# A Quantitative Study of Axial Performance of Rockbolts with an Elastic-Debonding Model
## 4 Parameter Study and Discussion
### Rock Diameter  
The impact of rock diameter on the axial performance of rockbolts was analysed. A highlight of this ED model was that it incorporated rocks. In fact, the cross-section area of rocks was an input parameter. For the lab test scenario, the cross-section area of rocks can \begin{table}
\begin{tabular}{c c} \hline \hline Bolt diameter (mm) & 16 \\ \hline borehole diameter (mm) & 22 \\ \hline Rock diameter (m) & 1 \\ \hline Installed length (m) & 2 \\ \hline Rockbolt modulus of elasticity (GPa) & 220 \\ \hline Rock modulus of elasticity (GPa) & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters for the tensile test scenario. \begin{table}
\begin{tabular}{c c} \hline \hline Bond coefficient (m/GPa) & 0.1 \\ \hline Shear strength (MPa) & 3 \\ \hline Slippage at the ultimate load (mm) & 1 \\ \hline Residual shear strength (MPa) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input parameters for the b/g face. be obtained by measuring. However, for the field test scenario, it was almost impossible to directly measure the cross-section area of rocks. Then, Equation (5) was used to calculate the cross-section area of rocks. \[A_{r}=\frac{\pi D_{r}^{2}-\pi D_{h}^{2}}{4} \tag{5}\]  
where \(D_{r}\): rock diameter and \(D_{h}\): borehole diameter. Substituting Equation (5) into the ED model, the axial performance of rockbolts can be calculated. Previous research indicated that for rockbolts, when the rock diameter was beyond the critical rock diameter, external rocks had a mild impact on the axial performance of rockbolts [26]. Therefore, it is necessary to first determine how the rock diameter affected the axial performance of rockbolts. Five rock diameters were used, varying from 0.1 m to 1.3 m. When the rock diameter varied, the corresponding axial performance of rockbolts is shown in Figure 3. Apparently, the rock diameter had an impact on the axial performance of rockbolts. This was more apparent when the rock diameter increased from 0.1 m to 0.4 m. It is also noted that when the rock diameter was beyond 0.4 m, the axial performance of rockbolts became almost stable. This was the reason why in Figure 3a, the force-deformation curves were overlapped when the rock diameter was beyond 0.4 m.  
When the rock diameter increased from 0.1 m to 0.4 m, the deformation at the peak force decreased from 6.77 mm to 5.88 mm, decreasing by 13.1% (Figure 4). It is also noted that when the rock diameter increased to over 0.4 m, the peak force of rockbolts was likely to level off. When the rock diameter increased from 0.4 m to 1.3 m, the peak force of rockbolts was around 213 kN. Moreover, when the rock diameter increased from 0.4 m to 1 m, the deformation at the peak force decreased from 5.88 mm to 5.83 mm, which showed a mild decreasing trend. Once the rock diameter was beyond 1 m, the deformation at the peak force remained at 5.83 mm. The above analysis showed that rock diameter can affect the axial performance of rockbolts. However, once the rock diameter was beyond 1 m, it had a mild impact on the axial performance of rockbolts. This was reflected in the peak force and the deformation at the peak force. Moreover, when the rock diameter was beyond 1 m, the force-deformation curve was almost unchangeable. Based on this analysis, in the following contents, the critical rock diameter was set to 1 m.  
[PERSON] [26] also studied the impact of the rock diameter on the axial performance of cable bolts. They found that for cable bolts with a diameter of 15.2 mm, the critical rock diameter was 250 mm. There was a significant difference between the critical rock diameter obtained in this article and the critical rock diameter obtained by [PERSON] [26]. The reasons were inferred as follows: [PERSON] [26] conducted lab experiment tests, and the installed length of cable bolts was only 200 mm, which was quite short. However, in this article, tensile tests were more consistent with field tests.