## 4 Results and Discussion  
### Specim Porosity Variation  
Porosity is an important parameter affecting the performance of materials. It directly indicates the degree of material density, and indirectly indicates a material's strength. The greater the material's porosity, the lower the strength of the material. There is an approximately linear proportional relationship between a material's strength and its porosity. The discrete element model established in this paper does not consider the role of water and assumes that coarse and fine particles have the same density. Assuming that a mixture's dry density is equal to its density, the following equation holds. \[\rho_{d}=\rho=\frac{m}{V}=\frac{\rho_{s}V_{s}}{V}=\rho_{s}\frac{V-V_{k}}{V}= \rho_{s}(1-p) \tag{2}\]  
where \(\rho_{d}\) is dry density; \(\rho_{s}\) is solid particle density; \(V_{s}\) is volume of solid particle; \(V_{k}\) is pore volume; \(V\) is specimen volume; \(p\) is porosity. Figure 4: Comparison of tamping settlement between the indoor compaction test and the discrete element simulation test. In the indoor compaction test, maximum dry density is generally used to evaluate compaction quality [33,34]. The above formula shows that dry density is linearly related to porosity; therefore, porosity can be used as an indicator to evaluate the compaction effect. The initial porosity of the simulated cement-stabilized macadam was set to 23%. As the 'DISTRIBUTE' command is limited (overlap of particles is allowed), generated specimens had a slightly higher porosity than the set value. The final initial porosity of the vibration molding specimen was 24.052%, and the initial porosity of the compaction molding specimen was 24.177%. Porosity values were recorded during the forming process, and the variation in porosity with the number of compactions was obtained, as shown in Figure 5.  
Figure 5a illustrates the specimen used for compaction molding. In order to better observe the change in voids inside the specimen, it was split, as shown in Figure 5b. Figure 5c-h represent slices of the unloaded compaction molding specimen (1 compaction, 5 compactions, 10 compactions, 17 compactions, and post compaction, respectively). Figure 5 illustrates that porosity decreased most after the first compaction, that as the number of compactions increased, porosity decreased, and that porosity's rate of decrease gradually slowed until it remained almost unchanged towards the last compactions. The change trend in porosity was consistent with the changing law of specimen height previously mentioned, and the decrease in porosity was significantly influenced by the first few compactions. The relationship between porosity and dry density can be deduced from Formula (2), as shown in Formula (3). CSM's maximum dry density was 5%; the indoor test detected a 2.557 water content. The porosity of the indoor test specimen was 7.85% after compaction molding, whereas the porosity of the simulation test specimen was 8.31% after molding. Although the simulation test specimen's porosity was slightly higher than that of the indoor test, there was particle overlap in the discrete element simulation; given this, the results obtained from the simulation experiment are reasonable. \[p=1-\frac{V_{S}}{V}=1-\frac{M_{d}}{\rho_{d}}/v \tag{3}\]  
where \(p\) is porosity;\(V_{S}\) is volume of solid particle; \(V\) is volume of specimen; \(M_{d}\) is dry weight; \(\rho_{d}\) is dry density. Figure 5: Changes in porosity during compaction molding. (**a**) is the specimen model used for compaction molding in this paper; (**b**) is the axial section of the specimen model; (**c**) is the axial section of the specimen before compaction; (**d**) is the axial section of the specimen after 1 compaction; (**e**) is the axial section of the specimen after 5 compaction; (**f**) is the axial section of the specimen after 10 compaction; (**g**) is the axial section of the specimen after 17 compaction; (**h**) is the axial section of the specimen after compaction is completed.