## 3 Results
### Influence of the EL on the Reinforcement Performance of Metal Rock Bolts  
After numerical PO tests were conducted on metal rock bolts, the reinforcement performance of metal rock bolts is shown in Figure 5.  
It showed that the EL had a paramount influence on the reinforcement performance of metal rock bolts. With the EL increasing, the largest anchorage force of metal rock bolts increased apparently. However, the increasing trend was apparently diverse. When the EL was smaller than 0.7 m, the anchorage force of metal rock bolts increased almost linearly with the PO displacement before the anchorage force reached the maximum. However, when the EL was longer than 1 m, there was a non-linear relation between the anchorage force and the PO displacement. This was more apparent when the EL was longer than 2 m.  
To better reveal the relation between the largest anchorage force and the EL, the largest anchorage force was extracted and plotted, as shown in Figure 6. It should be noted that in this scenario, when the EL was 3 m, the PO force reached the tensile rupture force of metal rock bolts. Consequently, tensile rupture of metal rock bolts occurred. Therefore, when the EL was 3 m, the failure mode of the anchorage system was diverse from the others. Figure 5: Reinforcement performance of metal rock bolts when the EL was diverse. Figure 6: Relation between the largest anchorage force of metal rock bolts and the EL. When the EL ranged between 0.5 m and 2.5 m, the anchorage system had a consistent failure mode of bonding failure at the surface between rock bolts and grout. To investigate how the EL influenced the reinforcement performance of metal rock bolts, linear fitting was conducted. It showed that when the EL ranged between 0.5 m and 2.5 m, the following equation was obtained:  
\[y=52.12x+68.55 \tag{1}\]  
where _y_: the largest anchorage force of metal rock bolts; _x_: the EL. The corresponding correlation coefficient was 0.9769. Apparently, the correlation coefficient was not ideal since it was even less than 0.98. As for the reason, it was found that when the EL was smaller than 0.7 m, the largest anchorage force of metal rock bolts was not stable. Specifically, when the EL was 0.5 m, the largest anchorage force was 101.8 kN. Then, when the EL increased to 0.7 m, the largest anchorage force was 106.2 kN, which was quite close to 101.8 kN. This indicated that when the EL was short enough, the anchorage force of metal rock bolts was not stable. According to this finding, it is recommended that when conducting the PO tests on metal rock bolts, the EL should not be too short. In this way, the obtained results can be more accurate and reliable. One more linear regression was conducted. In this case, the largest anchorage force when the EL was 0.5 m was eliminated. The reason is that when the EL was 0.5 m, it was too short to guarantee the accuracy of the anchorage force results. Therefore, the linear regression was conducted on the results when the EL ranged between 0.7 m and 2.5 m. The obtained equation is shown below:  
\[y=55.63x+61.71 \tag{2}\]  
In this case, the corresponding correlation coefficient was 0.9841. It showed that when the EL ranged between 0.7 m and 2.5 m, there was a paramount linear relation between the largest anchorage force and the EL. Moreover, this obtained equation can be used to predict the critical EL. To realise this, the tensile rupture force of the metal rock bolts was substituted into Equation (2). Then, the critical EL can be obtained. For this scenario, the predicted critical EL was 2.85 m.  
To confirm whether the predicted critical EL was accurate, further numerical PO tests were conducted. In this case, the EL was increased from 2.5 m. When the failure mode of the anchorage system changed from the bonding failure of the surface to the tensile rupture of rock bolts, the corresponding EL was regarded as the critical EL.