## 3 Simulation Results and Analysis
### Overall Three-Dimensional Displacement Field of the Model
#### 3.1.2 Overall X and Y-Direction Displacement Fields of the Model  
The horizontal displacements within the model, observed in the X and Y-directions, are primarily concentrated at the intersection of the shaft and the horsehead roadway. At this locus, the X-direction displacement contour lines exhibit a high density with a petal-like configuration, whereas the Y-direction displacement contours are more compactly arrayed along the longitudinal axis of the horsehead roadway's roof. Additionally, the subsidence displacement of the roadway's roof is observed to increase concurrently with the horizontal displacements of the overlying rock in both the X and Y-directions. In contrast to the Z-direction displacement, however, the significant influence of the horizontal displacements on the roof's subsidence displacement is confined to within a 33 m radius, as depicted in Figure 5.  
For the model's X-direction displacement field, a 0.5 m MSD at the horsehead roadway's roof results in the most pronounced displacement at the shaft and roadway junction, reaching up to 4 cm. This region is characterized by a petal-shaped contour line of high density. Within the X-Y plane at the roadway's roof level, the X-direction displacement attenuates with increasing distance from the shaft, leading to a more dispersed contour line distribution (see Figure 5a). At a roof subsidence displacement of 1.0 m, the overall pattern of the model's X-direction displacement field remains consistent with the 0.5 m scenario, yet it exhibits a notable increase in magnitude, with the maximum displacement at the shaft-roadway interface rising to 15 cm, an increment of approximately 10 cm. The contour line density at this juncture is exceptionally high, and the petal-shaped feature enlarges significantly (see Figure 5b). With the roof subsidence displacement advancing to 1.5 m, the displacement at the shaft and roadway connection continues to dominate the model's X-direction displacement field. Although the displacement pattern aligns with the 1.0 m subsidence displacement scenario, the maximum displacement further escalates by around 20 cm, underscoring a substantial intensification in deformation (see Figure 5c).  
In the model's Y-direction displacement field, for the MSD of 0.5 m at the horsehead roadway's roof, the displacement is predominantly localized along the roadway's axial position, peaking at 55 cm. Axial variations within this region are minimal. However, at the X-Y plane of the roadway's roof, the Y-direction displacement diminishes with increasing lateral distance from the axis, and the contour lines correspondingly become less dense, as illustrated in Figure 5d. Beyond a 33 m vertical distance from the roadway's roof, the horizontal displacement changes in both X and Y-directions are negligible. At a subsidence displacement of 1.0 m for the roadway's roof, the Y-direction displacement remains concentrated along the axial position, with the maximum value surging to approximately 110 cm, double the displacement observed at 0.5 m. The pattern of negligible displacement changes horizontally beyond the 33 m vertical threshold persists at this increased subsidence level, as depicted in Figure 5e.  
With the MSD of the horsehead roadway's roof set at 1.5 m, the model's Y-direction displacement is principally localized at the interface between the shaft and the horsehead roadway. The pattern of the Y-direction displacement field is analogous to that observed with a 1.0 m roof subsidence displacement; however, it is distinguished by an augmented maximum displacement, which escalates to approximately 180 cm, as evidenced in Figure 5f.  
Figure 5: X and Z-direction displacement fields of the model (cm).