## 3 Results
### Numerical Simulation
#### 3.1.2 Parametric Studies  
Parametric analyses are conducted to understand the sensitivity of the system. Three main parameters, including elastic modulus, mining height, and advancing rate, are investigated to quantify their influence on the principal stress and surface settlement in numerical simulation. A. Elastic modulus  
1. Max principal stress  
The max principal stress against the time of group A is plotted in Figure 11. By comparing the results of four subgroups with different elastic moduli (A1--11,055 MPa, A2--12,060 MPa, A3--9045 MPa, A4--8040 MPa), it is observed that subgroups A1 and A2 generally have larger principal stress values than subgroups A3 and A4 with lower elastic modulus, indicating the positive effect of Young's modulus on the max principal stress. Since there are two stress concentration areas, the positions of the maximum principal stress in these subgroups are found to be different. The maximum value occurs at point 1 for subgroups A1 and A2, while the maximum value appears at point 8 in subgroups A3 and A4. The result indicates that the [PERSON]'s modulus can determine the distribution of the principal stress and the maximum value. 2. Settlement  
Though the elastic modulus of PKS can effectively change the value and position of the maximum principal stress, its influence on surface settlement is not obvious. The vertical displacement against the time of group A with an interval of one second is plotted in Figure 12. With the increase in advancing time, the settlement curves at points 1, 2, and 3 for different subgroups are similar to each other. It is very hard to find out the difference. In addition, these curves also look nearly the same as that of group X.  
Figure 11: The max principal stress against the time of experiment group A. B. Mining height  
1. Max principal stress  
For group B, the mining height of the subgroups is 9 m, 12 m, and 3 m for B1, B2, and B3, respectively. The max principal stress against the time of group B is plotted in Figure 13. Most of the monitored principal stresses increase gradually with the excavation. The variation rate gently rises with time. Those at points 1, 2, 3, and 4 close at the excavation space are exceptions which has a more fluctuating curve. In other words, these points are more sensitive to the excavation. It is easy to understand. However, the differentiation of the principal stress in the whole process for different points is very close for points 5-10. The result indicates that the points with a certain distance from the excavation experience nearly the same stress variation, and the mining height has a higher influence on the working face than that at other positions. Figure 12: The settlement against the time of experiment group A.  
Figure 13: The max principal stress against the time of group B. Settlement  
The variation of the settlement of points 1, 2, and 3 at the surface is very similar to each other regarding the absolute value and the trend with different mining heights, as shown in Figure 14. The settlement increases with the excavation. The point on the side of the excavation start point has a higher settlement. Again, though the variation of the elastic modulus of PKS can obviously affect the distribution of the maximum principal stress, its influence on surface settlement is very limited. The result indicates that the limited change of the mining height has little influence on the settlement. C. Advancing rate  
1. Max principal stress  
The change in the advancing rate shows a distinct impact on the maximum principal stress, as shown in Figure 15. The advancing rates of the three subgroups (C1, C2, and C3) are 9, 12, and 3, respectively. This behavior is different from that in the above two cases. In the numerical simulation, the rate is controlled by adjusting the interval of the loading step. Faster excavation will produce a relatively higher undulation of the principal stress. However, such an influence on absolute value is still very limited.