## 4 Discussion  
In this study, how the EL influenced the reinforcement performance of rock bolts was investigated with numerical modelling. First, numerical modelling work was conducted on metal rock bolts. It is interesting to see that when the EL was short, there was no paramount increase in the largest anchorage force. For example, in this study, for metal rock bolts, when the EL increased from 0.5 m to 0.7 m, the largest anchorage force of metal rock bolts increased from 101.8 kN to 106.2 kN. This indicated that when the EL increased by 40%, the largest anchorage force of metal rock bolts increased by 4.32%. For the reason, it was inferred that when the EL was too short, the obtained anchorage force results were not reliable. Specifically, a scatter of results may occur. This finding was consistent with the conclusion obtained by [PERSON] [24]. When [PERSON] [24] conducted experimental PO tests on cable bolts, he found that when the EL was short enough, the obtained anchorage force was not reliable. This was because there was an apparent scatter of the anchorage force. Figure 12: Comparison between the metal rock bolts and FRP rock bolts when the EL was 2.5 m.  
Figure 13: Comparison between the metal rock bolts and FRP rock bolts when the EL was 3.5 m.  
Therefore, for this point, the numerical modelling results were consistent with the previous experimental results. Then, this numerical study revealed that when the anchorage system failed by bonding failure at the surface between rock bolts and grout, there was generally a linear relation between the largest anchorage force and the EL. This was more apparent if the too-short EL was eliminated. This finding was applicable to both metal rock bolts and FRP rock bolts. This finding agreed well with the experimental work conducted by [PERSON], [PERSON] and [PERSON] [12]. In their study, the correlation coefficient was 0.9936. In this study, the correlation coefficient was 0.9841 for metal rock bolts and 0.9997 for FRP rock bolts. Overall, the numerical investigating results were consistent with the previous experimental work. Moreover, according to this study, it was inferred that using the linear regression analysis method to predict the critical EL of rock bolts was reliable. It is noted that the relationship between the anchorage force and the EL is obtained based on considering the elastoplastic behaviour of the surface between rock bolts and grout. Before the shear stress reaches the peak, the shear stress increases linearly. After it reaches the peak, the shear stress drops to the residual shear strength and remains constant. Last, this study revealed that the initial stiffness of metal rock bolts was larger than that of FRP rock bolts, as shown in Figures 11-13. This finding was consistent with the in situ test results obtained by [PERSON] et al. [25]. Specifically, [PERSON], [PERSON] and [PERSON] [25] compared the reinforcement performance of two rock bolts. One was the traditional metal rock bolts and the other one was the FRP rock bolts. The in situ experimental PO tests were conducted. It showed that the metal rock bolts had similar anchorage force compared with the FRP rock bolts. However, at the initial loading stage, the initial stiffness was diverse. For metal rock bolts, the initial slope of the force-displacement curve was much larger. Therefore, the experimental results indicated that the metal rock bolts had larger initial stiffness than FRP rock bolts. This further confirmed that the current numerical modelling approach was robust in analysing the reinforcement performance of rock bolts. It is also acknowledged that this current paper is not able to fit all rock bolt application cases in mining engineering. The reason is that in the in situ environment, there are many uncertainties. The previous research indicates that these uncertainties can lead to the complexity of mining engineering cases and difficulty in solving the mining engineering issues [26; 27].