## 3 Discrete Element Model Building and Verification  
### Basic Theory of Discrete Elements  
The discrete element method is a numerical method using explicit equations. Its basic concept is to discrete a discontinuous medium into a certain number of rigid particles, so that each rigid body satisfies a series of motion equations. Next, the dynamic relaxation iteration method is used to solve the motion equations of each rigid element, and the **motion state** of the entire discontinuous body is obtained. In the discrete element method, mechanical action between particles is a non-static process, and displacement and force between particles can be calculated by tracking the **motion process** of a particle in space. In the calculation process of a discrete element, the **object of calculation** can be divided into elements connected by nodes. The **position relation** of adjacent elements can be contacted or separated. According to the relationship between force and displacement and the motion equation, the interaction force and its motion state between elements can be calculated, respectively [27]. Particle Flow Code (PFC) is a widely used discrete element software. It is often used to simulate dynamic problems such as discontinuous media mechanics and large deformations [28; 29]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Operating Frequency (HZ)** & **Nominal Amplitude (mm)** & \multicolumn{2}{c}{**Working Mass (Kg)**} \\ \hline
30 & 1.2 & Upper system & Lower system & Total mass \\  & 180 & 120 & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter Settings of Vibration Compactor. Figure 1: Schematic diagram of the structure of the vibration meter used in this study. The discrete element calculation method's key problem is the mechanical behavior of contact. Contact interconnects a large number of balls, clusters, and walls, which affects the whole by locally reflecting all types of mechanical behaviors when using mesoscopic view media. The parallel bonding model is used to characterize the mechanical behavior between bonded materials (similar to the bonding of epoxy resin glued glass beads and cement inter-aggregates). Its bonding components are parallel to linear elements, creating elastic interactions between contacts; parallel bonding can transfer forces and moments between different entities. The component and behavior of two interfaces of the linear parallel bond model is shown in Figure 2.  
The contract bond can be viewed as a set of springs with constant normal and tangential stiffness, uniformly distributed on the contact surface and at the central contact point, parallel to linear springs. The relative motion that occurs at contact after the creation of the parallel bond generates forces and moments within the bonded material. Such forces and moments act on the two contact blocks and are related to the maximum positive and shear stresses in bond-adjacent bonding material. If these stresses exceed their corresponding bonding strengths, the parallel bond breaks and the parallel bonding contact model degenerates to a linear model. In this study, the cement-stabilized macadam model was set up using different contact models for aggregate and mortar combinations, which reflect CSM's actual performance test characteristics more realistically [31]. Therefore, a parallel adhesion model was used to simulate the mechanical behavior between mortar and mortar, and mortar and aggregate specimens, and a linear contact model was used to simulate the contact behavior between coarse aggregates and coarse aggregates. There are two primary methods of external loading in the discrete element method. The first method uses a wall to apply the load; a certain velocity is applied to a wall, and then the wall's motion applies force to internal particles. The second method uses the clump command to generate a \"flat\" shaped particle cluster similar to a rigid plate, which does not deform; then the load is applied to the particle cluster. This method can achieve various forms of variable loads.