###### Abstract
Because the discrete element method (DEM) can offer microscopic insights into the soil densification mechanism, it has been widely used for simulating DC processes involving gravel soil [26; 27] and granular soils [28; 29]. Recently, [PERSON] et al. [30] investigated DC of rockfill and its efficiency using a newly developed material point method. These findings indicate that the improvement range of soil due to DC exhibits a significant partition feature. In order to directly and quickly evaluate the improvement range of soil induced by DC, it is commonly described using a specific geometric shape [8; 9; 14; 22; 23; 30]. [PERSON] et al. [8; 9] were the first to show that the improvement zone was approximately ellipsoidal by plotting the relative density contours of soil after DC based on model tests. [PERSON] et al. [14] found that the elliptic equation can fit well with simulated volumetric strain contours using a 3D FEM. It was assumed that the soil in an ellipsoidal region reached the same relative density or volumetric strain after tamping. However, this assumption was found to be inconsistent with the situation that the degree of soil improvement gradually decreases with increases in distance from the tamping point, so that the accuracy of predicted results was limited. Subsequently, [PERSON] et al. [22] and [PERSON] et al. [23] considered the partition feature of the improvement range and divided the ellipsoidal improved region into two zones: compacted, affected zones; and heavy, weakly reinforced zones. Similarly, changes in soil properties (relative density or internal friction) in the transition region were ignored. [PERSON] et al. [30] pointed out that the volumetric strain below the tamper point exponentially decreases along the depth. However, the soil near the tamping point should be considered as a special zone with the highest degree of improvement. To sum up, application of the ellipsoidal densification zone to represent the improvement range has been widely recognized by scholars. However, the influence of the partition feature upon the degree of soil improvement and its spatial distribution has not been well characterized in the existing models. For instance, the size of the compacted zone with the highest degree of density around the tamping point needs to be quantitatively described, the partition features of compacted zones with different degrees of density remain undefined, and spatial variation in soil dry density in the transition region between the compacted zone with the highest degree of density and the uncompacted zone is still unclear. For this purpose, an innovative confocal ellipsoidal densification model (CEDM) was established in the present study to predict the improvement range of soil under DC. Using this model, both the partition of the improvement range and its geometric relationships were defined. In addition, a mass balance equation considering the spatial distribution of soil dry density after DC was established. Subsequently, a designed laboratory test was carried out and a 2D FEM established to investigate the DC process. Finally, the applicability of the proposed CEDM was verified by comparing the simulated and predicted improvement ranges.