy, this paper has made several attempts to enlarge the particle size of the soil, so as to obtain reasonable enlargement results. After attempts, we finally obtained a radius multiplier of 2, and the particle size of sandy soils in the simulation ranged from 1 to 4 mm. The porosity of the sandy soil was 0.17 upon converting from 3D to 2D [28]. The contact model of sandy soil was chosen as a linear contact model, the contact between particles of the geogrid was the parallel bonding model and the contact between sandy soil and geogrid was the linear contact model. The particle size of the geogrid was 1.5 mm.